Metaheuristic and Evolutionary Computation: Algorithms and Applications [1st ed.] 9789811575709, 9789811575716

Table of contents :
Front Matter ....Pages i-xxix
Front Matter ....Pages 1-1
Introduction: Optimization and Metaheuristics Algorithms (Padam Singh, Sushil Kumar Choudhary)....Pages 3-33
Metaheuristics Paradigms for Renewable Energy Systems: Advances in Optimization Algorithms (Ahmad Faiz Minai, Hasmat Malik)....Pages 35-61
Tackling Power Quality Issues Using Metaheuristics (Peeyush Kala, Puneet Joshi, Medha Joshi, Sanjay Agarwal, Lokesh K. Yadav)....Pages 63-85
Meta-Heuristic Application in Suppression of Noise (Rohun Nisa, Asifa Baba)....Pages 87-106
A Review on Genetic Algorithm and Its Application in Power System Engineering (Vimal Singh Bisht, Navneet Joshi, Govind Singh Jethi, Abhijit Singh Bhakuni)....Pages 107-130
Different Variants of Particle Swarm Optimization Algorithms and Its Application: A Review (Ayush Mittal, Amruta Pattnaik, Anuradha Tomar)....Pages 131-163
Applications of Metaheuristics in Power Electronics (Peeyush Kala, Puneet Joshi, Medha Joshi, Sanjay Agarwal, Lokesh K. Yadav)....Pages 165-176
Cuckoo Search Algorithm: A Review of Recent Variants and Engineering Applications (Abhinav Sharma, Abhishek Sharma, Vinay Chowdary, Aayush Srivastava, Puneet Joshi)....Pages 177-194
Energy Management System for Hybrid Energy System: Renewable Integration, Modeling and Optimization, Control Aspects and Conceptual Framework (Geeta Kumari, Akanksha Sharma, H. P. Singh, R. K. Viral, S. K. Sinha, Naqui Anwer)....Pages 195-206
Recent Advances and Application of Metaheuristic Algorithms: A Survey (2014–2020) (Neha Khanduja, Bharat Bhushan)....Pages 207-228
Introduction to Renewable Energy Market and Metaheuristic Algorithms for Condition Monitoring of Photovoltaic Parameter Estimation (Pradeep Kumar)....Pages 229-250
Front Matter ....Pages 251-251
Applications of Meta-heuristics in Renewable Energy Systems (Manoj Kumawat, Nitin Gupta, Naveen Jain, Vivek Shrivastava, Gulshan Sharma)....Pages 253-282
Data-Driven Occupancy Detection Hybrid Model Using Particle Swarm Optimization Based Artificial Neural Network (Nuzhat Fatema, Hasmat Malik)....Pages 283-297
A Maiden Application of Competitive Swarm Optimizer for Solution of Economic Load Dispatch with Parameter Estimation (Abhishek Rajan, Abhay Sahu, Debashish Deka, Tanmoy Malakar)....Pages 299-335
Optimal Controller Parameter Tuning of PSS Using Sine-Cosine Algorithm (Ramesh Devarapalli, Biplab Bhattacharyya)....Pages 337-360
Application of Multi-objective Hybrid DE-PSO Optimization Technique for Network Congestion Management Through Distributed Energy Storage System (Divya Asija, Pallavi Choudekar)....Pages 361-385
Optimization Solutions Using Particle Swarm Optimization in Power Systems (Bartosz Tarakan, Marcin Sarnicki, Patrick D. Strankowski)....Pages 387-436
Switching Angles Computations Using PSO in Selective Harmonics Minimization PWM (Salman Ahmad, Atif Iqbal)....Pages 437-461
ACO with Heuristic Desirability for Web Page Positioning Problem (Harpreet Singh, Parminder Kaur)....Pages 463-475
Generating Functions of (p, q)-Analogue of I-Function Satisfying Truesdell’s Ascending and Descending \(F_{p,q}\)-Equation (Altaf Ahmad Bhat, Fozia S. Qazi, D. K. Jain)....Pages 477-489
Traffic Signal Control to Optimize Run Time for Energy Saving: A Smart City Paradigm (Tarkeshwar Mahto, Hasmat Malik)....Pages 491-497
Analysis of Lead-Acid and Lithium-Ion Batteries as Energy Storage Technologies for the Grid-Connected Microgrid Using Dispatch Control Algorithm (Mohd Alam, Kuldeep Kumar, Viresh Dutta)....Pages 499-515
Novel Application of Grid Search Algorithm for Optimization of Photovoltaic-Wind-Diesel Hybrid Systems with and Without Tracking Systems for Power Generation (Amit Kumar Yadav)....Pages 517-527
Comparison of Meta-heuristic with Evolutionary and Local Search Methods for Feature Selection (Ankita Bansal, Abha Jain)....Pages 529-554
Low Computational Artificial Intelligence Genetic Algorithm Assisted SLM PAPR Reduction Technique for Upcoming 5G Based Smart Hospital (Arun Kumar, Avireni Bhargav, Anitha Karthikeyan, Karthikeyan Rajagopal, Ashok Kumar Srinivasan, Adhena Nigus Tsegay)....Pages 555-567
Transmission Congestion Management Using Multi Objective Hybrid Flower Pollination and Particle Swarm Optimization Algorithm by Optimal Placement of TCSC (Pallavi Choudekar, Divya Asija)....Pages 569-583
Input Voltage and Slip Power Control Schemes Based Performance Optimization of Grid-Connected Induction Generator (Farhad Ilahi Bakhsh, Md. Tabrez, Salman Hameed)....Pages 585-594
A Computational Intelligence Approach for Power Quality Monitoring (Papia Ray, Monalisa Biswal)....Pages 595-627
Diagonal Recurrent Neural Network Based Prediction Model for Sales Forecasting (Raman Tiwari, Rajesh Kumar, Smriti Srivastava, Rajat Gera)....Pages 629-648
Depth Estimation Using Convolutional Neural Network with Transfer Learning (Umang Soni, Hemant Yadav)....Pages 649-664
Novel Application of Linear Scaling to Improve Accuracy of Optimized Artificial Neural Network Using Levenberg-Marquardt Algorithm in Prediction of Daily Nitrogen Oxide for Health Management (Vibha Yadav, Satyendra Nath)....Pages 665-688
Metaheurestic Algorithm Based Hybrid Model for Identification of Building Sale Prices (Nuzhat Fatema, Hasmat Malik, Atif Iqbal)....Pages 689-704
Comparative Analysis of Optimal Scheduling of Multi-objective Non-convex Combined Heat and Power Units Using AI Techniques (G. Rahul Prashanth, Siddharth Suhas Joshi, Vinay Kumar Jadoun, Nikhil Gupta, K. R. Niazi, Anil Swarnkar)....Pages 705-728
Optimization Solutions for Demand Side Management (Naladi Ram Babu, Tirumalasetty Chiranjeevi, Lalit Chandra Saikia, Dhenuvakonda Koteswara Raju)....Pages 729-746
Back Matter ....Pages 747-820

Citation preview

Studies in Computational Intelligence 916

Hasmat Malik · Atif Iqbal · Puneet Joshi · Sanjay Agrawal · Farhad Ilahi Bakhsh   Editors

Metaheuristic and Evolutionary Computation: Algorithms and Applications

Studies in Computational Intelligence Volume 916

Series Editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Computational Intelligence” (SCI) publishes new developments and advances in the various areas of computational intelligence—quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution, which enable both wide and rapid dissemination of research output. The books of this series are submitted to indexing to Web of Science, EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink.

More information about this series at http://www.springer.com/series/7092

Hasmat Malik Atif Iqbal Puneet Joshi Sanjay Agrawal Farhad Ilahi Bakhsh •

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•

•

Editors

Metaheuristic and Evolutionary Computation: Algorithms and Applications

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Editors Hasmat Malik ICE Division NSUT New Delhi, Delhi, India

Atif Iqbal Department of Electrical Engineering Qatar University Doha, Qatar

Puneet Joshi Department of Electrical Engineering Rajkiya Engineering College Ambedkar Nagar, Uttar Pradesh, India

Sanjay Agrawal Department of Electrical Engineering Rajkiya Engineering College Ambedkar Nagar, Uttar Pradesh, India

Farhad Ilahi Bakhsh Department of Electrical Engineering National Institute of Technology Srinagar, Jammu and Kashmir, India

ISSN 1860-949X ISSN 1860-9503 (electronic) Studies in Computational Intelligence ISBN 978-981-15-7570-9 ISBN 978-981-15-7571-6 (eBook) https://doi.org/10.1007/978-981-15-7571-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Artificial intelligence is the emulation of human intelligence such as decision making and problem solving in machines to mimic the human actions. Training of AI-based machine is conducted using machine learning algorithms that may include metaheuristic and evolutionary computations. Metaheuristics is an advanced algorithm to solve optimization problems especially with incomplete or imperfect data information. Metaheuristics is generally employed in large datasets which are random in nature. However, metaheuristics does not guarantee a global optimal solution in some problems. In large dataset, generally metaheuristics offers optimal solution using less computational effort when compared with other optimization algorithms and iterative methods. Metaheuristic algorithms are, in general, approximate and usually non-deterministic method and are not problem specific. The evolutionary computation method is a family of computational optimization algorithm for obtaining global optimization solution inspired by biological evolution. This is subfield of artificial intelligence and soft computing methods. These are a family of population-based trial-and-error problem solvers with a metaheuristic or stochastic optimization character. Evolutionary computation algorithms yield highly optimized solutions in a wide range of problem settings, making them highly popular in many fields of studies such as electrical engineering and computer science. In past few decades, research in the metaheuristic and evolutionary domain has grown rapidly. Numerous literature have been published on popular approaches like genetic algorithms, memetic algorithms, simulated annealing, Tabu search, evolutionary algorithms, ant colony algorithms, particle swarm optimization, cuckoo search, etc. This book is a collection of these approaches in a single volume. Unlike deterministic methods initiating with one solution, the metaheuristic methods instigate with several feasible solutions (both for single- and multi-objective optimization problems) distributed randomly over the entire search space. These methods are also highly preferred for solving multi-objective optimization problems where more than one conflicting objective functions are involved. The method is expected to converge to a single optimum solution commonly referred to as global solution in literature for single-objective optimization v

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problems and a set of solutions forming a Pareto optimal front for multi-objective optimization problems. The metaheuristic approach employed should congregate to the true Pareto front with high diversification in the solution set on the Pareto front. The choice for an apt approach for a given problem depends on several factors like the number and type of decision variables (continuous, discontinuous) and the nature of decision variable space; type of objective functions (minimization, maximization) and nature of objective space; nonlinearity and stiffness of model equations; type of constraints (equality and inequality); an ability of algorithm to handle the search spaces of objectives and decision variables. Metaheuristic approaches are classified into several categories based on the availability of data, values of variables, constraints involved, number of objective functions, online/offline, etc. Yet some common features clearly appear in most metaheuristics, such as the use of exploration (diversification) and exploitation (intensification). Exploration is the ability of an approach to investigate all promising regions of the solution space, whereas exploitation is the capability of improving the solution. Two being the cornerstones for a problem, initially, exploration is rigorous and in later epochs exploitation is more emphasized. Another similarity is the memory usage for archiving the best solutions over the iterations. One common shortcoming of most metaheuristics is the delicate tuning of numerous parameters; the theoretical results available are not adequate to help the user facing a new, difficult optimization problem. The goal of this book is to collect state-of-the-art contributions that discuss recent developments in a metaheuristic or highlight some general ideas that proved effective in adapting a metaheuristic to a specific problem. Some chapters are overview-oriented, while others describe recent advances in one method or its adaptation to a real-world application. It also covers the philosophy, design approach and applications of evolutionary algorithms, as embedded in the fields of engineering and technology. This book comprised of 34 different chapters divided in two main parts covering almost the entire domain of metaheuristic and evolutionary computational algorithms applied to various fields of engineering and technology. • Theory and Applications of Metaheurestic Algorithms in Engineering and Systems • Single and Multi Objective Optimization Studies of Metaheurestic Algorithms in Engineering and Systems The first part reviews the application of optimization algorithms in various domains of engineering in several chapters. well-regarded and recent evolutionary algorithms and optimization techniques. Quantitative and qualitative analyses of each algorithm are performed to understand the behavior and investigate their potentials to be used in conjunction with artificial neural networks. The second part presents the application of optimization algorithms in various domains of engineering in several chapters. Some popular optimization problems like the economic load dispatch, demand-side management, generator maintenance scheduling, tackling power quality issues, etc., are covered in this section. Most

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of the challenges that must be addressed when developing these evolutionary algorithms are discussed in detail. In addition, the book demonstrates the possible applications of these metaheuristic algorithms in several fields like that of renewable energy, smart grid and power electronics. Chapter “Introduction: Optimization and Metaheuristics Algorithms” provides a mathematical outlook to the optimization problem, some related postulates and definitions. In this chapter, a general overview from the era of Fermat and Lagrange who introduced calculus-based formulae to identify optima is given. Foundation of optimization problems, a brief introduction to the underlying nature of optimization and the common approaches to optimization problems, random number generation, the Monte Carlo method and the Markov chain Monte Carlo method are presented. This chapter introduces all the major metaheuristic algorithms and a wide range of applications that use metaheuristic algorithms to solve challenging optimization problems while also introducing various modifications used for multi-objective optimization. Chapters “Metaheuristics Paradigms for Renewable Energy Systems: Advances in Optimization Algorithms” and “Applications of Metaheuristics in Renewable Energy Systems” mainly deal with basic and important metaheuristics optimization techniques used for renewable energy resources. Metaheuristic optimization approaches like particle swarm optimization, differential evolution, Tabu search, simulation annealing, genetic algorithm, artificial bee colony, ant colony optimization, cuckoo search and biogeography-based optimization are discussed as applicable to renewable energy resources. In chapter “Tackling Power Quality Issues Using Metaheuristics,” various applications of metaheuristics in design of filters, FACTs controllers, static compensators and other power quality controllers have been exhaustively discussed. The merits and demerits of evolutionary algorithms (EA) over classical methods used in power quality improvement are presented and elaborated. The detailed comparative analysis of various EAs and metaheuristics used in various power quality applications is presented. Application of metaheuristics in harmonic elimination is shown in simulation results. The contribution of metaheuristics in tackling power quality issues is also well discussed in this chapter. Chapter “Metaheuristic Application in Suppression of Noise” is dedicated to the application of metaheuristics in noise cancelation in voice processing. The main challenge in reducing the background noise from speech signal is to achieve noise suppression techniques suitable in enhancing the quality of signal except reduction in the intelligibility of signal. This involves a trade-off between speech distortion and noise reduction. Metaheuristics is a powerful tool in dealing with this issue that is elaborated in this chapter. In chapter “A Review on Genetic Algorithm and Its Application in Power system Engineering”, basic concepts and functionality of genetic algorithm (GA) are discussed along with its application in economic load dispatch, unit commitment problem, distributed generation and load forecasting of power system. A review work has been done to understand the usefulness of genetic algorithm in above-mentioned domains. The future scope of GA is also highlighted.

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The early modifications to the original form of the algorithm and alteration in the equation are discussed along with the different types of PSO(s) and their hybrids in chapter “Different Variants of Particle Swarm Optimization Algorithms and Its Application: A Review”. Also, the chapter gives an insight into various applications of the PSO and some of the application-specified hybrid (or modified) PSO techniques. Based on the state of the art, discussion on performance comparison of the hybrid (or modified) PSO is also presented in this chapter. In chapter “Applications of Metaheuristics in Power Electronics”, EAs and metaheuristics proposed for the various power conversion applications such as FACTs controllers and devices, power filters, multilevel inverters, DC-DC converters, and PWM converters have been discussed. The merits and demerits of metaheuristics over conventional optimization methods are discussed. The detailed comparative analysis of various metaheuristics in power electronics systems is presented. The future perspectives of metaheuristics and EAs in power electronics are also discussed in this study. Chapter “Cuckoo Search Algorithm: A Review of Recent Variants and Engineering Applications” introduces with the mathematical concept of CS algorithm and summarizes different research articles where the algorithm has been explored in the field of engineering. Furthermore, the resent version of CS algorithm is addressed which mainly focuses on modified and hybrid versions. The novelty of this chapter is that it presents current trending research aspects of CS algorithm in the fields of engineering, machine and deep learning. Chapter “Energy Management System for Hybrid Energy System: Renewable Integration, Modeling and Optimization, Control Aspects and Conceptual Framework” presented a detailed study of different optimization techniques which can be applied to the renewable energy resources including the multi-agent solution as well as the artificial intelligence and micro-grid controller which can offer a clear vision for the researchers in this field. Certain recommendations considering the challenges in renewable energy (RE) development are also been provided. In the proposed framework, the smart grid is optimized by the use of different optimization methods. A general review and applications of different metaheuristic methods are discussed in chapter “Recent Advances and Application of Metaheuristic Algorithms: A Survey (2014–2020)”. Chapter “Introduction to Renewable Energy Market and Metaheuristic Algorithms for Condition Monitoring of Photovoltaic Parameter Estimation” summarizes the availability, existing status, key achievement and future potential of renewable energy, tradable REC certificates and their consequences on the aspects of promoting renewable energy using metaheuristics approach. It attempts to review a variety of plans and assesses commenced by administration of India for encouraging of renewable energy, the current policy mechanisms. In chapter “Data-Driven Occupancy Detection Hybrid Model Using Particle Swarm Optimization Based Artificial Neural Network”, the occupancy in smart building is determined by using simple measureable parameters of the inside environment of the building such as light (in lux), temperature (in Celsius), relative

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humidity (in %), CO2 level (in ppm) and humidity ratio (in kg-water-vapor/kg-air). The data-driven occupancy detection using particle swarm optimization (PSO)based artificial neural network (ANN) is designed in R language, and the proposed approach is validated with different 17 models by using the measured dataset. Chapter “A Maiden Application of Competitive Swarm Optimizer for Solution of Economic Load Dispatch with Parameter Estimation” presents a novel application of newly developed competitive swarm optimizer (CSO) in solving a nonlinear, non-convex and constrained economic load dispatch (ELD) problem of power systems. A comparative analysis is performed between particle swarm optimization (PSO) and CSO and reported. Chapter “Optimal Controller Parameter Tuning of PSS Using Sine-Cosine Algorithm” proposes an optimal parameter tuning of power system stabilizer and STATCOM using metaheuristic algorithms for the stability enhancement. The coordination among the damping devices has been achieved by a stochastic population-based sine cosine algorithm (SCA). The suggested algorithm has been compared with the most popular population-based optimization methods in recent time in the field of the solving engineering problems. In chapter “Application of Multi-objective Hybrid DE-PSO Optimization Technique for Network Congestion Management Through Distributed Energy Storage System”, solar PV along with energy storage system (ESS) is utilized as distributed energy storage system (DESS). ESS along with DG is used to store surplus energy during off-load period which will be utilized at peak load, thereby enhancing the overall efficiency of the system. Real 24 hours’ solar irradiance and temperature data of Delhi, India, are taken to mathematically model the power generated from solar PV. Congestion management is a methodology that helps us to resolve the issues prevailing in the network owing to restriction in path of power flow through transmission lines having certain power flow limits. Management of power flow congestion in huge electric power system remains a challenging and tough task which can be achieved by introducing distributed energy storage system (DESS) in the congested line and is considered in this chapter. Chapter “Transmission Congestion Management Using Multi Objective Hybrid Flower Pollination and Particle Swarm Optimization Algorithm by Optimal Placement of TCSC” is also devoted to the transmission line congestion problem. In this chapter, transmission congestion cost (TCC) has been used for determining best location of TCSC, while flower pollination and particle swarm optimization hybrid optimization have been used for optimal sizing of the device. Chapter “Optimization Solutions Using Particle Swarm Optimization in Power Systems” presents a concept of swarm algorithms, which can be applied in energy systems. This includes the group of renewable energy sources controlled by a superior control system that forces proper generator operation according to existing conditions. Research has been presented on the impact of selected renewable energy sources on the power system. Chapter “Switching Angles Computations Using PSO in Selective Harmonics Minimization PWM” illustrates the application of PSO in computing the switching angles for selective harmonic elimination used for modulation of voltage source

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inverters. The main challenge in implementation of selective harmonics minimization is in solving of these systems of highly nonlinear equations which exhibit multiple solutions, unique solution and no solution. The particle swarm optimization technique can be used to obtain switching angles from the system of highly nonlinear equations by properly formulating an objective function which needs to be minimized. Web page positioning problem (WPP) is about deciding the best locations of the Web pages in the hyperlink graph structure of the Web site. Ant colony optimization (ACO) is among the prominent algorithms to solve the optimization problems. In this regard, chapter “ACO with Heuristic Desirability for Web Page Positioning Problem” aims to solve the Web page positioning problem by formulating it as quadratic assignment problem (QAP). Chapter “Generating Functions of (p, q)-Analogue of I-Function Satisfying Truesdell’s Ascending and Descending Fpq-Equation” describes the use of metaheuristic in a pure mathematical function. A few identities for Gamma function as well as generating functions which satisfy ascending and descending Fpq-condition is illustrated. Different types of I-function are determined fulfilling ascending and descending Fpq-equation. By applying the various structures, some generating functions of I-function are obtained. Specific instances of the outcomes which seem, by all accounts, to be new have likewise been acquired. In chapter “Traffic Signal Control to Optimize Run Time for Energy Saving: A Smart City Paradigm”, traffic signal control is elaborated. First, the default traffic light controlling strategy was simulated; the tripe time of each vehicle has been recorded. It provides comprehensive study of the results attained with a reconfigured traffic light controlling strategy on the open source traffic simulator SUMO (Simulation of Urban Mobility) by revamping its predefined static routes during the runtime of simulation. In chapter “Analysis of Lead–Acid and Lithium–Ion Batteries as Energy Storage Technologies for the Grid-Connected Microgrid Using Dispatch Control Algorithm”, a feasibility and comparative performance analysis of lead acid and Li–ion-based energy storage systems for grid-connected microgrid is carried out using NREL, SAM simulation tool. Grid-connected microgrid consists of the solar photovoltaic (SPV) as the primary power generator. A detailed comparison of two types of energy storage system is discussed. Chapter “Novel Application of Grid Search Algorithm for Optimization of Photovoltaic-Wind-Diesel Hybrid Systems With and Without Tracking Systems for Power Generation” aims to study first time the techno-economic feasibility analysis of photovoltaic (PV)-wind (W)-diesel (D), PV-D, PV-W, W-D, PV and W only with and without tracking systems for mountainous region of Sikkim in India using grid search method. In chapter “Comparison of Metaheuristic with Evolutionary and Local Search Methods for Feature Selection”, the authors have conducted an exhaustive comparison among the search methods where a collection of nine meta-heuristic search methods (ant search, bat search, bee search, cuckoo search, elephant search, firefly search, flower search, harmony search, wolf search) is compared with three local

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search and four evolutionary search methods. These search methods are validated against two open-source datasets belonging to different domains (allow to provide stronger and reliable conclusion), viz. Pima Indians Diabetes dataset and hepatocellular carcinoma dataset found in UCI machine learning repository. Health monitoring is considered as a gigantic problem in emerging nations, particularly in inaccessible region. The development in radio telecommunication has upgraded the smart hospital in voluminous aspects. One of the visions of 5G communication systems is to deliver a dependable, protected and fast radio at anyplace and anytime for the forthcoming smart health care. In chapter “Low Computational Artificial Intelligence Genetic Algorithm Assisted SLM PAPR Reduction Technique for Upcoming 5G Based Smart Hospital”, the focus is to introduce a novel PAPR reduction technique, which is one of the necessities of 5G-based smart hospital. Artificial intelligence (AI)-based genetic algorithm (GA) supported selective mapping sequence (SLM), known as GA-SLM is suggested to diminish the PAPR of the NOMA system. Input voltage control scheme (IVCS) and slip power control scheme (SPCS) are used for performance optimization of grid-connected induction generator (GIG), this is discussed in chapter “Input Voltage and Slip Power Control Schemes Based Performance Optimization of Grid-Connected Induction Generator”. The comparison between the performance optimization of GIG using IVCS and GIG using SPCS has been presented. Chapter “A Computational Intelligence Approach for Power Quality Monitoring” sites some of those problems and some remedies to the power quality issues by monitoring power quality by using wavelet transform and stockwell transform (s-transform) and a firm comparison that distinguishes the advantages and disadvantages of using both LABVIEW and MATLAB software. Application of AI technique for sale prediction is discussed in chapter “Diagonal Recurrent Neural Network Based Prediction Model For Sales Forecasting”. This chapter describes the novel application of diagonal recurrent neural network (DRNN) for solving the sales forecasting problem. Predicting depth is crucial to understand the 3D geometry of a scene. While, “for stereo images, local correspondence suffices for estimation, finding depth from a single image is less straightforward, requiring integration of both global and local information”. In chapter “Depth Estimation Using Convolutional Neural Network with Transfer Learning”, depth estimation using convolutional neural network (CNN) using transfer learning as a baseline is presented. Chapter “Novel Application of Linear Scaling to Improve Accuracy of Optimized Artificial Neural Network Using Levenberg-Marquardt Algorithm in Prediction of Daily Nitrogen Oxide for Health Management” examines application of linear scaling for improving the developed model ANN-1 and ANN-2 prediction accuracy using artificial neural network. Normalized values of different input and output variable such as ambient temperature, rack temperature, toluene, xylene and nitrogen oxide are used for ANN-1 model. The ANN-2 model utilizes scaled stochastic as input and air pollutants as output variables.

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In chapter “Metaheurestic Algorithm Based Hybrid Model for Identification of Building Sale Prices”, a metaheuristic algorithm-based hybrid model for identification of building’s sales prices is presented, which is developed by using conventional feedforward neural network (FNN). The multi-objective non-convex combined heat & power (CHP) scheduling problem of the systems is dealt in chapter “Comparative Analysis of Optimal Scheduling of Multi-objective Non-convex Combined Heat and Power Units Using AI Techniques” which is a complex and arduous problem. The main objective in chapter “Optimization Solutions for Demand Side Management” is to analyze the load shifting as one of the demand-side management (DSM) technique to reduce the peak loads, energy bills and peak-to-average ratio (PAR). The movable items are shifted by vigorous involvement of clients in response to tariff of residential customers. DSM with load shifting technique and RES like wind are considered for investigations. Due to the simplicity of the metaheuristic methods and flexibility, readers from any field of study can employ them for optimization problems. The book shall serve as viable source on how to design, adapt and evaluate the algorithms, which would be beneficial for the readers interested in learning and developing metaheuristic algorithms. The book will find adaptability among researchers and practicing engineers alike. This single volume encompasses wide range of subject area with fundamental to advanced level information. We thank all the contributors of this book for their valuable effort in producing high-class literature for research community. We are sincerely thankful to the Intelligent Prognostic Private Limited India, to provide the all types of technical and non-technical facilities, cooperation and support in each stage to make this book in reality. We wish to thank our colleagues and friends for their insight and helpful discussion during the production of this edited book. We would like to highlight the contribution of Prof. Haitham Abu-Rub, Texas A&M University, Qatar; Prof. Sukumar Mishra, IIT Delhi, India; Prof. Imtiaz Ashraf, Aligarh Muslim University, India; Prof. M. S. Jamil Asghar, Aligarh Muslim University, India; Prof. Salman Hameed, Aligarh Muslim University, India; Prof. A. H. Bhat, NIT Srinagar, India; Prof. Kouzou Abdellah, Djelfa University, Algeria; Prof. Jaroslaw Guzinski, Gdansk University of Technology; Prof. Akhtar Kalam, Victoria University of Technology, Australia; Prof. Mairaj Ud Din Mufti, NIT Srinagar, India; Prof. YR Sood, NIT Hamirpur (HP), India; Prof. A. P. Mittal, NSUT Delhi, India; Prof R. K Jarial, NIT Hamirpur (HP), India; Prof. Rajesh Kumar, GGSIPU, India; Prof. Anand Parey, IIT Indore, India; Dr. Jafar A. Alzubi, Al-Balqa Applied University, Jordan; and Dr. D. K. Khatod, IIT Roorkee, India. We further would like to express our love and affection to our family members, Shadma (wife of Prof. Atif Iqbal), Abuzar, Abubaker (Sons of Prof. Atif Iqbal) and Noorin (daughter of Prof. Atif Iqbal). We would like to express our gratitude to Dr. N. Fatema (wife of Dr. Hasmat Malik), Zainub Fatema and Ayesha Fatema

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(daughters of Dr. Hasmat Malik) for their intense feeling of deep affection. Furthermore, we would like to express our deep gratitude to Ayeesha Parveen (wife of Dr. Farhad Ilahi Bakhsh), Azaan Ilahi and Adeel Ilahi (sons of Dr. Farhad Ilahi Bakhsh). Woodlands, Singapore/New Delhi, India Doha, Qatar Ambedkar Nagar, India Ambedkar Nagar, India Srinagar, India

Dr. Hasmat Malik Prof. Dr. Atif Iqbal Dr. Puneet Joshi Dr. Sanjay Agrawal Dr. Farhad Ilahi Bakhsh

Contents

Theory and Applications of Metaheurestic Algorithms in Engineering and Systems Introduction: Optimization and Metaheuristics Algorithms . . . . . . . . . . Padam Singh and Sushil Kumar Choudhary Metaheuristics Paradigms for Renewable Energy Systems: Advances in Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . Ahmad Faiz Minai and Hasmat Malik

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35

Tackling Power Quality Issues Using Metaheuristics . . . . . . . . . . . . . . . Peeyush Kala, Puneet Joshi, Medha Joshi, Sanjay Agarwal, and Lokesh K. Yadav

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Meta-Heuristic Application in Suppression of Noise . . . . . . . . . . . . . . . . Rohun Nisa and Asifa Baba

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A Review on Genetic Algorithm and Its Application in Power System Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Vimal Singh Bisht, Navneet Joshi, Govind Singh Jethi, and Abhijit Singh Bhakuni Different Variants of Particle Swarm Optimization Algorithms and Its Application: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Ayush Mittal, Amruta Pattnaik, and Anuradha Tomar Applications of Metaheuristics in Power Electronics . . . . . . . . . . . . . . . 165 Peeyush Kala, Puneet Joshi, Medha Joshi, Sanjay Agarwal, and Lokesh K. Yadav Cuckoo Search Algorithm: A Review of Recent Variants and Engineering Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Abhinav Sharma, Abhishek Sharma, Vinay Chowdary, Aayush Srivastava, and Puneet Joshi

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Energy Management System for Hybrid Energy System: Renewable Integration, Modeling and Optimization, Control Aspects and Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Geeta Kumari, Akanksha Sharma, H. P. Singh, R. K. Viral, S. K. Sinha, and Naqui Anwer Recent Advances and Application of Metaheuristic Algorithms: A Survey (2014–2020) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Neha Khanduja and Bharat Bhushan Introduction to Renewable Energy Market and Metaheuristic Algorithms for Condition Monitoring of Photovoltaic Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Pradeep Kumar Single and Multi Objective Optimization Studies of Metaheurestic Algorithms in Engineering and Systems Applications of Meta-heuristics in Renewable Energy Systems . . . . . . . 253 Manoj Kumawat, Nitin Gupta, Naveen Jain, Vivek Shrivastava, and Gulshan Sharma Data-Driven Occupancy Detection Hybrid Model Using Particle Swarm Optimization Based Artificial Neural Network . . . . . . . . . . . . . . 283 Nuzhat Fatema and Hasmat Malik A Maiden Application of Competitive Swarm Optimizer for Solution of Economic Load Dispatch with Parameter Estimation . . . . . . . . . . . . 299 Abhishek Rajan, Abhay Sahu, Debashish Deka, and Tanmoy Malakar Optimal Controller Parameter Tuning of PSS Using Sine-Cosine Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Ramesh Devarapalli and Biplab Bhattacharyya Application of Multi-objective Hybrid DE-PSO Optimization Technique for Network Congestion Management Through Distributed Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Divya Asija and Pallavi Choudekar Optimization Solutions Using Particle Swarm Optimization in Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Bartosz Tarakan, Marcin Sarnicki, and Patrick D. Strankowski Switching Angles Computations Using PSO in Selective Harmonics Minimization PWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Salman Ahmad and Atif Iqbal ACO with Heuristic Desirability for Web Page Positioning Problem . . . 463 Harpreet Singh and Parminder Kaur

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Generating Functions of (p, q)-Analogue of I-Function Satisfying Truesdell’s Ascending and Descending Fp;q -Equation . . . . . . . . . . . . . . . 477 Altaf Ahmad Bhat, Fozia S. Qazi, and D. K. Jain Traffic Signal Control to Optimize Run Time for Energy Saving: A Smart City Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 Tarkeshwar Mahto and Hasmat Malik Analysis of Lead-Acid and Lithium-Ion Batteries as Energy Storage Technologies for the Grid-Connected Microgrid Using Dispatch Control Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 Mohd Alam, Kuldeep Kumar, and Viresh Dutta Novel Application of Grid Search Algorithm for Optimization of Photovoltaic-Wind-Diesel Hybrid Systems with and Without Tracking Systems for Power Generation . . . . . . . . . . . . . . . . . . . . . . . . 517 Amit Kumar Yadav Comparison of Meta-heuristic with Evolutionary and Local Search Methods for Feature Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 Ankita Bansal and Abha Jain Low Computational Artificial Intelligence Genetic Algorithm Assisted SLM PAPR Reduction Technique for Upcoming 5G Based Smart Hospital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 Arun Kumar, Avireni Bhargav, Anitha Karthikeyan, Karthikeyan Rajagopal, Ashok Kumar Srinivasan, and Adhena Nigus Tsegay Transmission Congestion Management Using Multi Objective Hybrid Flower Pollination and Particle Swarm Optimization Algorithm by Optimal Placement of TCSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569 Pallavi Choudekar and Divya Asija Input Voltage and Slip Power Control Schemes Based Performance Optimization of Grid-Connected Induction Generator . . . . . . . . . . . . . . 585 Farhad Ilahi Bakhsh, Md. Tabrez, and Salman Hameed A Computational Intelligence Approach for Power Quality Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Papia Ray and Monalisa Biswal Diagonal Recurrent Neural Network Based Prediction Model for Sales Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 Raman Tiwari, Rajesh Kumar, Smriti Srivastava, and Rajat Gera Depth Estimation Using Convolutional Neural Network with Transfer Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 Umang Soni and Hemant Yadav

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Novel Application of Linear Scaling to Improve Accuracy of Optimized Artificial Neural Network Using Levenberg-Marquardt Algorithm in Prediction of Daily Nitrogen Oxide for Health Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Vibha Yadav and Satyendra Nath Metaheurestic Algorithm Based Hybrid Model for Identification of Building Sale Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689 Nuzhat Fatema, Hasmat Malik, and Atif Iqbal Comparative Analysis of Optimal Scheduling of Multi-objective Non-convex Combined Heat and Power Units Using AI Techniques . . . 705 G. Rahul Prashanth, Siddharth Suhas Joshi, Vinay Kumar Jadoun, Nikhil Gupta, K. R. Niazi, and Anil Swarnkar Optimization Solutions for Demand Side Management . . . . . . . . . . . . . 729 Naladi Ram Babu, Tirumalasetty Chiranjeevi, Lalit Chandra Saikia, and Dhenuvakonda Koteswara Raju Appendix A: Dataset Used for Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819

Editors and Contributors

About the Editors Dr. Hasmat Malik BEARS, University Town, NUS Campus, Singapore; and NSUT Delhi, India. Hasmat Malik (M’16) received B.Tech degree in electrical and electronics engineering from the GGSIP University, Delhi, India, the M.Tech degree in electrical engineering from National Institute of Technology (NIT) Hamirpur, Himachal Pradesh, India, and the Ph.D. degree in Electrical Engineering from Indian Institute of Technology (IIT), Delhi. He is currently a postdoctoral fellow at BEARS, University-Town, NUS Campus, Singapore and since January, 2019, served as an assistant professor for 5+ years at Division of Instrumentation and Control Engineering, Netaji Subhas University of Technology (NSUT) Delhi, India. He has organized five international conferences, and proceedings has been published by Springer Nature. He is a Life Member of Indian Society for Technical Education (ISTE), Institution of Electronics and Telecommunication Engineering (IETE), International Association of Engineers, Hong Kong (IAENG), International Society for Research and Development, London (ISRD) and Member of the Institute of Electrical and Electronics Engineers (IEEE), USA, Computer Science Teachers Association (CSTA), USA, Association for Computing Machinery (ACM) EIG,

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Computer Science Teachers Association (CSTA) and Mir Labs, Asia. He has published widely in International Journals and Conferences his research findings related to intelligent data analytic, artificial intelligence, and machine learning applications in power system, power apparatus, smart building & automation, smart grid, forecasting, prediction and renewable energy sources. Dr. Hasmat has authored/co-authored more than 100 research papers and eight books and 18 chapters in twelve other books, published by IEEE, Springer and Elsevier. His research interests include power systems, power quality studies and renewable energy. He has published more than 100 research articles, including papers in international journals, conferences and book chapters. He is Guest Editor of Special Issue of Journal of Intelligent & Fuzzy Systems, 2018 (SCI, Impact Factor 2018:1.426), (IOS Press). He is Guest Editor of Special Issue of Journal of Intelligent & Fuzzy Systems, 2018, 2020 (SCI, Impact Factor 2019:1.637) (IOS Press). He received the POSOCO Power System Award (PPSA-2017) for his Ph.D. work for research and innovation in the area of power system. He has received best research papers awards at IEEE INDICON-2015 and full registration fee at IEEE SSD-2012 (Germany). He has supervised 23 PG students. He is involving in several large R&D projects. His principle areas of research interests are artificial intelligence, machine learning and intelligent data analytics for renewable energy, power system, smart grid, smart building & automation, condition monitoring and online fault detection & diagnosis (FDD).

Editors and Contributors

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Prof. Atif Iqbal Department of Electrical Engineering, Qatar University, Doha, Qatar. Atif Iqbal, Fellow IET (UK), Fellow IE (India) and Senior Member IEEE, DSc (Poland), PhD (UK)Associate Editor IEEE ACCESS, Editor-in-Chief, I’manager journal of Electrical Engineering, Former Associate Editor IEEE Trans. On Industry Application; Full Professor at the Dept. of Electrical Engineering, Qatar University; and Former Full Professor at Electrical Engineering, Aligarh Muslim University (AMU), Aligarh, India; and Recipient of Outstanding Faculty Merit Award academic year 2014-2015 and Research excellence awards 2015 and 2019 at Qatar University, Doha, Qatar. He received his B.Sc. (Gold Medal) and M.Sc. Engineering (Power System & Drives) degrees in 1991 and 1996, respectively, from the Aligarh Muslim University (AMU), Aligarh, India and Ph.D. in 2006 from Liverpool John Moores University, Liverpool, UK. He obtained DSc (Habilitation) from Gdansk University of Technology in Control, Informatics and Electrical Engineering in 2019. He has been employed as a lecturer in the Department of Electrical Engineering, AMU, Aligarh, since 1991, where he served as Full Professor until August 2016. He is recipient of Maulana Tufail Ahmad Gold Medal for standing first at B.Sc. Engg. (Electrical) Exams in 1991 from AMU. He has received several best research papers awards, e.g., at IEEE ICIT-2013, IET-SEISCON-2013, SIGMA 2018 and IEEE CENCON 2019. He has published widely in International Journals and Conferences his research findings related to power electronics, variable speed drives and renewable energy sources. Dr. Iqbal has authored/co-authored more than 390 research papers and two books and three chapters in two other books. He has supervised several large R&D projects worth more than 8 million USD. He has supervised and co-supervised several Ph.D. students. His principal areas of research interest are smart grid, complex energy transition, active distribution network, electric vehicle drivetrain, sustainable development and energy security, distributed energy generation.

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Editors and Contributors

Dr. Puneet Joshi Rajkiya Engineering College, Ambedkar Nagar, UP, India. Dr. Puneet Joshi received B.E. degree in electrical engineering from the G.B. Pant Engineering College, Uttarakhand, India, M.Tech. degree in electrical engineering from G.B. Pant University of Agriculture and Technology, Uttarakhand, India, and the Ph.D. degree in electrical engineering from G.B. Pant University of Agriculture and Technology, Uttarakhand, India. He is currently working as Assistant Professor in the Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh, India. His research interests include optimization techniques, power systems, power electronics, renewable energy and artificial intelligence/ soft computing/ machine learning applications in electrical engineering. He has published several research articles, including papers in international journals, conferences and book chapters. Dr. Joshi is a Life Member of the International Association of Engineers, Hong Kong (IAENG) and Member of the Institute of Electrical and Electronics Engineers (IEEE), USA. Dr. Sanjay Agrawal Assistant Professor, Electrical Engineering Department, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh, India. Sanjay Agrawal received B.Tech. degree in electrical and electronics engineering from the Uttar Pradesh Technical University, Lucknow, India, M.Tech degree in electrical engineering from NIT Hamirpur, India, in 2012, and the Ph.D. degree in electrical engineering from Motilal Nehru National Institute of Technology (MNNIT), Allahabad, India, in 2017. He has worked with the School of Electrical and Electronic Engineering (SEEE), Dublin Institute of Technology, Ireland, for seven weeks in the year 2016 under the SFI-ISCA sponsorship scheme of Ireland Government.

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Since December 2017, he has been Assistant Professor with the Electrical Engineering Department, Rajkiya Engineering College Ambedkar Nagar, Uttar Pradesh, India. His research interests include signal processing, artificial intelligence, renewable energy, and condition monitoring. He has published research articles in peer-reviewed international journals, conferences and also written book chapters. Dr. Farhad Ilahi Bakhsh Assistant Professor, Electrical Engineering Department, National Institute of Technology Srinagar, J&K, India. Dr. Farhad Ilahi Bakhsh received Diploma and B. Tech degree in Electrical Engineering from Aligarh Muslim University (AMU), Aligarh, India, in 2006 and 2010, respectively. He was awarded University Medal (Gold) for standing first throughout diploma in electrical engineering. He has been awarded first position in SPOTLIGHT and third position in overall solar conference during cognizance 2010 in Indian Institute of Technology Roorkee. Then, he pursued Masters in power system and drives from the Aligarh Muslim University. In Masters, he secured first position in his branch. He joined IEEE during Masters, and since then, he is an IEEE member. He also worked as head of Research & Development cell, IEEE student chapter, AMU for around two years. Under this cell, he developed five new systems, i.e., a rotor power control-based flexible asynchronous AC link (FASAL) system, a missed-call based switching system for multiple loads or appliances, a power controller circuit-based flexible asynchronous AC link (FASAL) system for induction generator applications, a combined voltage control and rotor power control-based flexible asynchronous AC link (FASAL) system and a waste fluid pressure-based energy generation system. Among these five systems, four systems have been published by an official Journal of Patent Office. Then, he pursued Ph.D. from Indian Institute of Technology Roorkee, India. During his Ph.D., he developed a new method for grid integration for wind energy generation system which has been recognized

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Editors and Contributors

worldwide. Currently, he is serving as Assistant Professor in Department of Electrical & Renewable Energy Engineering, School of Engineering & Technology, Baba Ghulam Shah Badshah University, Rajouri, J & K, India. He is also Coordinator of Massive Open Online Courses (MOOC’s) under SWAYAM platform in Baba Ghulam Shah Badshah University and Co-ordinator of NBA, School of Engineering & Technology, Baba Ghulam Shah Badshah University. Recently, he developed an automatic solar tracking system which has been appreciated by IEEE India Council, Centre for Embedded Product Design, Centre for Electronics Design and Technology, Netaji Subhas Institute of Technology in association with IEEE Delhi Section & IEEE CAS, Bangalore Chapter. Currently, he is serving as Assistant Professor in Department of Electrical Engineering, National Institute of Technology Srinagar, Jammu & Kashmir, India. Here, he is having many departmental and institutional responsibilities. He started IEEE Student Branch in NIT Srinagar, and since then, he is serving as Counselor of it. Recently, he has won “10 for 10 Typhoon HIL Award” from Switzerland, Europe. He delivered a number of keynote talks, invited talks and expert lectures at national and international levels in conferences, workshops, STC, etc. He have more than 50 published papers in international reputed Journals, international reputed conferences and national conferences. Moreover, he have four published patents in his credit. His research areas of interests include application of variable frequency transformer, renewable energy systems (Solar & Wind), drives and alternate energy vehicles.

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Contributors Sanjay Agarwal Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh, India Salman Ahmad Islamic University of Science and Technology, Awantipora, India Mohd Alam Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi, India Naqui Anwer Teri School of Advanced Studies, New Delhi, India Divya Asija Amity University, Noida, Uttar Pradesh, India Asifa Baba Islamic University of Science and Technology, Awantipora, Kashmir, India Naladi Ram Babu EED, NIT Silchar, Silchar, Assam, India Farhad Ilahi Bakhsh Department of Electrical Engineering, National Institute of Technology Srinagar, Hazratbal, J & K, India Ankita Bansal Department of Information Technology, Netaji Subhas University of Technology, Delhi, India Abhijit Singh Bhakuni Electronics Engineering Department, GEHU, Bhimtal, India Avireni Bhargav Department of IT and Engineering, La Trobe University, Melbourne, Bundoora, VIC, Australia Altaf Ahmad Bhat Department of Mathematical Sciences, IUST, Awantipora, J&K, India Biplab Bhattacharyya Department of Electrical Engineering, Indian Institute of Technology (ISM), Dhanbad, India Bharat Bhushan Delhi Technological University, Delhi, India Vimal Singh Bisht Electronics Engineering Department, GEHU, Bhimtal, India Monalisa Biswal Department of Electrical Engineering, National Institute of Technology, Raipur, India Tirumalasetty Chiranjeevi EED, REC Sonbhadra, Sonbhadra, Uttar Pradesh, India Pallavi Choudekar Amity University, Noida, Uttar Pradesh, India Sushil Kumar Choudhary Department of Mechanical Engineering, Mahamaya College of Agricultural Engineering & Technology, Akbarpur, Ambedkar Nagar, Uttar Pradesh, India

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Vinay Chowdary Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh, India Debashish Deka Samsung India R&D, Bengaluru, India Ramesh Devarapalli Department of Electrical Engineering, Indian Institute of Technology (ISM), Dhanbad, India Viresh Dutta Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi, India Nuzhat Fatema Intelligent Prognostic Private Limited, Delhi, India Rajat Gera Faculty of Management Studies, Manav Rachna International Institute of research and studies, Faridabad, India Nitin Gupta Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, JLN Marg, Jaipur, India Nikhil Gupta Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, India Salman Hameed Department of Electrical Engineering, ZHCET, Aligarh Muslim University, Aligarh, UP, India Atif Iqbal Department of Electrical Engineering, Qatar University, Doha, Qatar Vinay Kumar Jadoun Department of Electrical and Electronics Engineering, Manipal Institute of Technology, MAHE, Manipal, Karnataka, India Abha Jain Department of Computer Science, Shaheed Rajguru College of Applied Sciences for Women, Delhi, India D. K. Jain MITS, Gwalior, Madhya Pradesh, India Naveen Jain Department of Electrical Engineering, CTAE, MPUAT, Udaipur, India Govind Singh Jethi Department of CSE, GEHU, Bhimtal, India Medha Joshi EED, SLSET Group of Institutions, Kichha, India Navneet Joshi Mathematics Department, GEHU, Bhimtal, India Puneet Joshi Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh, India Siddharth Suhas Joshi Department of Electrical and Electronics Engineering, Manipal Institute of Technology, MAHE, Manipal, Karnataka, India Peeyush Kala Electrical Engineering Department, Technology, Sudhowala, Dehradun, Uttarakhand, India

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Anitha Karthikeyan Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam Parminder Kaur Department of Computer Science, Guru Nanak Dev University, Amritsar, India Neha Khanduja Delhi Technological University, Delhi, India Arun Kumar Department of Electronics and Communication, JECRC University, Jaipur, India Kuldeep Kumar Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi, India Pradeep Kumar EEED, NIT Sikkim, Ravangla, India Rajesh Kumar Department of Electrical Engineering, Delhi Technological University, Delhi, India Geeta Kumari Department of Electrical and Electronics Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh, India Manoj Kumawat Department of Electrical and Electronics Engineering, National Institute of Technology Delhi, Narela, Delhi, India Tarkeshwar Mahto Birla Institute of Technology Mesra, Ranchi, Jharkhand, India Tanmoy Malakar Electrical Engineering Department, NIT Silchar, Silchar, Assam, India Hasmat Malik Division of ICE, NSIT Delhi, New Delhi, India; BEARS, University Town, NUS Campus, Singapore, Singapore Ahmad Faiz Minai Department of Electrical Engineering, Integral University, Lucknow, UP, India Ayush Mittal HMR Institute of Technology and Management, New Delhi, India Satyendra Nath Department of Environmental Sciences and NRM, College of Forestry, Sam Higginbottom University of Agriculture, Technology and Sciences, Allahabad, Uttar Pradesh, India K. R. Niazi Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, India Rohun Nisa Islamic University of Science and Technology, Awantipora, Kashmir, India Amruta Pattnaik Dr. Akhilesh Das Gupta Institute of Technology and Management, Delhi, India

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Fozia S. Qazi Department of Mathematical Sciences, IUST, Awantipora, J&K, India G. Rahul Prashanth Department of Electrical and Electronics Engineering, Manipal Institute of Technology, MAHE, Manipal, Karnataka, India Karthikeyan Rajagopal Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam Abhishek Rajan Electrical and Electronics Engineering Department, NIT Sikkim, Ravangla, India Dhenuvakonda Koteswara Raju EED, NIT Silchar, Silchar, Assam, India Papia Ray Department of Electrical Engineering, Veer Surendra Sai University of Technology, Burla, Sambalpur, Odisha, India Abhay Sahu Oil and Natural Gas Corporation, Mumbai, India Lalit Chandra Saikia EED, NIT Silchar, Silchar, Assam, India Marcin Sarnicki Baltic EcoEnergy Sp. z o.o., Borkowo, Poland Abhinav Sharma Department of Electrical and Electronics Engineering, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India Abhishek Sharma Department of Research and Development, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India Akanksha Sharma Department of Electrical and Electronics Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh, India Gulshan Sharma Department of Electrical Power Engineering, Durban University of Technology, Durban, South Africa Vivek Shrivastava Department of Electrical and Electronics Engineering, National Institute of Technology Delhi, Narela, Delhi, India H. P. Singh Department of Electrical and Electronics Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh, India Harpreet Singh Department of Computer Science & Engineering, DAV University, Jalandhar, India Padam Singh Department of Applied Sciences (Mathematics), Galgotias College of Engineering and Technology, Greater Noida, Uttar Pradesh, India S. K. Sinha Department of Electrical and Electronics Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh, India Umang Soni Department of MPAE, Netaji Subhas University of Technology, Delhi, India

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Ashok Kumar Srinivasan School of Electrical and Computer Engineering, Ethiopian Institute of Technology—Mekelle, Mekelle University, Mek’ele, Ethiopia Aayush Srivastava Department of Electrical and Electronics Engineering, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India Smriti Srivastava Division of Instrumentation and Control, Netaji Subhas University of Technology (Formerly Netaji Subhas Institute of Technology), New Delhi, India Patrick D. Strankowski Baltic EcoEnergy Sp. z o.o., Borkowo, Poland Anil Swarnkar Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, India Md. Tabrez Department of Electrical and Electronics Engineering, Motihari College of Engineering, Motihari, Bihar, India Bartosz Tarakan Baltic EcoEnergy Sp. z o.o., Borkowo, Poland Raman Tiwari Faculty of Management Studies, Manav Rachna University, Faridabad, India Anuradha Tomar Eindhoven University of Technology, Eindhoven, The Netherlands; JSS Academy of Technical Education, Noida, India Adhena Nigus Tsegay School of Electrical and Computer Engineering, Ethiopian Institute of Technology—Mekelle, Mekelle University, Mek’ele, Ethiopia R. K. Viral Department of Electrical and Electronics Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh, India Amit Kumar Yadav Electrical and Electronics Engineering Department, National Institute of Technology Sikkim, South Sikkim, India Hemant Yadav Department of MPAE, Netaji Subhas University of Technology, Delhi, India Lokesh K. Yadav Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh, India Vibha Yadav Department of Environmental Sciences and NRM, College of Forestry, Sam Higginbottom University of Agriculture, Technology and Sciences, Allahabad, Uttar Pradesh, India

Theory and Applications of Metaheurestic Algorithms in Engineering and Systems

Introduction: Optimization and Metaheuristics Algorithms Padam Singh and Sushil Kumar Choudhary

Abstract Present chapter embodies an introductory overview of optimization and metaheuristic algorithms. An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of Applied Mathematics. More generally, optimization consists of finding best available values of some objective function given a defined domain including a variety of different types of objective functions and different types of domains. One of the most significant trends in the field of optimization is the continually increasing emphasis on the interdisciplinary nature. Optimization has been a basic tool in all areas of Applied Mathematics, Engineering, Economics, Medical Science and other field of Sciences. The latest developments over the last few decades tend to use metaheuristic algorithms. In fact, a vast majority of modern optimization techniques includes metaheuristic algorithms. Metaheuristic algorithms such as Particle Swarm Optimization, Ant Colony Optimization, Artificial Bee Colony, Genetic Algorithm, Simulated Annealing, Cuckoo Search, Differential Evaluation, Biography Based Optimization and Harmony Search etc. are becoming very powerful in solving hard optimization problems and they have been applied in almost all major areas of science and engineering as well as industrial applications. In this chapter a general overview from the era of Fermat and Lagrange who introduced calculus based formulae to identify optima is given. Also, foundation of optimization provides a brief introduction to the underlying nature of optimization and the common approaches to optimization problems, random number generation, the Monte Carlo method, and the Markov chain Monte Carlo method. This chapter P. Singh (B) Department of Applied Sciences (Mathematics), Galgotias College of Engineering and Technology, Greater Noida, Uttar Pradesh 201306, India e-mail: [email protected] S. K. Choudhary Department of Mechanical Engineering, Mahamaya College of Agricultural Engineering & Technology, Akbarpur, Ambedkar Nagar, Uttar Pradesh 224122, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_1

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P. Singh and S. K. Choudhary

introduces all the major metaheuristic algorithms and a wide range of applications that use metaheuristic algorithms to solve challenging optimization problems while also introducing various modifications used for multi-objective optimization. Throughout this chapter, the author presents worked out examples and real world applications that illustrate the modern relevance of the topic. In addition, references to the current literature enable readers to investigate individual algorithms and methods in greater detail. Keywords Optimization · Metaheuristics algorithms · Optimality criteria · Objective function

1 General Overview An important goal of engineering activities is to improve and to optimize technical designs, structural assemblies and structural components. The task of optimization is to support the Engineer’s in searching for the best possible alternatives of specific problem. The “best possible” or “optimal” solution is the solution which is highly corresponding to the desired concept and objectives [1]. In comparison to the “trial and error” method generally used in the engineering environment and based on an intuitive empirical approach, the determination of optimal solutions by applying mathematical optimization procedures is more reliable and efficient if correctly applied. These procedures are increasingly entering in the industrial practice. In order to be able to apply the optimization methods to an optimization task, it must be possible to express both the design objectives and the constraints by means of Mathematical functions. Optimization is one of the most powerful tools in process integration. The degree of goodness of the solution is quantified using a goal function which is to be optimized. The search process is undertaken subject to the system model and restrictions which are termed constraints. Hence, the purpose of optimization is to maximize (or minimize) the value of goal/objective function subject to a number of constraints imposed on decision variables [2]. These constraints are in the form of equality and inequality expressions. Examples of equality constraints include process modeling equations, material and energy balances, and thermodynamic requirements. On the other hand, the nature of inequality constraints may be environmental, technical or thermodynamic. Optimization is everywhere; however, to realize that everything is optimization does not make the problem-solving easier. In fact, many seemingly simple problems are very difficult to solve. A well-known example is the so called Traveling Salesman Problem in which the salesman intends to visit, say, 50 cities, exactly once so as to minimize the overall distance traveled or the overall traveling cost. No efficient algorithms exist for such hard problems.

Introduction: Optimization and Metaheuristics Algorithms

5

2 Meaning and Definition of Optimization Optimization is a process or methodology of making decision as fully perfect, functional or as effective as possible. Optimization of a product or process is the determination of the conditions resulting in its optimal performance on the basis of optimization parameters introduced in the mathematical formulation of the real model. A decision variable in a mathematical model is referred to as an optimization parameter. For example, the number of security guards to hire at some point of the night shift in an industry may also be an optimization parameter in a model of industrial expenditure. It is possible to have more than one optimization parameter in any complex mathematical model. Optimization parameters can be classified as follows (Fig. 1): In General, an optimization problem can be written in mathematical form (i = 1, 2, 3 . . . P)

(i)

g j (x) = 0, ( j = 1, 2, 3 . . . Q)

(ii)

h k (x) ≤ 0, (k = 1, 2, 3 . . . R)

(iii)

min x∈R n f i (x),

Subject to

where f i (x), g j (x) and h k (x) are the functions of decision vector x = [x1 , x2 , x3 . . . xn ]T . The components of x are called decision variables. The functions f i (x), (i = 1, 2, 3, . . . P) are called objective functions with P different objectives and in the case of P = 1, there is only a single objective. In Eq. (ii), g j (x) denotes the equality constrained function and in inequality (iii), h k (x) denotes inequality constrained function. The space spanned by the decision variables is referred to as the search space R, while the space formed through the objective function values is known as the solution space. The objective functions can be either linear or nonlinear. We can additionally write the inequalities in the other way ≥ 0, and we can also formulate the objective function as maximize. This is because the maximization OPTIMIZATION iPARAMETERS

VARIABLE iTYPE

INDEPENDENT

DEPENDENT

Fig. 1 Types of optimization parameters

PROBLEM iTYPE

CONSTRAINED

UNCONSTRAINED

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P. Singh and S. K. Choudhary

of f i (x) is equivalent to the minimization of − f i (x), and any inequality g j (x) ≤ 0 is equal to −g j (x) ≥ 0 for the constraints, the simplest case for a decision variable xi is xi,min ≤ xi ≤ xi,max which are called bounds.

3 History of Optimization Optimization is likewise ancient as the science itself. In ancient time Greek solved many optimization problems. Around 300 BC, Euclid proved that a square encloses the greatest region among all feasible rectangles. Subsequently in 100 BC, Heron advised about the minimum path in between 2 points along the route reflect by a mirror. This is well known Heron’s problem, as fist time it was presented in Heron’s Catoptrica. During 1613, German astronomer, J. Kepler, is in most cases well-known for solving secretary related problem or marriage issue along with the great discovery of his 3 laws of planetary motion. That technique on marriage issues was found in his non-public letter dated 23 October 1613 to the Baron S., such as the stability of merits and drawbacks of every person, hesitation, dowry, and suggestion of contacts. Out of 11 participants, Kepler selected the 5th, even though his buddy recommended him to select the 4th candidate. It indicates that he was making an attempt to optimize some feature of some sort. Informally M. Gardner in 1960 brought into picture this issue in the mathematical games column in 1960s publication of Scientific American. Till then, it was known as optimal stopping into a discipline of probability optimization. In 1621, W. V. R. Snell introduced the law of refraction, that result later referred by Christiaan Huygens as Snell’s results in his Dioptrica in 1703. In 1687, body structure problem of smallest resistance solved in Principia Mathematica by Sir Isaac Newton that he posed formerly in 1685 as a revolutionary optimization problem. Subsequently, he introduced the resistance law. In a paper published in June 1696 in Acta Eruditorum, J. Bernoulli challenged to all the mathematicians to discover the curve shape that join 2 points at some height so that a falling body along the curve in the shortest time under gravity, although that solution known by Bernoulli in advance [3]. In 1781, French engineer G. Monge, investigated the well known problem of transportation for most reliable transportation and distribution of assets. After some time, in 1801, Gauss used the technique of least squares to estimate the orbital position of the asteroid Ceres. That was later published in 1809 with more precise mathematical foundation. The “law of diminishing returns” for the agricultural field was proposed by D. Ricardo, in 1815. As an example based on this law, the yield of an agricultural field or a manufacturing unit will only grow with supplementary enhance of input raw material. This law is known as “law of increasing opportunity cost”. This implies a vital association between possibility and insufficiency of resources. An iterative way for solving systems of equations was proposed by L. A. Cauchy in 1847 in a short note. This in actuality leads two iterative methods: steepest descent

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7

and gradient method, for some particular properties of multivariable functions. In 1906, J. Jensen proposed the concept of convexity in the form of inequality, presently known as Jensen’s inequality. Those have been widely used in different optimization techniques. Later in 1766, L. Euler deliberates the Knight tour problem. After that, in 1856, Sir W. R. Hamilton got world fame due to his Icosian Game. Noteworthy improvement was made during the 2nd World War, and it extended to get most efficient or close to expected optimal solution of real world difficult problems existing in interdisciplinary areas viz. transport planning, network communication, planning of projects, task scheduling and management related issues. Optimization techniques have a broad historic background past from more than a century. Initially, differential calculus was the fundamental tool utilized for finding maxima or minima of functions, which arose in many problems. There is a clear evidence of the use of mathematical models and optimization techniques at the turn of the twentieth century such as, H. L. Gantt in 1900 used charts to correctly schedule jobs on machines, currently known as Gantt charts. After that F. W. Harris in 1915 derived the typical economic order quantity in stock management. H. First book on optimization i.e. “Theory of Minima and Maxima” published by Hancock in 1917. At the same period A. K. Erlang also derived some formula for automatic telephone switchboard issues, presently known as queuing systems. At the era of Second World War, the British authorities organized civilian scientific groups to help area commanders in solving complicated problems. The motive was to maximize their battle effort with the confined assets they had. In 1939, L. Kantorovich first time improved an algorithm for LPP also formulated the manufacturing problem to planning high-quality techniques for finding options using LP. For this great work, he shared the Noble prize with T. Koopmans in 1975 [4, 5]. After Second World War, a drastic change and refinement of operations research strategies occurred with an analogous growth from singularly addressing army problems to troubles encountered in almost all areas of public and non-public enterprise as nicely as in government services. Most of managers and planner realized that the financial savings incurred from applying operations research tactics to solving issues were very substantial due to the fact even a cent saved per unit on a massive manufacturing run could complete up to thousands and thousands of dollars [6]. Dynamic programming approach can be trace back to 1944 when J. V. Neumann and O. Morgenstern proposed the sequential decision problems [7]. J. V. Neumann also has significant contribution for the improvement in the area of operational research. Dantzig’s, in the area of O.R. developed simplex method for L.P.P., which gave him world fame in this discipline. L.P. is one of the fundamental techniques widely used in optimization. The dissertation work of W. Karush done in 1939, analyzed by H. Kuhn and A. W. Tucker and re-developed the optimality condition in 1951. From 1952 to 1956, at the Rand Corporation in US, the sequential development performed under the direction of Dantzig for computational methods to solve LPP. That time excellent progress had been made on 1st generation computers. However computer scientist L. Lovasz, in 1980 described the significance of linear programming methods.

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Also that year, E. Lawler wrote LP to allocate resources, workers, design production, plan scheduling, funding portfolios and formulate advertising (and army) strategies. In addition to many other traditional optimization strategies developed over the previous half century. The latest development of contemporary heuristic techniques such as simulated annealing, tabu search, genetic algorithms, neural computing, fuzzy logic, and ant colony optimization are presenting practitioners with some state-ofthe-art tools to tackle more complex conditions. After the 1980s, the literature on optimization was exploded [8].

4 Types of Optimization Techniques In the optimization process, an important step is to classify developed model in optimization, since algorithms for solving optimality related problems are referred to a particular type of problem. Here we provide Taxonomy to help you classify your optimization model (Fig. 2). • Stochastic Versus Deterministic Optimization In deterministic optimization, it is assumed that the data for the given problem are known accurately. However, for many actual problems, the data cannot be known accurately for a variety of reasons. The first reason is due to simple measurement error. OPTIMIZATION UNCERTAINITY

STOCHASTIC iPROGRAMMING

UNCONSTRAINED

DETERMINISTIC

ROBUST iOPTIMIZATION

CONSTRAINED

MULTIOBJECTIVE

CONTINUOUS

INTEGER iPROGRAMMING

DISCRETE

COMBINATORIAL iOPTIMIZATION

NONLINEAR iLEAST iSQUARES

LINEARLY iCONSTRAINED

LINEAR iPROGRAMMING

NONLINEAR iEQUATIONS

NETWORK iOPTIMIZATION

QUADRATIC iPROGRAMMING

NONDIFFERENTIABLE iOPTIMIZATION

BOUND iCONSTRAINED

DERIVATIVE iFREE iOPTIMIZATION

GLOBAL iOPTIMIZATION

NONLINEAR iPROGRAMMING

2nd i iORDER iCONE iPROGRAMMING

SEMIDEFINITE iPROGRAMMING

QUADRATICALLY iCONSTRAINED iPROBLEMS

SEMIINFINITE iPROGRAMMING MIXED iINTEGER iPROGRAMMING

COMPLIMENTARITY iPROBLEMS

Fig. 2 Types of optimization techniques

EQUILIBRIUM iCONSTRAINTS

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The second and more fundamental reason is that some data represent information about the future like product demand or price for a future time period and simply cannot be known with certainty. In optimization under uncertainty, or stochastic optimization, the uncertainty is incorporated into the model. Robust optimization techniques can be used when the parameters are known only within certain bounds; the goal is to find a solution that is feasible for all data and optimal in some sense. Stochastic programming models take advantage of the fact that probability distributions governing the data are known or can be estimated; the goal is to find some policy that is feasible for all the possible data instances and optimizes the expected performance of the model. • Multi-objectives Optimization Many optimization problems have a single objective function; however, there are fascinating instances when optimization problems have no objective function or multiple objective functions. Feasibility problems are problems in which the goal is to find values for the variables that satisfy the constraints of a model with no particular objective to optimize. Complimentarily problems are pervasive in engineering and economics. The purpose is to find a solution that satisfies the complimentarily conditions. Multi-objective optimization problems occur in many fields, such as engineering, economics, and logistics, when optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. For example, creating a new component may contain minimizing weight whilst maximizing strength or choosing a portfolio may involve maximizing the predicted return whilst minimizing the risk. In practice, problems with multiple objectives regularly are reformulated as single objective problems by means of either forming a weighted mixture of the different objectives or by replacing some of the goals by constraints. • Discrete Versus Continuous Optimization Some models only make sense if the variables take on values from a discrete set, frequently a subset of integers, whereas other models incorporate variables that can take on any real value. Models with discrete variables are discrete optimization problems; models with continuous variables are continuous optimization problems. Continuous optimization problems have a tendency to be less complicated to solve than discrete optimization problems; the smoothness of the functions means that the objective function and constraint function values at a point x can be used to deduce information about points in a neighborhood of x. However, enhancements in algorithms coupled with developments in computing science have dramatically increased the size and complexity of discrete optimization problems that can be solved efficiently. Continuous optimization algorithms are essential in discrete optimization due to the fact many discrete optimization algorithms generate a sequence of continuous sub problems.

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• Linear Versus Non-linear Programming When the objective function and all the constraints are linear functions of decision variables, the problem is a linear programming problem. Problems of this type are probable the most widely formulated and solved of all optimization problems, particularly in management and financial applications. Non-linear programming problems, in which at least some of the constraints or the objectives are non-linear functions, tend to occur naturally in the physical sciences and engineering and are becoming more widely used in management and economic sciences as well [9]. • Constrained Versus Unconstrained Optimization A necessary difference is between problems in which there are no constraints on the decision variables and problems in which there are constraints on the decision variables. Unconstrained optimization problems occur directly in many realistic applications; they also arise in the reformulation of constrained optimization problems in which the constraints are replaced by a penalty term in the objective function. Constrained optimization problems arise from applications in which there are explicit constraints on the variables. The constraints on the variables can differ widely from simple bounds to systems of equalities and inequalities that model complex relationships among the variables. Constrained optimization problems can be furthered categorized in accordance to the nature of the constraints viz linear and nonlinear and convex, the smoothness of the features viz differentiable or non-differentiable. • Global and Local Optimization Many algorithms for non-linear optimization problems are searching for only a local solution, a point at which the objective function is smaller than at all different feasible nearby points. They do not usually find the global solution, which is the point with the lowest function value amongst all feasible points. Global solutions are needed in some applications, but for many problems, they are challenging to recognize and even greater challenging to locate. For convex programming problems, and more particularly for linear programs, local solutions are additionally global solutions. General non-linear problems, both constrained and unconstrained, might also possess local solutions that are no longer global solutions.

5 Aims and Scope of Optimization Algorithms Optimization theory and methods have been applied in many fields to handle various real world problems. In light of advances in computing techniques, optimizations have become increasingly important and popular in different engineering fields. The aim of this book is to present some recent developments in the area of optimization and metaheuristics algorithms with their engineering applications. Some typical objectives are:

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• To promote the development of necessary high-level theory to meet the needs of complex optimization problems and establish appropriate cooperation with the International Mathematics Union and similar organizations. • To provide an international clearing house for computational (as well as related theoretical) aspects of optimization problems in diverse areas and to share computing experience gained on specific applications. • To foster interdisciplinary activity on optimization problems spanning the various areas such as Economics (Including Business Administration and Management), Biomedicine, Meteorology, etc., in cooperation with associated international bodies. • Increasing the quality and quantity of products and industry and at the same time reducing costs and thereby being competitive. • Fulfilling the permanently increasing specification demands as well as considering reliability and safety, observing severe pollution regulations and saving energy and raw materials. • Introducing inevitable rationalization measures in development & design offices in order to save more time for the staff to work creatively. Computational aspects of optimization problems arising in such areas as manufacturing, Planning, Aerospace, Biomedicine, Economics, Meteorology, and public services like health, environment, police, fire, transportation etc. Some specific examples are: • • • • • •

Trajectory analysis and computation. Optimization of man-machine systems. Optimization of power systems operation. Optimization of resource allocation in urban systems. Optimization of pollution-control systems. On-line and off-line computational techniques in modeling and control of dynamic systems. • Optimization of decentralized systems (macro-economic systems) and systems with multicriteria.

6 Optimization Algorithms Most of the optimization algorithms are iterative. They start with an initial guess of the decision variable and generate a sequence of improved iterations until they terminate, hopefully at a solution. The strategy used to move from one iterate to the next distinguishes one algorithm from another. Most strategies make use of the values of the objective function, the constraint functions, and possibly the first and second derivatives of these functions. Some algorithms accumulate information gathered at preceding iterations, whilst others use only local information obtained at the current point. Regardless of these specifics proper algorithms have to possess the following properties:

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• Efficiency: They should not require excessive processing time or storage. • Accuracy: They have to be able to perceive a solution with precision, without being overly sensitive to errors in the data or to the arithmetic rounding errors that occur when the algorithm is implemented on a computer. • Robustness: They should perform properly on a broad range of problems in their class, for all reasonable values of the starting point. These goals may additionally conflict. For example, a rapidly convergent approach for a large unconstrained non-linear problem might also require too much computer storage. On the other hand, a strong method may also be the slowest. Tradeoffs between convergence rate and storage requirements, and between robustness and speed, and so on, are central issues in numerical optimization. There are three sorts of optimization algorithms which are widely used; Zero-order algorithms, first Order Optimization Algorithms, and 2nd-Order Optimization Algorithms.

6.1 Zero-Order or Derivative Free Optimization Algorithms Zero-order algorithms use only the criterion value at some positions. It is popular when the gradient and Hessian information are tough to obtain, i.e. when no explicit function forms are given.

6.2 First Order Optimization Algorithms First Order Optimization Algorithms minimize or maximize a Loss function using its Gradient values with respect to the parameters. The most extensively used first-order optimization algorithm is Gradient Descent. The first order derivative shows whether or not the function is reducing or growing at a particular point. First-order derivative essentially will provide us a line that is tangential to a point on its error Surface. An example of first-order optimization algorithm is Gradient descent for finding the minimal of a function. θ = θ −η ·∇ J (θ ) is the formula of the parameter updates, where η is the learning rate, ∇ J (θ ) is the gradient of loss function J (θ ) with respect to parameters θ . Gradient descent is the most popular optimization algorithm used in optimizing a neural network. Gradient descent is used to update and tune the Model’s parameters in a direction so that we can minimize the Loss function in a neural network model. A neural network trains by a technique called back-propagation, in which propagating forward calculating the dot product of inputs signals and their corresponding weights and then applying an activation function to these sum of products, which transforms the input signal to an output signal and additionally is essential to model complex non-linear functions and introduces non-linearity to the model which allows the model to analyze almost any arbitrary functional mapping.

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6.3 2nd-Order Optimization Algorithms A 2nd-order optimization algorithm uses the 2nd-order derivative which is additionally referred to as Hessian to minimize or maximize the loss function. The Hessian is a matrix of 2nd-order partial derivatives. Since the 2nd derivative is costly to compute, the 2nd-order is no longer used much. The 2nd-order derivative tells us whether or not the first derivative is increasing or decreasing which hints at the function’s curvature. It also gives us with a quadratic surface that touches the curvature of the error surface.

7 Heuristics and Metaheuristics Algorithms In heuristic and metaheuristic there is small difference. Typically, heuristic approach primarily based on trial and error to find or discover solutions of the problems. There are some heuristics besides finitely terminating algorithms and converging iterative methods. Best solutions to a complex problem can be found in least time, infact there is no assurance to get an ultimate solutions. Probably these algorithms efficiently work most of the time, but still no longer every time. Sometime these are good enough when we do not expecting the satisfactory solutions but rather good solutions which can be obtained easily. A heuristic is any algorithm which is no longer assured to find the solution; however which is nevertheless useful in certain realistic situations. Some popular heuristics are: Hill mountaineering with random restart, Dynamic relaxation, Evolutionary algorithms, Memetic algorithm, Nelder-Mead simplicial heuristic. Additional improvement over these heuristic algorithms is the so-called metaheuristic algorithms. The word meta- means ‘beyond’ or ‘higher level’, and they generally perform better than simple heuristics. Informally, all metaheuristic uses certain tradeoff of randomization and local search. Interestingly no agreed definitions of heuristics and metaheuristics exist in literature, some use ‘heuristics’ and ‘metaheuristics’ interchangeably. However, recent trends have a tendency to name all stochastic algorithms with randomization and local search as metaheuristic. Randomization provides a good way to move away from local search to global search. Therefore, almost all metaheuristic algorithms look appropriate for global optimization. Most metaheuristic algorithms are nature-inspired as they have been developed based on some abstraction of nature. Nature has evolved over millions of years and has found perfect solutions to nearly all the problems she met. Two fundamental components of any metaheuristic algorithms are: selection of the best possible solutions and randomization. The selection of the best ensures that the options will converge to the optimality, whilst the randomization avoids the solutions being trapped at local optima and, at the same, enlarge the diversity of the solutions. The suitable aggregate of these two components will generally ensure to reach at global optimality. Metaheuristic algorithms can be classified in many ways. One way is to classify them as: population-based and trajectory-based. For example,

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genetic algorithms are population-based as they use a set of strings [10], so is the particle swarm optimization (PSO) which uses a couple of agents or particles. PSO is also referred to as agent-based algorithms [11–13]. On the other hand, simulated annealing makes use of a single agent or solution which moves through the design space or search space in a piecewise style.

7.1 Applications of Metaheuristic Algorithms in Engineering Metaheuristic algorithms are important tools that in recent years have been used extensively in several fields. In engineering, there is a big amount of problems that can be solved from an optimization point of view. Their use produces accurate results in problems that are computationally expensive. Experimental results support the performance obtained by the selected algorithms in such specific problems as digital filter design, image processing and solar cells design. Many design optimization problems in engineering are highly nonlinear and can be challenging to solve using traditional methods. In many cases, metaheuristic algorithms can be an effective alternative and thus suitable in engineering applications such as the optimization of tuned mass dampers, neural networks, data mining, industrial engineering, mechanical engineering, electrical engineering, software engineering, location theory and cost optimization of reinforced concrete. In the last several decades, there is a trend in the scientific community to solve complex optimization problems by using metaheuristic optimization algorithms. The most interesting and most widely used metaheuristic algorithms are swarm-intelligence algorithms which are based on a collective intelligence of colonies of ants, termites, bees, flock of birds, and so forth. The reason of their success lies in the fact that they use commonly shared information among multiple agents, so that self-organization, co-evolution, and learning during cycles may help in creating the highest quality results. Although not all of the swarm intelligence algorithms are successful, a few techniques have proved to be very efficient and thus have become prominent tools for solving real-world problems [14].

8 Limitations of Optimization Techniques Optimization covers such a wide range of techniques, the only known limits on their use in the physical and biological phenomenon are the limits on present technology, the limits given by physical laws, limits given by complexity and finally the limits of computation. Various methodologies can be employed for optimizing a goal function. Each method has its own advantages or drawbacks. Some of the major disadvantages are: • In many fields, there is insufficient quantization and formalism for it to be applicable at the present time, but that may change as these fields change.

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Fig. 3 Number representation on real line

• There are fields, such as certain metaphysical and/or spiritual systems, where mathematical methods are by definition not applicable. • The need to determine both the structure and the parameters of the engineering systems for optimization makes the modeling of these systems a difficult task. • Artificial Neural Networks usually do not give a deep insight into the process for which they obtain a solution.

9 Mathematical Pre-requisites 9.1 Real Number System We start with the natural numbers which are the collection of counting numbers 1, 2, 3, 4, 5, 6, 7 … so on. The symbol N is used to indicate this collection. Thus n ∈ N means that n is a natural number from one of these numbers 1, 2, 3, 4, 5, 6, 7 … so on. The natural numbers prove to be rather limited in representing problems that arise in applications of Mathematics to the real world. Thus they are enlarged by adjoining the negative integers and zero. Thus the collection . . . , −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, . . . is denoted by Z and called the set of integers. At some point the problem of the failure of division in the sets of natural number N and set of integer Z becomes acute and the learner must progress to an understanding of fractions. This larger number system is denoted by Q, where the symbol chosen is meant to suggest quotients, which is after all what fractions are. The collection of all numbers of the form QP , where P, Q ∈ Z and Q = 0 is called the set of rational numbers and is denoted by Q. The next step, needed for all calculus students, is to develop the still larger system of real numbers, denoted as R. The real line can be thought of as a part of the complex plane. Most calculus students would be hard pressed to say exactly what these numbers are. They recognize that R includes √ all of N, Z, and Q and also many new numbers, such as π, 2 and e (Fig. 3).

9.2 Sequence A sequence in a set A is a function from a certain kind of subset of integers Z into A. It will be assumed that the set of integers is non-empty, consists of consecutive integers, and consists of no greatest integer. In particular, the domain of any sequence

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is infinite. The subset of integers may also contain all non-negative integers or all positive integers. Sometimes the subset of integers includes all integers, and the sequence, in this case, is often known as doubly infinite. The value of a sequence f at the integer n is usually written fn , and the sequence itself may be denoted by an expression like fn , n ≥ 1 [15].

9.3 Convergent Sequence A sequence fn in R is convergent if there exists a real number L such that for every ∈> 0, there is an integer N with |fn − L| 0, there is a δ > 0 such that |f(x) − f(a)| < ε for all x with |x − a| < δ. Any function that does not satisfy the above continuity condition is called discontinuous function. We often use C0 to denote the set of all continuous functions. A function is said to be of class Cn if its all derivatives up to nth order exist and continuous. It is also called n-continuously differentiable. So C1 is the set of all differentiable functions whose first derivatives are continuous.

9.11 Smoothness A function is said to be smooth if it has derivatives of all orders. That is to say, a smooth function belongs to class C∞ . For example, ex is a smooth function because it’s all orders derivatives exist. Similarly, x2 is also smooth as it has derivatives of all orders, though the third and higher derivatives are all zero. However, not all functions have derivatives of all orders. A function f(x) in an interval [a, b] is called piecewise smooth if it can be partitioned into a finite number of smaller sub-intervals, continuity holds cross the joins of the sub-intervals and smoothness holds in each interval. In each interval, the function has a bounded first derivative that is continuous except at a finite number of points at the joints.

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Y (a) f’’(x)>0 iii

(b) f’’(x)=0

(c) i if’’(x) 0, the function f(x) achieves a local minimum at the stationary point else if f (x) < 0, the stationary point corresponds to a local maximum.

9.14 ε-Neighbourhood of a Point Let S ⊆ R, is called ε-Neighbourhood of a point a if there exists ε > 0 s.t. (a − ε, a + ε) ⊂ S. It is denoted by Nε (a) (Fig. 7).

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a i-

iii

a

a i-

Fig. 7 ε-neighbourhood of a point x = a

9.15 Optimality Criteria A point x∗ is called strong local maxima of the nonlinearity constrained optimization problem if f(x) is defined in Nε (x∗ ) and satisfies f(x∗ ) > f (y) for all y ∈ Nε (x∗ ) where ε > 0 and y = x∗ . If x∗ is not a strong local maxima, the inclusion of equality in the condition f(x∗ ) ≥ f(y) for all y ∈ Nε (x∗ ) defines the point x∗ as a weak local maximum. Similarly, a point x∗ is called strong local minima of the nonlinearity constrained optimization problem if f(x) is defined in Nε (x∗ ) and satisfies f(x∗ ) < f (y) for all y ∈ Nε (x∗ ) where ε > 0 and y = x∗ . Also in the same manner, If x∗ is not a strong local minima, the inclusion of equality in the condition f(x∗ ) ≤ f(y) for all y ∈ Nε (x∗ ) defines the point x∗ as a weak local minima. In Fig. 8, shows various local minima and maxima. At Point E curve gives weak local maxima, while at point F a local maxima with a jump discontinuity exists. G and H are the local minima and maxima, respectively. Point J has weak local minima because there are many different values of x which will lead to the same value of f(x). Point I gives the global maxima which is also a strong maxima. Finally, At K is the strong global minima. However, at point B, there exists a discontinuity, and f (x) is I

Local iMaxima iwith iDiscontinuity

Strong iGlobal iMaxima

F Weak iLocal

H

iMaxima

E

G J Weak iLocal iMinima

Strong iGlobal iMinima

K

Fig. 8 Strong and weak maxima and minima

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not defined unless we are only concerned with the special case of approaching from the right. In this discussion, we consider only those objective functions which belong to class C0 . Informally, the notation using ‘max’ or ‘min’ is just an abbreviation, and it refers to minimize or maximize certain objectives or goals. In general, the max/min of a function can only occurs at stationary point; A critical point when the function is not differentiable or at the boundaries.

9.16 Norm of a Vector Consider an n-vector v = (v1 , v2 , v3 . . . vn )T , its pth-norm is denoted by vp and   n p 1/p defined as vp = where p ∈ Z+ with the following properties: i=1 |vi | v ≥ 0, for all v. (Non-Negativity) v = 0, iff (if and only if) v = 0 (being positive definite or point-separating) αv =| αv, for any real number α. (Homogeneity or Scaling Property) u + v ≤ u + v, (triangle inequality for the uniqueness and consistency of norms) Three well-known norms are l1 (1-norm), l2 (2-norm) and l∞ (infinity-norms) for p = 1, 2 and ∞ respectively. These can be defined as follows: l1 = v1 =

n  |vi |.

(5)

i=1



n  |vi |2 l2 = v2 =

1/2 (6)

i=1

l∞ = v∞ = max|vi | = max(|v1 |, |v2 |, |v3 | . . . |vn |) i

(7)

Example, consider u = (1, 2, −1, 4, 3)T and v = (2, 1, −3, 0, 4)T two 5-dimensional vectors. Then, u1 = (|1| + |2| + |−1| + |4| + |3|) = 1 + 2 + 1 + 4 + 3 = 11 u2 =



|1|2 + |2|2 + |−1|2 + |4|2 + |3|2 =

(i)

√ √ 1 + 4 + 1 + 16 + 9 = 31 (ii)

u∞ = max(|1| + |2| + |−1| + |4| + |3|) = max(1, 2, 1, 4, 3) = 4

(iii)

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Similarly, v1 = (|2| + |1| + |−3| + |0| + |4|) = 2 + 1 + 3 + 0 + 4 = 10 v2 =



|2|2 + |1|2 + |−3|2 + |0|2 + |4|2 =

√

4 + 1 + 9 + 0 + 16 =

√

(iv) 30 (v)

v∞ = max(|2| + |1| + |−3| + |0| + |4|) = max(2, 1, 3, 0, 4) = 4

(vi)

Also, u + v = (1 + 2, 2 + 1, −1 − 3, 4 + 0, 3 + 4)T = (3, 3, −4, 4, 7)T

(vii)

Now, we can find norms for this sum u + v1 = (|3| + |3| + |−4| + |4| + |7|) = 3 + 3 + 4 + 4 + 7 = 21 u + v2 =



|3|2 + |3|2 + |−4|2 + |4|2 + |7|2 =

√

9 + 9 + 16 + 16 + 49 =

u + v∞ = max(|3| + |3| + |−4| + |4| + |7|) = max(3, 3, 4, 4, 7) = 7

(viii) √

99 (ix) (x)

We see that u1 , u2 , u∞ , v1 , v2 , v∞ , u + v1 , u + v2 and u + v∞ all are positive and obviously satisfying scaling property of norm as well as triangular inequality [16] u + v1 = 21 ≤ 11 + 10 = 21 = u1 + v1 u + v2 =

√

99 ≤

√

31 +

√

30 = u2 + v2

u + v∞ = 7 ≤ 4 + 4 = 8 = u∞ + v∞

(xi) (xii) (xiii)

⎡

⎤ 14 2 Example, we have matrix A = ⎣ 0 3 −1 ⎦ then, by definition we can find 32 1 A1 = max(|1| + |0| + |3|, |4| + |3| + |2|, |2| + |−1| + |1|) = max(4, 9, 4) = 9 (i)  √  A2 = |1|2 + |4|2 + |2|2 + |0|2 + |3|2 + |−1|2 + |3|2 + |2|2 + |1|2 = 45 (ii) A∞ = max(|1| + |4| + |2|, |0| + |3| + |−1|, |3| + |2| + |1|) = max(7, 4, 6) = 7 (iii)

Introduction: Optimization and Metaheuristics Algorithms

25

9.17 Eigen Values and Eigen Vectors   The Eigen values λ of any square matrix A = aij n×n can be determined by AX = λX or (A − λI)X = 0

(8)

Any non-trivial solution requires |A − λI| = 0, which is known as characteristic equation of A. It gives a polynomial equation of degree n in the following form [15]: λn + an−1 λn + an−2 λn + an−3 λn . . . + a0 = 0

(9)

As a consequence Eq. (9) having n roots λ1 , λ2 , λ3 . . . λn which are known as Eigen values. For each Eigen value λ there is an Eigen vector X such that AX = λX. The direction of each vector can be determined uniquely. However, the length of the eigenvector is not unique because any non-zero multiple of X will also satisfy Eq. (8), and thus can be considered as an Eigen vector. For this reason, it is usually necessary to apply an additional condition by setting the length as unity, and subsequently the Eigen vector becomes a unit Eigen vector. The Eigen values of A−1 are the reciprocals of the Eigen values of A. And, the trace of square matrix A is the sum of all Eigen values of A which is equal to the sum of diagonal elements of A [17]. Trace(A) =

n 

λi =

n 

i=1

aii

(10)

i=1

In addition the product of Eigen values of A is equal to the determinant of A, i.e. Det(A) =

n 

λi

(11)

i=1

 Example, consider a square matrix A =

 01 . The Eigen values of A can be 10

determine by solving λ2 − trace(A)λ + Det(A) = 0 where trace(A) = 0 and Det(A) = −1. We have λ2 − 0, λ − 1 = 0 or λ = ±1. Thus the Eigen values are λ = 1 and λ = −1. An Eigen vector corresponding to the Eigen value λ = −1 is given by AX = λX or (A − λI)X = 0  where λ = −1 and X =

 x1 . x2

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P. Singh and S. K. Choudhary

      0 1 1 x1 1 = ∴ => x1 + x2 = 0. We get, X = . 0 1 1 x2 −1 Now, the Eigen vector corresponding to the Eigen value λ = 1 is the solution of 

(A − λI)X = 0 where  λ = 1.       0 1 −1 1 x1 = => x1 − x2 = 0. which gives X = . i.e. 0 1 1 −1 x2

9.18 Definiteness A square symmetric matrix A is said to be positive definite if all its Eigen values are strictly positive (λi > 0, i = 1, 2, . . . , n). Since AX = λX or XT AX = XT λX = λXT X

(12)

which leads to λ=

XT AX XT X

(12)

this means that XT AX > 0 if λ > 0. In fact, for any vector Y, the following relationship holds YT AY > 0

(13)

For y can be a unit vector; thus all the diagonal elements of A should be strictly positive as well. If the equal sign is included in the definition, we have semidefiniteness. That is, A is called positive semi-definite if XT AX ≥ 0, and negative semi-definite if XT AX ≤ 0 for all X. If all the Eigen values are non-negative or λi ≥ 0, then the matrix is called positive semi-definite. If all the Eigen values are non-positive or λ ≤ 0, then the matrix is called negative semi-definite. In general, an indefinite matrix can have both positive and negative Eigen values. Furthermore, the inverse of a positive definite matrix is also positive definite. For a linear system, in case when A is positive definite, then a matrix decomposition method is more efficient to solve such a system.

Introduction: Optimization and Metaheuristics Algorithms

27

9.19 Linear Functions A function T(x) is called linear if it satisfies 1. T(x + y) = T(x) + T(y) 2. T(αx) = αT(x) For any vector x and y, and any scalar α ∈ R.

9.20 Affine Functions A function F is called affine if there exists a linear function T: Rn → Rm and a vector constant b such that F = T(x) + b

(14)

In general, an affine function is a linear function with a translation, which can be written as a matrix form F = Ax + b

(15)

where A is an m × n matrix, and b is a column vector in Rn .

9.21 Quadratic Form Quadratic forms are widely used in convex optimization and engineering optimization. In general, a quadratic form is simply a homogeneous polynomial of degree 2 in several variables, that is to say, an expression like 4x2 + 3xy − 5y2 with each term of degree 2 (without linear or constant terms). It should be noted that not all arbitrary quadratic functions are in quadratic form like x2 + 5xy − 2y2 − y − 5 is not in binary quadratic form.   For the real symmetric matrix A = aij n×n and an n-vector X, the combination Q = XT AX is called a quadratic form. In the 2 × 2 case, binary form ax2 + hxy + by2 can be written as      a h/2 x h h 2 ax + xy + yx + by = x y h/2 b y 2 2 2

(16)

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P. Singh and S. K. Choudhary

9.22 Gradient of Multivariable Function The gradient of multivariable function f(x) is defined as  grad(f) = ∇f =

∂f ∂f ∂f ∂f , , ... ∂x1 ∂x2 ∂x3 ∂xn

T

T  = fx1 , fx2 , fx3 . . . fxn

(17)

where x ∈ R n .

9.23 Hessian Matrix The Hessian matrix of a function f(x) is given by ⎡

∂2f ∂x21

⎢ . H(x) = ∇ 2 f(x) = ⎢ ⎣ ..

∂2f ∂xn x1

... .. . ...

∂2f ∂x1 xn

⎤

.. ⎥ ⎥ . ⎦

(18)

∂2f ∂x2n

which is symmetric due to the fact that ∂x∂ i xf j = ∂x∂ j xf i . In case, when Hessian matrix H(x) = A is a constant matrix, the function f(x) is called a quadratic function, and can subsequently be written in the following generic form 2

f(x) =

2

1 T x Ax + kT x + c 2

(19)

where kT = (gardf)T is the constant vector and c is any real constant. We use the factor 1/2 in the expression is to avoid the appearance of a factor 2 everywhere in the derivatives, and this choice is purely for convenience.

9.24 Optimality of Multivariate Function For the case of stationary points, the maximum or minimum of a multivariate function f(x) requires ∇f(x) = 0 or

∂f = 0, (i = 1, 2, 3, . . . n) ∂xi

(20)

which leads to a stationary point x∗ . Whether the point x∗ gives maximum or minimum is determined by the definiteness of its Hessian matrix as follows:

Introduction: Optimization and Metaheuristics Algorithms Nature of H(x)

Type of Max/Min

Positive definite

Local minima

Negative definite

Local maxima

Indefinite

Saddle point

29

9.25 Convexity Understanding the nature of a function can be useful for finding an optimum value of the function. In optimization, non-linear problems are mostly classified according to the convexity of the function(s) under consideration. Geometrically, an object is convex if for any two points within the object, every point on the straight line segment joining them is also lie within the object. Examples are a solid spherical ball, cuboids, a pyramid and circular surface. Hollow objects are not convex.

9.26 Affine Set A set A is called an affine set if the set contains the line through any two distinct points x1 and x2 in the set A as shown in figure. That is, the whole line as a linear combination x = λx1 + (1 − λx2 ), λ ∈ R

(21)

is contained in A. All the affine functions form an affine set. For example, all the solutions to a linear system AX = b form an affine set (X |AX = b).

9.27 Convex Set Any set A ∈ R n in a real vector space is called a convex set if x = λx1 + (1 − λx2 ), for all x1 , x2 ∈ A and λ ∈ [0, 1]

(22)

Thus, an affine set is always convex, but the converse is not necessarily true.

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P. Singh and S. K. Choudhary

Fig. 9 (a) Convex (b) Non-convex

9.28 Convex Hull A convex hull is a set Aconvex formed by the convex combination x = λ1 x1 + λ2 x2 + λ3 x3 · · · + λp xp =

p 

λi xi , s.t.

i=1

p 

λi = 1

(23)

i=1

where λi ≥ 0, ∀i = 1, 2, 3, . . . p. A convex hull is also called convex envelope. It can be considered as the minimal set containing all the points (Fig. 9).

9.29 Convex Functions A function f (x) defined on a convex set A is called convex function if and only if it satisfies [18] f (ax + by) ≤ a f (x) + b f (y) ∀x, y ∈ A

(24)

a ≥ 0, b ≥ 0, a + b = 1

(25)

Also

Introduction: Optimization and Metaheuristics Algorithms

31

9.30 Algorithm Complexity For the sorting algorithm for a given number of n data entries, sorting these numbers into either descending or ascending order will take the computational time as a function of the problem size n. O(n), which means a linear complexity, and O n 2 has a quadratic complexity. That is, if n is doubled, then the time will double for linear complexity, but it will quadruple for quadratic complexity [18].

10 Exercise 1. 2.

3.

Find the minimum value of f(x) = x2 − x − 6 in [−∞, ∞]. Design a cylindrical water tank which uses the minimal materials and holds the largest volume of water. What is the relationship between the radius of the base and the height? Find the domain of each function: (i) (ii) (iii) (iv)

4. 5. 6. 7. 8. 9. 10. 11.

12. 13.

y y y y

1 = x+5 = 4x √ − 17 = x +9 = x 2 + 99

What is a function? What are the characteristics of a function? How is a function different from a relation? Why is it important to know which variable is the independent variable? Find the stationary points and inflection points of the following: (i) sin x (ii) 2 e−2x . Find the global maximum of sin x/x. Find the maximum of f(x) = x2 + p cos2 x with p > 0. How many minima exists? Will the number of minima depends on p? Test whether the following matrices are positive definite or not: ⎡ ⎤ ⎡ ⎤   171 1 0 −5 2 4 (i) (ii) a ⎣ 2 2 2 ⎦ (iii) ⎣ −1 1 0 ⎦ −1 3 503 −2 0 1 Test whether the following functions are convex or non-convex? 2 2 , y > 0. (i) f = ex + 2y2 (ii) f = 1 − x2 + y2 (iii) x y+y 2 Define the following terms: • • • • •

Bounded set Supremum and Infimum Smoothness Norm of a Vector Hessian Matrix

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P. Singh and S. K. Choudhary

11 Conclusions The present chapter introduces the important tools and techniques of metaheuristics and optimization widely used to solve real-world problems and their successive historical development. The content of this chapter has been designed in a systematic way so that learners get benefitted from a better understanding of the subject. This chapter provides a fundamental understanding of the subject like problem formulation, classification, limitation, and validation with simple examples, figures, diagrams, and mathematical prerequisites. It will also help learners for a better understanding of identification and optimization techniques selection to solve complex problems. Acknowledgements We (Dr. Padam Singh and Dr. Sushil Kumar Choudhary) would like to thank management of Galgotias College of Engineering and Technology, Greater Noida and Mahamaya College of Agricultural Engineering and Technology, Ambedkar Nagar for all cooperation and contribution. We are also thankfull to reviewers, editorial board, publication and marketing team for their valuable suggestions and for further improvement of quality and standard of the present work.

References 1. H.A. Eschenauer, G. Thierauf, Discretization Methods and Structural Optimization—Procedures and Applications (Springer, Berlin, 1989) 2. S. Smriti et al., Special issue on intelligent tools and techniques for signals, machines and automation. J. Intell. Fuzzy Syst. 35(5), 4895–4899 (2018). https://doi.org/10.3233/JIFS169773 3. History of Mathematics and Mathematicians. http://turnbull.dcs.st-and.ac.uk/history/Mathem aticians 4. History of Optimization. http://hse-econ.fi/kitti/opthist.html 5. X.S. Yang, Mathematical Foundations (Wiley, New York, 2018) 6. S. Dreyfus, Richard Bellman on the birth of dynamic programming. Oper. Res. 50(1), 48–51 (2002) 7. X. Yang, Engineering Optimization: An Introduction with Metaheuristic Applications (Wiley, New York, 2010) 8. R. Dorfman, The discovery of linear programming. Ann. Hist. Comput. 6(3), 283–295 (1984) 9. S. Das, A. Abraham, A. Konar, Metaheuristic Clustering (Springer, New York, USA, 2009) 10. A. Khatri et al., Optimal design of power transformer using genetic algorithm, in Proceedings of IEEE International Conference on Communication System’s Network Technologies (2012), pp. 830–833. https://doi.org/10.1109/csnt.2012.180 11. T. Mahto et al., Load frequency control of a solar-diesel based isolated hybrid power system by fractional order control using particle swarm optimization. J. Intell. Fuzzy Syst. 35(5), 5055–5061 (2018). https://doi.org/10.3233/JIFS-169789 12. H. Malik et al., PSO-NN-based hybrid model for long-term wind speed prediction: a study on 67 cities of India, in Applications of Artificial intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 319–327. https://doi.org/10.1007/ 978-981-13-1822-1_29

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13. T. Mahto et al., Fractional order control and simulation of wind-biomass isolated hybrid power system using particle swarm optimization, in Applications of Artificial intelligence Techniques in Engineering, Advances in intelligent Systems and Computing, vol. 698 (2018), pp. 277–287. https://doi.org/10.1007/978-981-13-1819-1_28 14. W. Sun, Y.X. Yuan, Optimization Theory and Methods (Springer, Science and Business Media LLC, 2006) 15. H.H. Sohrab, Basic Real Analysis (Springer Science & Business Media, 2011); D.B. Bridges, Computability (Springer, New York, 1994) 16. S.K. Mishra, S. Wang, K.K. Lai, V-Invex Functions and Vector Optimization (Springer, New York, USA, 2008) 17. X.S. Yang, Introduction to Computational Mathematics (World Scientific, 2008) 18. S.P. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, 2004)

Metaheuristics Paradigms for Renewable Energy Systems: Advances in Optimization Algorithms Ahmad Faiz Minai and Hasmat Malik

Abstract In recent days, many novel techniques and technologies are developing for power generation. Most of them are in its developed phase but its efficiency and reliability are low. Some of them have no running cost but its installation is costly. Some others are not cost effective and its cost to benefit ratio is poor. Because of all these reasons optimization techniques are required to expand the productivity, reliability and decrease the expense by optimal utilization of the resources and controlling methods. This chapter is mainly deals with basic and important metaheuristics optimization techniques used for power generation through renewable energy resources. Metaheuristic optimization approaches like Particle-Swarm Optimization (PSO), Differential-Evolution (DE), Tabu-Search (TS), Simulation-Annealing (SA), Genetic-Algorithm (GA), Artificial-Bee Colony (ABC), Ant-Colony Optimization (ACO), Cuckoo-Search (CS), and Biogeography-Based Optimization (BBO) are applicable on power generation using renewable energy resources. Some optimization techniques are good for solar PV system like PSO, ACO, ABC, DE etc., and some other optimization techniques like GA, CS, TS, BBO etc. for Battery storage using renewable hybrid system and design wind farm layouts. Applications of various metaheuristics optimization approaches for different renewable energy and hybrid systems are present in this chapter. Keywords Optimization · Metaheuristic · Renewable energy · Design · Battery · Solar-PV · Wind farm

A. F. Minai (B) Department of Electrical Engineering, Integral University, Lucknow, UP, India e-mail: [email protected] H. Malik Division of ICE, NSIT Delhi, New Delhi, India e-mail: [email protected] BEARS, University Town, NUS Campus, Singapore, Singapore © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_2

35

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A. F. Minai and H. Malik

1 Introduction For the performance enhancement and efficient intelligent system, optimization techniques have been used from last many years. These techniques have been developed to utilize the system parameters and resources. The response of these intelligent systems is controlled through the different algorithms. Some of the metaheuristics optimization approaches applicable for power generation renewable energy resources are shown in Fig. 1. The main challenges with the renewable sources are efficiency, installation, reliability, availability, cost effectiveness etc. These algorithms are used to control the system operation for maximum utilization [1]. Renewable energy systems have following problems associated with them:

Fig. 1 Metaheuristics paradigms in renewable energy system

Metaheuristics Paradigms for Renewable Energy Systems: Advances …

37

• Availability of resource for solar, so a good backup storage system is needed when the main source is not available or in a cloudy weather. • Constant wind speed is required for power generation through wind energy with proper wind speed i.e. in between 5 and 25 m/s with adequate space for wind farm. • Proper battery charging with automatic turn-off/on is required when primary source is unavailable as a backup. • Automatic switch over system is needed for efficient hybrid renewable energy systems etc. So an attempt is made in this chapter to overcome all these problems using metaheuristics optimization approaches with algorithms which are shown for the better understanding of the reader. This chapter is in eleven significant parts. First part manages the Particle-Swarm Optimization (PSO) strategy utilizing for Maximum point tracking (MPPT) under fractional shading condition for efficient sun powered PV system. Standard pseudocodes are mentioned [2] with the correct control activity of MPPT utilizing PSO algorithm [3]. Then second and third section is about Artificial Bee Colony (ABC) based efficient MPPT and same problem is also discussed using Differential Evolution (DE) with their Pseudocodes [2] and algorithm [3]. Next segment is Ant Colony Optimization based efficient charging/discharging of battery for SPV hybrid grid connected system. It is very important part for many type of power generation systems, because battery storage is needed for approx. All types of stand-alone system. Pseudocodes [2] and algorithm [4] of ACO for specifically mentioned application is also presented. Fifth section of this chapter is Simulated Annealing based Battery Storage System applied for Renewable Energy Resources. This is also a very important part like previous section because of similar application. But in this pseudocodes [5] and algorithm [6] of SA streamlining method is utilized to take care of the issue of battery charging and discharging. In sixth part utilization of Genetic Algorithm is discussed for Optimal Design of Renewable Energy System with its pseudocodes [2] and algorithm [7]. In seventh section pseudocodes [8] and algorithm [8] of Cuckoo search is discussed for Design and Simulation of Hybrid System. Segment eight is Wind farm design utilizing Biogeography-Based Optimization. In this part, issue of the sizing of wind farm is discussed with its pseudocodes [9] and algorithm [10]. In section Nine Pseudocodes [2] and algorithm [11] of Tabu Search based Energy mix capacity factor optimization is discussed. Key features of applied metaheuristics optimization techniques for power generation through renewable energy systems are discussed in last section.

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A. F. Minai and H. Malik

2 Metaheuristics Paradigms 2.1 Metaheuristic Paradigms for MPPT Analysis 2.1.1

Particle Swarm Optimization Based MPPT for Efficient Solar PV System

Brief Details of Particle Swarm Optimization (PSO) PSO is a stochastic method of optimization [12–14], which imitates the “swarming” conduct of creatures, for example, flying creatures or creepy crawlies. Fundamentally, PSO builds up a populace of particles that move in the hunt space through participation or cooperation of individual particles. PSO is fundamentally a type of coordinated change. Any particle j is considered in two sections: particle’s area Aj and its speed S j . At any second, the situation of a molecule j is registered dependent on its earlier position Ai and a rectification term relative with its speed ε · S j [2]. In its turn, the speed doled out to every molecule is figured utilizing four segments: (a) The impact of the past estimation of speed S j ; (b) The impact of the best solution for particle j, A Pj ; (c) The impact of the best neighbourhood solution so far for sources of particle j, A Lj and (d) The impact of the best worldwide solution so far for the whole swarm, AG . These segments are contemplated utilizing three weighting factors, indicated by a, b and c. The reader may refer [2] to understand the pseudo code of PSO.

PSO Implementation for MPPT From that point onward, it is utilized in numerous issues enhancements like building plans, labourers planning for businesses and computational insight [15]. The working standard of PSO is motivated by the nature’s conduct of swarm, for example, fish tutoring and birds hailing. In PSO, the single directions of particles search the whole pursuit space of target work a specific way by modifying their locations. [3] The transformation of particles includes two significant segments: stochastic and deterministic. Every particle transforms haphazardly from its situation to a worldwide situation in the inquiry space of enhancement work. If the particle location ‘A’ and speed ‘S’ are refreshed by utilizing Eqs. 1 and 2.

Metaheuristics Paradigms for Renewable Energy Systems: Advances …

39

    Skt+1 = W Skt + λv1 lbest,k − Atk + μv2 pbest,k − Atk

(1)

At+1 = Atk + St+1 k k

(2)

where Skt+1 and At+1 are the refreshed kth particle speed and location at interim t + k 1. The factors v1 and v2 are the irregular vectors, λ and μ are the requirements of learning. The best location of particle k is lbest,k whereas the acquired particles best location is pbest,k [3]. The PSO strategy is utilized in MPPT following irregular shading on account of its alluring highlights are high tracking speed and across MPP it has less consistent oscillations. In addition, this method gives good precision in following through MPP at various insolation and climatic behaviour [3]. Furthermore, this procedure needs a single-directional vector for following through MPP. [16], the deterministic PSO MPPT strategy is used to manage the pattern of the duty cycle of chopper. Here, various duty cycles (locations) are arbitrarily started to all particles and SPV source is selected as an objective function (OF). In the main cycle, all locations of the particles or duty cycles are balanced by using Eqs. 3 and 4. The particle speed is constrained by changing the two particles’ location. This is achieved by using the learning requirements [3].     = W ckt + λv1 cbest,k − ctk + μv2 Cbest,k − ctk ct+1 k

(3)

ct+1 = ctk + ct+1 k k

(4)

In above expression, ‘W ’ represents the weight of inertia and change in duty cycle (c) is c. d k is the particle k’s optimized ‘d’ and the optimal duty value C best,k in the wake of figuring all particles when the PV power E pvmax is achieved. The primary preferred position of the PSO strategy is great convergence velocity to acquire the estimation of duty cycle for accomplishing large converter yield voltage however the speed of the convergence depends on the underlying situation of particles. The reader may refer [3] to understand the demonstration of flowchart and algorithm.

2.1.2

Artificial Bee Colony Based MPPT for Efficient Solar PV System

Brief Details of Artificial Bee Colony (ABC) Optimization Artificial Bee Colony (ABC) algorithm is a hunt technique that impersonates the mating procedure in Bee Colony (BC), utilizing determination (selection), hybrid (crossover) and change (mutation) [2].

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In a BC a queen honey bee, automatons (drones) and labours are exists. The sovereign honey bee is had experience in egg laying; rambles (drones) are fathers of the BC and mate with the sovereign honey bee. During the mating flight the sovereign mates with automatons (drones) to frame a hereditary pool. After the hereditary pool was loaded up with chromosomes, hereditary administrators are applied. During the hybrid stage, rambles are arbitrarily chosen from the present populace and mate with the sovereign utilizing a Simulated Annealing-type acknowledgment rule dependent on the distinction between the function of fitness of the chosen ramble (drone) and the sovereign (queen) [2]. The last phase of the developmental procedure comprises in generating the broods produced during the subsequent stage, and making nextgen of GB agonizes, in view of transformation (mutation) administrators. Another generation of GC rambles (drone) is made dependent on a particular measure. The reader may refer [2] to understand the demonstration of pseudo code.

ABC Implementation for MPPT ABC calculation is motivated by the scavenging conduct of bees. The bees live is as a state. The bumble bee can speak with one and another as pheromone (synthetic trade) and waggle movement. On the off chance that any bee discovers the source of food and it gets back home some food and it shares source area of the food by waggle movement. The waggling movement changes starting with one gathering of animal varieties then onto the next gathering of species and a few bees utilized the directional moving and qualities to share the heading and area of food source. Along these lines, the enhancement method of ABC is used for the discontinuous and additional critical thinking use. The primary segments associated with bee rummage choice is a food source, the correspondence of bees is reliant on the food source’s nature. The likelihood utilized sharing of their data is legitimately relative to the benefit of food source. Along these lines, the bees discover the food source [3]. At the underlying stage, all the bees examined the nearby MPP’s and worldwide MPP. From that point forward, it pushes ahead to refresh the honey bee’s positions. Here, boost converter’s duty cycle is considered as the source of the food and the PV power is viewed as a function of fitness. In this strategy, the quantity of iterations needed to choose the ideal shortest paths from food source to home is less. Therefore, the convergence rate of ABC is diminished [3]. The bees are haphazardly instated with various duty cycles (positions of the food source) in the hunt area by using Eq. 5. Di = Cmin +

(k − 1) ∗ (Cmax − Cmin ) Np − 1

(5)

Metaheuristics Paradigms for Renewable Energy Systems: Advances …

41

In above expression, bees’ position is represented by Di and k showed as various honey bees (k = 1, 2, 3… Nd ). Here, the most extreme duty (C max ) and least Duty (C min ) values are chosen as 10–15%. The assessment of PV power for every duty cycle significantly relies upon the simulink model and the amount of nectar (source of food). The bees are named utilized honey bees and non-utilized bees (spectators). The utilized bees and spectators are isolated into two stages to follow worldwide MPP. In the principal stage, Eq. 6 is utilized to refresh the utilized bees’ situations inside its neighbour bee positions and in the subsequent stage, the amount of reactor is high then the spectator is drawn nearer to the utilized bees. The spectator locations are refreshed by utilizing Eq. 7. Di (n + 1) = Di (n) + α(xi (n) − xk (n)) Di (n + 1) = Di (n) + α

(Cmax − Cmin ) Nd 2

−1

(6) (7)

In above expression, ‘n’ represents the no. of iterations and α is the irregular no. which is a limitation to acquire the ideal solution of multidirectional issue. The reader may refer [3] to understand the demonstration of flowchart and algorithm.

2.1.3

Differential Evolution Based MPPT for Efficient Solar PV System

Brief Details of Differential Evolution (DE) Optimization Differential Evolution (DE) was grown essentially as another EA [17]. In contrast to other transformative calculations, DE change progressive approximations of arrangements or people dependent on the contrasts between arbitrarily chosen potential arrangements. This methodology utilizes in a roundabout way data about the hunt space geography in the area of the present arrangement. At the point when applicant arrangements are picked in a wide zone, changes will have huge amplitudes. Alternately, if applicant arrangements are picked in a thin region, changes will be of little significance. For every generation, every single current person that depicts potential arrangements are considered as reference for which the DE are applied [2]. In this manner, for a reference singular Y i , two distinct people Y r1 and Y r2 , other than Y i , are haphazardly chosen and a number juggling change is applied to Y i dependent on the contrast somewhere in the range of Y r1 and Y r2 , to deliver a freak Y i  . At that point a number juggling hybrid, in view of the contrast among current and transformed arrangements, is applied to produce the new estimation Y i  . Y i  will supplant the reference arrangement and the best one whenever its function of fitness is improved. The reader may refer [2] to understand the demonstration of DE’s pseudo code.

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DE Implementation for MPPT The DE method is anything but difficult to execute on the grounds that it requires not many administrators to acquire an ideal arrangement [18]. When all is said in done, there are not many populaces of particles and emphases required to take care of the commotion issues. In each cycle, the contrast in mid of the two bodies is assessed to change each other. Here the two-dimensional vectors are utilized in DE for each emphasis or generation with a populace (pn ; n = 1, 2, 3, 4 … Qp ) [3]. The quantity of bodies (Qp ) required in each cycle is a similar which is portrayed. In the main emphasis, the primary objective vector is chosen to look through the whole hunt space. In the wake of getting the main emphasis results, there are three asymmetric vectors chosen and a transformation factor ‘x’ is used to instate the weight an incentive to the two vectors and the distinct weight between the two vectors is cascaded to the third vector to get the benefactor vector [3] which is outlined in Eq. 8. Bv = Pn1 + x ∗ (Pn2 − Pn3 )

(8)

In above expression, the scope of transformation ‘x’ is in the middle of ‘0’ and ‘1’. Along these lines, in light of the change esteem, the benefactor vector covers the whole populace and it is cascaded with the irregular vector to produce another preliminary vector (pv ) and this procedure is called hybrid. The state of the preliminary vector is expressed in Eq. 9. After consummation of hybrid, a determination is completed between the preliminary and arbitrary vectors [3].  pv =

Bv ; 0 < d < 1 Pn < 0

(9)

Equation 9 is utilized to acquire the ideal arrangement which is utilized for the following iteration. This procedure proceeds until accomplishing the ideal arrangement [3]. The half shaded PV array comprises of more than one MPP. The dc-dc converter is interfaced in the middle of the PV framework and electrical burden. Boost converter’s duty cycle is refreshed by utilizing the MPPT applied through DE optimization to work the MPP of PV closer to the worldwide MPP. Here, duty cycle (C i ) is the objective function. At the underlying stage, distinctive obligation esteems are haphazardly started to every one of particle’s location (Li , i = 1, 2, 3 … n) to look through the whole search of the PV curve. After introduction, the most noteworthy maximum Power of particle’s location is considered as Pmax and Cmax is considered its duty cycle [3]. The reader may refer [3] to understand the demonstration of flowchart and algorithm.

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2.2 Metaheuristic Paradigms for Battery Storage 2.2.1

Ant Colony Optimization Based Efficient Battery Charging/Discharging Operation in Grid Connected Hybrid Solar PV System

Brief Details of Ant Colony Optimization (ACO) The exemplary Ant Colony Optimization (ACO) calculation is roused from the characteristic conduct of ants, which can discover their direction utilizing pheromone trails. Ants travel between two fixed focuses X and Y on the briefest path, deserting them trail of pheromone that imprint picked ways. After the main ant arrives at the Y point, it returns in X after its own pheromone trail, and multiplying the pheromone layer thickness. Further, more ants will probabilistically want to pick a way with higher pheromone thickness, and bit by bit an expanding number of ants will follow a similar way. For every ant, a rundown might be characterized to remember its route [2]. The ants transfer between segments Ai and Aj with likelihood Qij , characterized dependent on the pheromone thickness between parts, the perceivability between the two segments and two weighting factors. After every ant finishes its way, the pheromone thickness for each segment is refreshed dependent on the function of fitness. The reader may refer [2] to understand the demonstration of ACO’s pseudo code.

ACO Implementation for Battery Storage System A strategy which is reproduced and dependent on the biological conduct of ants, with the component of associated and adjustment is termed as ACO. The algorithm of ACO is originated through the genuine ant colony settlement and foraging conduct of ants [19]. Anyway ants are visually impaired creatures in this way circuitous correspondence is conceivable by synthetic pheromone preliminaries, which enable them to follow the optimized path from origin to goal. The ACO consists positive input trademark, which engage fast disclosure of optimal solution [4]. For efficient battery charging/discharging conditions in grid connected hybrid solar PV system are: Battery in storage mode: Power(ACO SPV Grid) ≤ Power(SPV Grid) Optimization will refreshed data: Power(ACO SPV Grid) > Power(SPV Grid) In above conditions, Power utilized for charging the battery through ACO based Solar Grid is Power(ACO SPV Grid) and power utilized for charging the battery through ordinary SPV Grid is Power(SPV Grid).

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The likelihood of route of ant differs on every cycle which follows heuristic inclination. The change likelihood is determined in the accompanying condition. y

[λixj (t)] − [φi j (t)] likj = Ai y x f =1 [λi j (t)][φi j (t)]

(10)

In above expression, λi j is attractive coefficient and φi j is pheromone coefficient and x ≥ 0, y ≥ 1

(11)

Now, λi j (t) is pheromone intensity of cycle on (i, j) at iteration t. The cycle intensity can be refreshed by λij (t + 1) = ρλij (t) + λikj

(12)

In above expression, ρ is a coefficient, (1 − ρ) is coefficient of pheromone’s vaporization and λikj =

m 

ikj

k=1

where ikj is the pheromone intensity laid on edge (i, j) by the kth ant at this iteration; emphasize by  ikj

=

D , PK

i f (i, j) is in the position o f ant k 0, other wise

(13)

In above expression, D is a non-variable quantity and PK is k ant’s function of fitness [4]. The reader may refer [4] to further understand the demonstration of flowchart and algorithm.

2.2.2

Simulated Annealing Based Battery Storage System Applied for Renewable Energy Resources

Brief Details of Simulated Annealing (SA) Optimization Studies on Simulated Annealing (SA) was motivated by measurable thermodynamics, where the connection between the probabilities of two expresses X and

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Y, with Power PX and PY , at a typical temperature T, proposes that states with higher energies are less likely in thermodynamic frameworks [5]. In this manner, if the framework is in express X, with vitality PX , another state Y of lower vitality (PY < PX ) is consistently conceivable. On the other hand, a state B of higher vitality (PY > PX ) won’t be prohibited, however it will be considered with likelihood exp(−(PY − PX )/T ) [5]. Utilization of Metropolis calculation in search issues is known as SA and depends on the chance of moving in the inquiry space towards states with less fortunate estimations of the function of fitness. Beginning from a temperature T and an underlying estimation An , with a function of fitness (An ), a perturbation is applied to An to produce another guess An+1 , with Fitness (An+1 ). On the off chance that An+1 is a superior solution, at that point An , for example Fitness (An+1 ) > Fitness (An ), the new estimate will alter the previous one. Something else, when Fitness (An+1 ) < Fitness (An ), the new estimation will be considered with likelihood pi = exp(−[Fitness(An ) − Fitness(An+1 )]/T ) [5]. The above advances are rehashed for a given number of times for a steady estimation of temperature, at that point temperature is refreshed by diminishing its worth, and the iterative procedure proceeds until a halting standard is met. The reader may refer [5] to understand the demonstration of SA’s pseudo code.

SA Implementation for Battery Storage System The annealing simulation as a methodology that diminishes a reduction of a component of enormous number of factors to the factual equilibration mechanics (annealing) of the scientifically identical counterfeit multi nuclear framework [6]. SA deciphers normal cooling as a normal lessening in the likelihood of achieving more terrible solutions as it investigate the space of solution. Tolerating more awful solutions is an essential property of metaheuristic in light of the fact that it takes into account an increasingly broad quest for the ideal arrangement (battery charging). The reader may refer [6] to understand the demonstration of SA based battery storage system using flowchart and algorithm. Although it is not a sufficient solution, because SA is not capable for ideal solution alone. Some hybridization is needed with SA to make a system near to perfect, and this is also applicable for battery storage system and in a general renewable energy system where SA is utilized.

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2.3 Metaheuristic Paradigms for Design the Renewable System 2.3.1

Genetic Algorithm Based Design of Optimal Renewable Energy System

Brief Details of Genetic Algorithm (GA) GAs are search methodologies that depend on explicit instruments of hereditary qualities and common choice, utilizing three essential administrators: choice, crossover (hybrid) and mutation (change) [20]. For every age, choice is utilized to pick parent, in light of their function of fitness. In the wake of choosing a couple of parent chromosomes, they enter the hybrid stage to create two off-springs. Hybridization is helpful to make new samples that acquire great qualities from the parents [2]. New samples will be modified by little scope changes in the qualities (genes), applying transformation (mutation) formulation. Changes guarantee the presentation of “novelty” in the hereditary material. In the wake of finishing the posterity populace, this will supplant the guardians from the past generations and the choicehybridization-change procedure will be continued for samples to come. To prevent from losing the best arrangement because of the stochastic nature of the inquiry an uncommon substitution method called “elitism” that makes a duplicate of the best individual from the present populace and move it unaltered in the new sample to come. The reader may refer [2] to understand the demonstration of GA’s pseudo code.

GA Implementation for Optimal Renewable Energy System Design Main used components [7, 21] in the genetic algorithm are as follows: (1) Coding Scheme, (2) Populace, (3) Regular determination, (4) Determination, (5) Mating, (6) Transformation, (7) New samples. The reader may refer [7] to understand the demonstration of flowchart and algorithm. Some design factors are discussed as following: • Operational Methodology The operational methodology utilized in this sustainable power source framework was portrayed as underneath: – When the total requested load was lesser than the delivered yield inexhaustible generation frameworks, the rest of the vitality would be transferred into the battery. – When the battery limit was full (and there was as yet some energy available) charging, it is proceeded to the Fuel-Cell (FC). – When the FC had fully charge, the surplus power would be released into dump load.

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– When the requested load was more prominent than the energy that could be provided by the sustainable generation, the deficiency would be provided by the battery. – When the requested load stays more prominent, in spite of being provided by the battery, the power deficiency would be satisfied by the FC [7]. • Total Loss Factor (TLF) The Total Loss Factor will contrast with one another sum the vitality created to the load necessities in a single year. Determined TLF utilizing (14). TLF =

X 1  G(i) X i=1 B(i)

(14)

H was the all-time steps (8760), G(i) was the full burden that couldn’t be met and B(i) was the complete burden requested per time step [7]. • Oblige A few limitations which used to upgrade objective function in sustainable generation frameworks are as per the following [7]: (1) The perceived Power framework 

E t,t ≥ Eload,t − Yt



(15)

(2) Index of system reliability E[T L F] ≤ T L Fmax

(16)

(3) Number of units and equipment n wt , n pv , n bat , n el , n tank , n f c ≥ 0

(17)

Bbatmin ≤ Bbat (t) ≤ Bbatmax

(18)

(4) Boundary of batteries

(5) Limitation of hydrogen tank Ltankmax ≤ Ltank (t) ≤ Ltankmax

(19)

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• Monetary Modelling Based on Total Current Cost (TCC) The financial part was determined utilizing the Total Current Cost (TCC) comprising of expense of the venture (substitution cost, working cost, upkeep cost and capital cost). This expense would be determined by the estimation of cash as of now. This strategy can be portrayed by (20): TCC = VCi + SCi · Pi + WCi · YIPW(ir , R)

(20)

Where VCi is the venture cost ($/unit). SCi is the substitution cost ($/unit). While WCi is working and upkeep costs ($/unit-year). Substitution cost SCi will be the product of Pi and A change factor an incentive for cash at a specific time to the present time on the grounds that the estimation of the expense was determined by the estimation of cash as of now. While the working and support costs will be increased by YIPW (Yearly Instalment Present Worth) that is utilized to change over yearly expense of working and keeping up in reversing mode [7]. The optimized framework comprised of sunlight based cells, wind turbines and batteries (electrolyzer, hydrogen tank and FC). Multiple times simulation was performed for the same. The task time was accepted for a long time [21]. The batteries were expected full when the framework built up. Ideal structure of sustainable multi power source frameworks comprising of sunlight based cells, wind turbines, batteries and an energy unit was recreated utilizing hereditary calculations (GA). The outcomes achieved could be clarified and calculation is exhibited in [7]. The reader may refer [7] to understand the flowcharts and algorithm also.

2.3.2

Cuckoo Search Based Design and Simulation of Hybrid System

Brief Details of Cuckoo Search (CS) Optimization There are three admired standards utilized for Cuckoo Search (CS) have been utilized, these guidelines are [8]: 1. Every cuckoo lays every egg in turn and places it in a temporarily picked home. 2. The best home with best eggs will continue to the nextgen. 3. The no. of possible homes is fixed and the host bird found the egg laid by cuckoo with a likelihood of L e , where L e ∈ [0, 1]. On the other hand, if the host birds are found the cuckoo’s eggs, the host fledgling can relinquish its home or pulverize cuckoos’ eggs or for this situation another home will be produced with likelihood L e . In straightforward structure, the last supposition can be assumed by the portion L e and the n homes are supplanted by new homes (with new arbitrary arrangements). In a basic structure the accompanying straightforward portrayal is utilized, each egg speaks to a solution and a cuckoo egg speaks to novel

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solution [22]. In this segment, a straightforward methodology is utilized where each home has just a solitary egg. The reader may refer [8] to understand the demonstration of CS’s pseudo code.

CS Implementation for Hybrid System Two basic crucial traits of these progressed metaheuristic algorithms are increment (Exploitation) and upgrade (examination). If the models don’t supporting each other, all the power calculations of the comparative tests are evaluated and are taken care of in the wellbeing bunch [8]. By surveying the bunch, the model with most critical force is picked as the best model. From that point on each and every other model are constrained to go towards this best regard. The movement sizes are controlled by playing out the Levy trip as portrayed by conditions [8]. X in+1 = X in + φ ⊕ levy(β)

(21)

  D = φq X bn − x j ⊕ le(β)

(22)

In above expression, X it is the old solution X in+1 is the modified new solution using CS algorithm. With the help of CS algorithm maximum power point tracking (MPPT) can be achieved in solar PV system. This technique allows adapting best possible product of voltage and current and repeats till best output power is achieved. The reader may refer [8, 23] to understand the demonstration of hybrid system and MPP tracking using flowchart and algorithm.

2.4 Biogeography-Based Optimization for Wind Farm Layout 2.4.1

Brief Details of Biogeography-Based Optimization (BBO)

Biogeography is the study of the geological conveyance of natural living beings over reality. Which shows that the species lavishness of an island can be anticipated as far as such factors as territory zone, migration rate, and elimination rate. Further an Algorithm is developed for Biogeography based optimization (BBO), where a solution vector is closely resembling an environment (habitat), the solution segments are similar to a lot of suitability index variables (SIVs), and the arrangement wellness is comparable to the species lavishness or habitat suitability index (HSI) of the natural surroundings [24]. Vital to the calculation is the harmony hypothesis of island

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biogeography, which demonstrates that large value of HSI natural surroundings have a large species displacement (emigration) rate and small HSI living spaces have a large species migration (immigration) rate. For instance, in a linear problem of animal group’s lavishness [9] a habitat Qi ’s movement (immigration) rate α i and displacement (emigration) rate β i are determined dependent on its wellness (fitness) i as follows:  n max − n i (23) αi = M n max − n min  n i − n min βi = D , (24) n max − n min In above expressions, nmax is the greatest and nmin is the least fitness functions, among the populace and M is the most extreme conceivable movement rate and D is the displacement rate. In any case, there are other nonlinear numerical models of biogeography that can be utilized for ascertaining the relocation rates. Relocation is utilized to change natural surroundings by blending specialities inside the populace. BBO likewise has a transformation administrator for changing SIV inside a living space itself and consequently presumably expanding assorted variety of the populace. For every natural surroundings Qi , a species check likelihood L i figured from α i and β i shows the probability that the living space was relied upon from the earlier to exist as an option for the issue. In this specific circumstance, high HSI living spaces and exceptionally low HSI environments are both similarly unlikely, and medium HSI living spaces are moderately plausible. The change pace of natural surroundings Qi is contrarily corresponding to its probability [9]:  Li , φi = φmax 1 − L max

(25)

In above expression φ max is a function of control and L max is the greatest living space likelihood in the populace. A roulette wheel technique may be utilized for problem solution, the complexity of time is C(t). It isn’t hard to see that the unpredictability of every emphasis of the calculation is C(t 2 D + tC(n)), where C(n) is the complexity of time registering the function of fitness n [9]. Algorithm depicts the general structure of BBO for a D-dimensional worldwide numerical optimization issue and rand is a capacity that creates an arbitrary worth consistently appropriated in [0, 1]. The reader may refer [9] to understand the demonstration of BBO’s pseudo code.

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BBO Implementation for Wind Farm Layout

BBO has just been set up as one of the most encouraging non-discrete optimal solver. This segment presents moderately an ongoing methodology Biogeographybased Optimization (BBO) to explaining Wind farm layout optimization problem (WFLOP). The fundamental target is to examine the appropriateness of the BBO calculation in calculating WFLOP. Now attempt is made to discover the ideal areas of turbines blades of the Wind farms and most extreme conceivable no. of wind turbine blades with radii 1000 (m), 750 (m) and 500 (m) in the wind farms [10]. In this segment, BBO based WFLOP is considered to understand. The principle goal of WFLOP is to boost the vitality creation alongside the decrease of wake impact challenge. The presentation of BBO technique was assessed on two wind informational collections (wind informational collection (I) with steady c and wind informational collection (II) with variable c).This paper additionally suggests the most extreme conceivable number of wind turbines which can be efficiently set in a wind farm. Numerical trials presume that BBO can locate the better ideal situation of wind turbines in the wind farms with no wake loss than earlier examinations. Prior systems can fit most extreme 3 turbines in a ranch of sweep 500 (m) while BBO can fit greatest 7 turbines in a similar homestead efficiently. So also, BBO outflanks for different sizes of wind farms. Hence BBO is suggested as a productive solver for WFLOP [10]. The reader may refer [10] to understand the demonstration of flowchart and algorithm.

2.5 Tabu Search Based Hybrid Energy Capacity Factor Optimization 2.5.1

Brief Details of Tabu Search (TS) Optimization

Taboo Search (TS) is a pursuit methodology that abstains from coming back to solutions previously visited by keeping up a list of Tabu, which stores progressive approximations. Since the list of Tabu is limited long, eventually, after various advances, a few arrangements can be returned to. Adding another answer for a total Tabu list is finished by expelling the most established one from the list, based on a FIFO standard (First In-First Out). New approximations can be created in various manners. The pseudocode introduced in [2] uses the accompanying strategy: at each stage a given number of new approximations are produced in the area of the present arrangement X, however considering as practical just the ones which are not in the list of Tabu. Among the new approximations the best one is picked to supplant the present arrangement, being additionally presented in [2]. The reader may refer [2] to understand the demonstration of its pseudo code.

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2.5.2

TS Implementation for Hybrid Energy Capacity Factor

The multisource framework comprises of various power innovations associated with hybrid energy sources. These innovations are portrayed by their adaptation by their Capacity Factor (CF), Weight and expense (E i ). ‘i’ distinguishes the current advancements form in the trend (1 ≤ i ≤ N). The innovations expenses are generalised. For every one there are different renditions. Providers are available to recommend it. Accessibilities are utilized here to mean CF, they express the genuine yearly power to be delivered by a given power framework partitioned by the power that will be created in a single year if the framework completes in its full evaluated power the entire time. The exhibition measures the limit of advances. Repetition of advances permits accessibility increment, however builds the expense. The goal is to structure the power framework in a less expense, subject to a multi-position accessibility constraint [11]. Given a framework structure characterized as a vector V of measurement N(V = (V i )), where V i is various chosen advances of form i. The complete expense is determined by adding all the expenses of the chosen components. The total expense (objective function) is expressed by: E(V ) =

N 

Vi E i

(26)

i=1

The issue can be defined as follows: limit the total cost of framework E(V ) for example, its total accessibility S(V ) meets or surpasses the necessary accessibility S 0 . That is, minimi ze E(V ) =

N 

Vi E i

i=1

Subject to S(V ) ≥ S0 .

(27)

Vi ∈ {0, 1, . . . , Max(Vi )} ∀i, 1 ≤ i ≤ N

(28)

Equation 27 presents the accessibility imperatives while Eq. 28 determines that, the quantity of chosen advancements of form i is a whole number which can’t be greater than a presumed most extreme no. Max(V i ) accessible in the trend [11]. The framework accessibility S t (V ) for a expressed set at moment t is given by:   St (V ) = L r B(t) ≥ B.0

(29)

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In above expression, B(t) is the power framework limit and B.0 is the necessary required limit. It is expected that the innovation states are commonly s-autonomous, and that there presents a consistent state dissemination of likelihood of Multi-State Power System (MSPS).    After sufficient opportunity, the likelihood L B(t) ≥ B.0 gets consistent. In the consistent state the circulation of states likelihood is given by: L m = lim [L r (B(t) = Bm )]

(30)

t→∞

While the multi-state fixed accessibility is detailed by:

. 

lm .

Bm ≥B.0

It is expected that the interest is spoken to as a unit-wise total burden curve. An activity period T is considered that is separated into K interims. Every interim has span and a necessary demand stage (k = 1 … K). For this situation, the MSPS accessibility work is: S(V ) =  K

. K  

1

K =1

Tk

lm

(31)

K =1 Bk ≥Bk0

For taking care of the combinatorial streamlining issue detailed in Eqs. 26–28, it is important to have a powerful and quick strategy to assess S(V ). For this assessment, the all-inclusive second creating capacity (ISCC) is utilized. S(V ) is regularly identified with the loss of burden likelihood (LOBL) record in power building. LOBL = 1 − A(V ) is the likelihood that the framework can’t fulfil a given demand electrical burden [11]. Now characterize the location of an arrangement V as: position(V ) =

N  

Vp



(32)

p=1

An inquiry subspace of location ‘b’, indicated by Sb is characterized as the arrangement of equal structures (arrangements) which have a similar location, equivalent to ‘b’. It can be understand from the  above terminologies that its lower limit of ‘b’ and   upper limit is expressed by 1 and Np=1 Max V p respectively. The reader may refer [11] to understand more about the algorithm.

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3 Key Features of Metaheuristics Optimization Techniques (MOT) Applied for Renewable Energy System In this section some relevant literature is reported for the application of metaheuristics used for renewable energy systems. Findings proved that which technique is good for which type of system. Merits, demerits and scope are provided with proper references. If reader wanted to explore more on any issue, it is easy to track and learn about the metaheuristics for the specific application [25] (Table 1). Table 1 Summary key-features of MOT applied in renewable energy system MOT Reference

Key features

PSO

Faia et al. [16]

• Close estimation to the deterministic outcomes • Its arrangement utilizing the best mix asset situation is superior to the ordinary working arrangement • Robust streamlining considering the forecasting mistake in PV creation and household utilization can likewise be had to break down the effect of figures blunders in the power bill

Mohammed et al. [26]

• Can accomplish the ideal arrangement in two-fold speed • Has been tackled to accomplish different target capacities and giving adaptability in the choosing of framework segments • The solution of the issues of the ideal estimation, energy management and system expansion planning for any type of multisource energy system is valid throughout the world

Renuka et al. [15]

• Utilized to streamline the parameters for expanding the inexhaustible coordination with less stable signal • Dynamic higher-request model of the lattice has been fused in the examination. Also, the Eigen esteem is registered for distinguishing the most impacting states that influences the greatest entrance of the breeze and sunlight based force in the force framework • The advancement is performed for improving the damping proportions and consequently the small signal security. It is likewise investigated that the proposed multistage advancement procedure expanded the sustainable power source penetration by fulfilling all the framework necessities • Efficiently enhanced the small signal dependability by tuning the control factors

Manas [27]

• MPPT is more impressive than P&O at various insolation and temperature • More reasonable for achieving maximum power from PV framework (continued)

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Table 1 (continued) MOT Reference

GA

Key features

Gavrilas [2]

• High following pace and less steady state motions across MPP • High precision in MPP following at various sun orientation and temperature conditions

Mao [21]

• Effective in estimate sun based power dependent on natural parameters like, insolation, direction of sun, temperature, and so forth

Abbas [28]

• The vulnerabilities related with the sustainable power source framework are dealt with by an opportunity obliged model, and sorted

Utami [7]

• Optimal financially savvy sustainable multisource power system comprising of sun based cells, wind turbines, batteries and an energy component can be recreated and structured using different software

Ahangar et al. [29]

• One of the major devices for any progression is having a power grid fit for continuing those associated with it. Also, with microgrid innovation, executed in a productive way

Gavrilas [2]

• Solar power as a function of fitness and obligation esteems haphazardly started to all specialists to follow MPP with less solving complexity

ACO Suhane and Rangnekar [19] • Gives least expense of vitality, better an incentive as contrast with different procedures for Wind-PV based Hybrid Energy Sources (HES) advancement • Optimal estimating measures results affirm pre-distinction for thought about HES Dong et al. [30]

• Although such heuristic calculations could give the worldwide ideal answer for NP issues, the precision couldn’t be ensured totally inside a sensible measure of time constantly

Jun-man and Yi [31]

• Effectively handle combinatorial improvement issues • Produces more encouraging outcomes than PSO and HS • For the test framework, PV/wind multisource system is more cost effective than PV alone or wind alone frameworks for a long time life length • Efficient device for ideal measuring of multisource system

Gavrilas [2]

• ACO MPPT utilized for PV voltage and current control application to move the ideal voltage from the PV framework to resistive burden (continued)

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Table 1 (continued) MOT Reference

SA

CS

Key features

Kumar and Pal [4]

• The battery charging is done similarly quickly and furthermore the power required to charge the battery is diminished

Luckehe et al. [6]

• Able to enhance the arrangements, yet the decision of suitable parameters for neighbourhood separation and temperature is significant • Not able to resolve deadlock conditions • Not adequate for the ideal solver alone

Katsigiannis et al. [32]

• Presents quicker assembly in the area of ideal solutions • More productive in finding the best arrangement in a given neighbourhood • Hybridization is required, since SA alone isn’t successful

Mosaad et al. [33]

• Capable of following the MPP productively • No variances

Mareli and Twala [8]

• Performs well when it contrasted with other evolutionary algorithm based existing power planning approaches financially

Ullah et al. [34]

• Can limit the expended energy cost by moving some heap to low-request load hours, without upsetting its activity. Along these lines, the weight on utility is decreased as PAR and amplified client comfort

Baba et al. [23]

• MPP tracker is extremely straightforward on the grounds that lone the estimation of the insolation and the temperature are required. In correlation with other traditional MPP trackers, for example, PSO, and Fuzzy trackers, the proposed MPP trackers are progressively robust and exact

Mohamed et al. [35]

• Optimal structure and size choice for HRES for least vitality cost and most noteworthy unwavering quality inside the imperative • The arrangement is worldwide and the outcomes got are not from the snare in any nearby minima • The best site out of the accessible destinations and the best WT for the site can resolved • One of the noteworthy focal points of the proposed procedure is the utilizing of smart grid guideline in dealing with the load to be increasingly related with the accessible generation from sustainable power sources • Emphasizes the structure and improvement precision

ABC Mohamed et al. [36]

• PV module power is amplified and the existence cycle cost (LCC) is limited • More proficient than GA in getting the ideal expense of the PV framework to cover a load at any area (continued)

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Table 1 (continued) MOT Reference

Key features

Baba et al. [23]

• Solving financial load dispatch with smooth and non-smooth cost work by assessing different framework requirements • Problem detailing with wind energy vitality to exhibit and asses the monetary advantages of incorporation power plant into power systems • Capable of accomplishing worldwide solutions, computationally proficient and has stable dynamic convergence attributes

Wang et al. [37]

• Good for taking care of the recognized issues with parameters of complex nonlinear PV based models

Geleta and Manshahia [38]

• Superior than different techniques in framework cost limiting

Paliwal et al. [39]

• Results in better execution of Battery Storage (BS), the SOC phenomenon is smoother maintaining a strategic distance from quick charging, profound releasing, and as often as possible on/off of BS. It improves the BS life cycles • BS activity is advanced and making the framework progressively dependable, reasonable, and eco-friendly • Robust method, which characterizes its materialness in a real-time framework

Yıldırım and Aydo˘gdu [40] • To streamline the sun based air warmers • Design parameters, for example, channel profundity and activity parameters, for example, air mass stream rate can be assessed for ideal thermo water powered proficiency TS

DE

Redouane et al. [11]

• To streamline the repetition allocation issue of equal multi-state power frameworks

Hana et al. [41]

• Can leap out of the neighbourhood minima and grow the pursuit territory thus to settle the nearby assembly of the inclination strategy • Improve forecast accuracy just as the convergence rate

Amaran et al. [42]

• For productive household issue of energy management • Synchronizes the vitality utilization in fulfilling the maximal power limitation and the client comfort stays at a decent level • However, it is hard to tune a TS procedure for all circumstances

Lampinen and Storn [43]

• Finds the best outcomes in regards to the nature of the acquired arrangement • Hybridizations required so as to locate the most proper calculation that conveys a superior answer for the issue

Lorente et al. [44]

• Provides the best outcomes to its harmony among investigation and misuse • Rand transformation plans beat the DE plans

Gavrilas [2]

• The DE MPPT procedure union speed is less however the MPP following precision is high (continued)

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Table 1 (continued) MOT Reference

Key features

BBO Li et al. [45]

• • • •

Mostly utilized for process observing More vigorous and stable than others Separates free parts more precisely than others Detects faults more effectively than others

Ahangar et al. [29]

• BBO can locate the better ideal position of wind turbines in the wind farm with no wake loss than earlier examinations • Outperforms for different sizes of wind farms • Efficient solver for WFLOP

Raviprabakaran [46]

• Produces the prevalent quality outcomes when contrasted and direct pursuit procedure • Decreases the additional costs by ideal scheduling

Iftikhar et al. [24]

• Perform well in PAR minimization and cost decrease • Can be used for cost minimization and buyer to be prosumer

Soares et al. [47]

• Has a decent variety saving system to discover ideal solution • Can give a superior solution than other strategies, for example, SA, PSO and GA techniques • Capable of giving the ideal solution for optimization issue in a micro grid

4 Conclusion Metaheuristic approaches are useful to make the system proficient and savvy. These optimization techniques become more helpful when it is used with the renewable energy resources, which are free and available in a large quantity. For power generation, this combination of renewable energy and metaheuristics will provide new platform to develop Renewable energy systems which will be used to generate electricity efficiently. With the help of above available literature, readers can easily opt metaheuristic techniques applied for renewable systems on which work can be done further.

References 1. K. Krystel, C. Villar, Metaheuristic algorithms applied to bioenergy supply chain problems: theory, review, challenges, and future. Energies 7, 7640–7672 (2014). https://doi.org/10.3390/ en7117640, ISSN 1996-1073 2. M. Gavrilas, Heuristic and metaheuristic optimization techniques with application to power systems, in Selected Topics in Mathematical Methods and Computational Techniques in Electrical Engineering (2010), pp. 95–103. ISSN: 1792-5967, ISBN: 978-960-474-238-7 3. C.H.B. Hussaian, C. Rani, Evolutionary and metaphor-metaheuristic MPPT techniques for enhancing the operation of solar PV under partial shading condition. Int. J. Innov. Technol.

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Tackling Power Quality Issues Using Metaheuristics Peeyush Kala, Puneet Joshi, Medha Joshi, Sanjay Agarwal, and Lokesh K. Yadav

Abstract Power electronics has become an essential part of modern power system over the last few decades. Power electronic converters and controllers contribute an important role in power transmission and distribution. The rising penetration of intermittent renewable energy systems into the grid further prompted not only the bulk use of power electronics converters in power system but also rise in several power quality issues. Despite their numerous advantages, power electronic converters are responsible for the generation of harmonics in the power system. The other sources of harmonics in power system are non-linear loads such as arc furnaces; variable frequency drives (VFDs), computers, rectifiers, magnetising in-rush current of transformers, switched mode power supply (SMPS), interference with telecom systems, welding, and uninterruptible power supply (UPS) etc. The switching operation of power converter devices and harmonic generated by the nonlinear load in power system raises the issues of power quality such as voltage distortion, poor power factor, voltage sag and swells, flicker, and voltage imbalance. The various conventional methods to tackle these issues related to power quality are to utilize the active and passive filter, flexible alternating current transmission (FACTs), Dynamic voltage P. Kala Electrical Engineering Department, Women Institute of Technology, Sudhowala, Dehradun, Uttarakhand 248007, India e-mail: [email protected] P. Joshi (B) · S. Agarwal · L. K. Yadav Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh 224122, India e-mail: [email protected] S. Agarwal e-mail: [email protected] L. K. Yadav e-mail: [email protected] M. Joshi EED SLSET Group of Institutions, Kichha, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_3

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restorer (DVR), unified power quality controller (UPQC), PWM controllers, multilevel inverters (MLIs) in distribution network of power system. Researchers have used the classical control techniques for the switching control of these devices. In the recent years, the evolutionary algorithms (EAs) and metaheuristic algorithms have proven their capability to solve many electrical engineering problems. Some of these applications include selective harmonic elimination (SHE) problem in MLIs, design of active and passive filters, development of control algorithms for FACTs devices and controllers. In this chapter, various applications of metaheuristics in design of filters, FACTs controllers, static compensators, and other power quality controllers have been exhaustively discussed. The merits and demerits of EAs over classical methods used in power quality improvement are presented and elaborated. The detailed comparative analysis of various EAs and metaheuristics used in various power quality applications is presented. Application of metaheuristics in harmonic elimination is shown in simulation results. The contribution of metaheuristics in tackling power quality issues is also well discussed in this study. Keywords Evolutionary algorithms · Power quality · Harmonics · Metaheuristics

1 Introduction The efficient generation, transmission, and distribution of electric power is not alone sufficient for the proper utilization of electricity. The major challenge in modern power system is to maintain and assess good quality of power so that electric power can be utilized in efficient manner. It is found that the distortion in electric power is much severe at the utilization level [1]. The term power quality includes continuity of service, voltage regulation, harmonics, harmonic filters, voltages/currents transient, and harmonic content in the output voltage/current waveforms. There are some issues related to power quality problems since the beginning of electric power. In Sect. 1.1, some of the power quality terms are defined [2, 3]. Section 1.2 discuss the various power quality (PQ) issues and standards used in power system. In Sect. 1.3, various statistics about the effects of PQ on various loads and frequencies of PQ issues have been prsented. The various metaheuristic techniques are being applied in solving PQ issues. The classification of these techniques is discussed in Sect. 2. A detailed discussion with analysis and simulation results are shown in Sect. 3 which includes applications of various metaheuristics in PQ applications.

1.1 Power Quality Terminologies and Their Definitions Flicker—Luminance of a light source generally fluctuates with time. The unsteady visual sensation generated by the light source is known as flicker.

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Fluctuation—It is a series of deviation in voltage from its nominal magnitude over the cycle. Transient—A sudden variation in frequency in the voltage or current while in steadystate condition. It can be impulsive or oscillatory. Harmonics—According to fourier analysis “any periodic non sinusoidal waveform can be represented by the sum of sinusoids which have frequency in integer multiple of fundamental frequency”. Such sinusoids are known as harmonics. Interharmonic—These are sinusoids of frequency component that is non-integer multiple of the fundamental frequency. For e.g., for a 50 Hz supply system, interharmonics are of frequencies such as 75, 125, 175 Hz etc. Total demand distortion (TDD)—It is defined as “the total RMS harmonic current distortion, in percent of the maximum demand load current (15 or 30 min demand)”. Voltage regulation—It denotes the pu change in the RMS value of load voltage with respect to full load voltage. Swell—It is defined as “increase in the RMS voltage or current for durations from half cycle to 1 min”. Undervoltage—It denotes to an event when measured voltage value is found less than the nominal voltage for a time interval greater than 1 min. The typical values of undervoltage are 0.8–0.9 pu. Frequency deviation—It is defined as “a rise or dip in the power frequency from the nominal value of frequency”. The deviation in frequency can occur for duration from few cycles to hours. Point of common coupling (PCC)—It corresponds to the point where the consumer loads interface with electric utility. Sag—It is defined as “a decrease in RMS voltage or current for duration of half cycle to 3000 cycles”. The typical value of sag lies in range of 0.1–0.9 pu. Nominal voltage—A nominal voltage of a system is defined as a reference magnitude of voltage which conveniently designates its voltage class.

1.2 Problems in Power Quality Most of the electrical loads used today show the nonlinear behavior. These nonlinear loads draw harmonic currents from the AC mains. The electrical power system components such as generators, transformers, reactors, and power converters etc. behave as nonlinear loads. The causes of harmonics generation in these components are mainly attributed to their geometry, distribution of winding, asymmetry in air-gap, saturation of core, and switching operation [4]. The nonlinear loads

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such as computers, battery chargers, variable speed drives, elevators etc. draw a non-sinusoidal current from the AC mains which deteriorate the quality of power. The issues in power quality are as follows. • • • • • • • • • • • •

Increased losses due to increase in RMS value of the input current. Losses due to low power factor operation. Increased heating in elements of distribution network. De-rating of machines. At point of common coupling, the distortion in voltage is quite large. Effect on communication lines due to interference. Faulty operation of protection systems. Overloading of capacitor bank. Resonance phenomena. Excessive neutral current. Increased harmonics at neutral. Poor efficiency of system.

For the minimization of these power quality issues, monitoring of power quality is essential. The further reasons for monitoring of power quality are as follows: • • • •

To diagnose power quality issues in supply and consumer load. To select the right power quality monitors for data collection. To compensate the active and reactive power at PCC. To evaluate the performance of equipment.

There are some international organizations like IEEE and international electrotechnical committee (IEC) which have published PQ standards. These standards are followed over all of the world to mitigate the deterioration of quality of power. Table 1 mentions these PQ standards. Table 1 Description of PQ Standards Organization and years

Name of standard

Description of standard

Domain of application

IEEE, 1992

519

Harmonic control

power system applications

IEEE, 1995

1159

PQ monitoring

Distribution networks

IEEE, 1999

1100

Input supply and grounding requirement for electronic equipment

Distribution system

IEC, 2002

61000-2-2

Low voltage supply applications

Distribution network

IEC, 2018

61000-3-2

Limit for harmonic current Power system emission

IEC, 2015

61000-4-30

Testing and measurement methods

Power system

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1.3 Statistics of Power Quality This sub-section presents some statistics about the power quality issues. Figure 1 shows the distribution of PQ issues in study performed in USA. Sag and swells in voltage causes a lot of distortion in power qualtiy. It is followed by distortion due to harmonic and grounding issue as shown in figure. Other main problems in PQ are switching of capacitor banks, overload, interference, and use of power conditioning equipments [5]. In Fig. 2, PQ issues distribution is shown in graph for countries of Europe. The interruption of power and transients in voltage hold the major share in PQ issues followed by voltage dip, harmonics and miscellaneous issues [6]. In India, some application such as traction, cement plants, casting plants, chemical industries are found major cause of harmonic pollution. Figure 3 demonstrate the problems faced in operation of various equipments owing to PQ issues in percentage of annual occurrence of failure during operation. It can

Sag & swell Harmonic distoron Grounding issue Capacitor switching Overload EMI power condioning Miscellaneous Fig. 1 Problems faced in power quality in USA

Dip in voltage interupon Harmonics Voltage transients Miscellaneous

Fig. 2 Power quality problems in Europe

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80 70 60 50 40 30 20 10 0

Fig. 3 Percentage of equipments affected due to PQ issues

be seen that electronic equipments suffers the most occurrence of failure followed by converters, motors and telecom & networks. From the above discussion, it is clear that PQ issues are need to be addressed. Recently, several researchers have proposed the use of metaheuristic algorithms in various engineering problems. Over the years, metaheuristics have also found their applications in solving PQ issues. Some of these metaheuristics are being discussed in Sect. 2.

2 Metaheuristic Algorithms The heuristic algorithms are used to find the good solutions to a particular problem. These algorithms do not put emphasis on whether the achieved solution is correct or optimal. Therefore, metaheuristic algorithms are envisioned to enhance the capabilities of heuristic algorithms by utilising one or more heuristic methods using a higher-level strategy [7]. The metaheuristic algorithm can provide optimal solution for many optimisation problems [8]. The merits of metaheuristics are as follows: • These algorithms perform the exploration of the search space to reach the optimal solutions. • These are usually non-deterministic and have stochastic behaviour. • In the exploitation step, they avoid trapping in local minima in the search space. • These can be used in any optimization problem i.e. they are not problem-specific.

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Metaheuristics

Evolutionary Algorithms

Swarm Intelligence

Nature Inspired Algorithms

GA

PSO

Firefly

IA

BA

CSA

DE

ACO

Bat

HS

LSA

FPA

ICA

BFA

Fig. 4 Classification of metaheuristic algorithms

The metaheuristics are classified into three categories in general as shown in Fig. 4 [9–14]. Some of the evolutionary type algorithms are genetic algorithm (GA), immune algorithm (IA), differential evolution (DE), harmony search (HS), incremental colonial algorithm (ICA). Some techniques are categorized as PSO, bee algorithm (BA), ant colony optimization (ACO), lightworm search algorithm (LSA) and bacterial foraging algorithm (BFA). Examples of nature inspired algorithms are firefly, cuckoo search algorithm (CSA), bat algorithm, flower pollination algorithm. In Sect. 3, the applications of abovementioned metaheuristics is being presented.

3 Applications of Metaheuristics in Power Quality Improvement 3.1 Selective Harmonic Elimination (SHE) in Inverters Over the past few years, Multilevel inverters (MLIs) have find their applications in many industrial applications including grid connected and off-grid renewable energy systems. Nowadays, MLIs are replacing the conventional pulse width modulation (PWM) inverters owing to their numerous advantages over PWM inverters. The merits of MLIs are as follows: 1. Low THD output voltage waveform 2. Low switching losses 3. Low dv/dt stress on switches

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Less requirement of filter Better harmonic profile of staircase voltage waveform Lower common mode voltage It can work in fault condition with lower output voltage level Ease of operation with renewable energy systems Equal power sharing among the switches.

There are several modulation schemes proposed for MLIs. Among these methods, multicarrier PWM and fundamental switching scheme are quite popular. In order to minimize the switching losses in MLIs, low frequency switching methods are now becoming popular. The selective harmonic elimination (SHE) technique is a low switching frequency method. It serves two objective simulaneouly. First objective is to obtain the desired fundamental component of voltage. Second objective of SHE technique is to eliminate the dominant non triplen odd order harmonics. The SHE problem for 11-level inverter is expressed as in Eqs. (1)–(5). cos(β1 ) + cos(β2 ) + cos(β3 ) + cos(β4 ) + cos(β5 ) = 5M

(1)

cos(5β1 ) + cos(5β2 ) + cos(5β3 ) + cos(5β4 ) + cos(5β5 ) = 0

(2)

cos(7β1 ) + cos(7β2 ) + cos(7β3 ) + cos(7β4 ) + cos(7β5 ) = 0

(3)

cos(11β1 ) + cos(11β2 ) + cos(11β3 ) + cos(11β4 ) + cos(11β5 ) = 0

(4)

cos(13β1 ) + cos(13β2 ) + cos(13β3 ) + cos(13β4 ) + cos(13β5 ) = 0

(5)

M=

V1d π

4.s.V

; where 0 < M < 1

(6)

where, s symbolizes the count of sources and V1d is the desired magnitude of fundamental voltage. Equations (1)–(6) are subjected to switching angle constraint i.e. all the angles lies between 0 to π /2 rad. It is a difficult and complex task to find the optimal solution which can satisfy these Eqs. (1)–(6). The optimum solution set enables the reduction of harmful low order harmonics in output voltage of MLI. Solving the SHE problem requires complex techniques such as algebraic method, methods of resultant theory, iterative methods and optimization techniques etc. Out of these methods metaheuristics based optimization techniques are becoming popular due to their several merits over conventional methods. Genetic algorithm (GA), variants of particle swarm optimization (PSO) [15], colonial competitive algorithm (CCA), Bee algorithm (BA), Gravitational Search Algorithm (GSA), firefly algorithm etc. are the metaheuristic techniques that were used by several researchers in solving SHE problem. Here, GA is employed for solving SHE problem for 11-L inverter. Figure 5 shows the percent of harmonics present in output of 11-level inverter. It can be that

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Fig. 5 Content of harmonics in percentage of fundamental voltage versus mi

for modulation indices 0.44–0.86 the dominant harmonics have been eliminated. The THD in line voltage is also quite low for this modulation index range. Using the switching angles computed for modulation index 0.78, 11-level inverter simulation model was simulated in MATLAB/Simulink. For instance, a simulation model of 5-level inverter is shown in Fig. 6. It consists of 8 switches and two dc sources. 11level stepped voltage waveform is shown in Fig. 7. The harmonic spectrum of output is shown in Fig. 8. It is clearly shown that 5th, 7th, 11th, and 13th order harmonics were eliminated from output voltage of 11-level MLI. The switching angles were computed as β1 = 7.9; β2 = 19.4°; β3 = 29.8°; β4 = 47.8° ; β5 = 63.3o .

3.2 State Estimation of Harmonic Distortion The measurement of current and voltage harmonics of each order at each bus is monitored using power quality measurement meters. The cost of these measurement meters is quite high. From the point of economy, few points for measurements are generally chosen so that fewer power quality meters are required. The use of evolutionary algorithms can provide the solution to this harmonic distortion state estimation (HDSE) problem. Arruda et al. [16] proposed an evolutionary algorithm based strategy to estimate harmonic distortions in the non monitored buses. The voltage value of harmonics represent the state of system for buses. In this method, first a population of 100 agents is generated. Mutation rate is chosen to be 5 operations per individual. Self adaptation parameter was chosen 2. Recombination was also performed to generate new population by mixing two original agents. It also helps to avoid premature convergence to local minima. THD for kth bus is calculated using Eq. (7).

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Fig. 6 Simulation model of 5-level CHB MLI Fig. 7 11-level inverter waveform

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Fig. 8 Harmonic analysis of 11-level inverter

 ∞ THDk =

i=2

Vik

2



V1k

(7)

The performance of agents in population is assessed through an objective function. It determines the degree of closeness to calculated distortion in voltage harmonic from the measured distortion in harmonic. In the evolution process, the best solution agents survive. The IEEE 14-bus test network was taken for study to estimate lower order harmonic voltages. Estimated errors were found less than 1%.

3.3 Use of ACO in Dynamic Voltage Restorer (DVR) Tuning of PI controller is a time consuming and tedious task under varying operating conditions. To achieve the best performance of PI controller, optimal tuning of parameters is required. Benachaiba et al. [17] presented the ant colony optimization (ACO) based Dynamic Voltage Restorer (DVR) in which tuning of parameters of controller was done by ACO. In the simulation results it was shown that the ACO based optimized PI controller took the little response time as compared to the PI controller. The ants drop pheromone on the ground when the food is found. Ants find the shortest path to food by communicating with each other using the pheromone trail. As the time lapse, the most of the ants follow the shortest path to the route. Optimum values of kp and ki were obtained using ACO algorithm. Overshoot decreases, The number of agents chosen were 8. The ACO provided a faster response of PI controller for different voltage disturbances as compared to response of classical PI controller. The simulation results in [15] showed that applied metaheuristic approach effectively found the optimal parameters of controller which helped in refining the quality of power.

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3.4 Improvement in Voltage Profile of Distribution Networks The quality of power and voltage is largely affected in distribution system due to large load variation and nature of nonlinear load. Therefore, the essential requirement in the distribution systems is to maintain good quality of voltage and power. The compensation of reactive power is commonly used for maintaining the power quality. The power capacitors are installed in distribution networks for compensation of reactive power. However, for economic operation their optimal sizing and placement is required. In Ovidiu Ivanov et al. [18], the crossover type GA was applied. GA found the optimum placing of capacitors with their optimum size in distribution system. In the study, it was found that uniform crossover GA gave the best performance.

3.5 Power Factor Correction and Harmonic Distortion Minimization The induction of nonlinear loads in distribution network often lead to issue of poor power factor (PF). It not only causes increase in line losses, and heating of power cables but also causes disturbance in operation of connected equipment. The improvement over PF requires use of PF correction devices. Ahmet Karaarslan [19] proposed a bee colony optimization (BCO) technique in converter of Sheppard–Taylor type. This control strategy is proposed to reduce the harmonics in current input to the converter by computing the switching instants for switches. The BCO algorithm is inspired by natural food searching habit of bees. The steps of BCO are as follows: Bees are categorized as scout bees, on-looker bees and employed bees. Employed bees carry the information regarding location of food source and amount of juice in it. This information is transferred to on-looker bees through the dance. The amount of juice in a food is determined through the time of dance. The function of scout bees is to explore the search space while on-looker bees and employed bees exploit the food source. Steps in BCO are as follows: 1. 2. 3. 4. 5. 6. 7.

Population of ‘n’ scout bees is randomly generated. Evaluation of fitness of population. Selection of best ‘m’ sites selected out of n visited sites. Patch size calculation in neighborhood. Recruitment of more bees for patches visited by elite ‘e’ bees. Selection of the most fit bee among group. Check whether stopping criteria reached. If yes, then stop. Else continue the search with ‘n-m’ remaining bees. 8. Generate next generation scout bees and jump to step ‘2’. Using BCO, duty cycles for switches were computed for 50% of a period and saved in lookup table. The converter operates in continuous conduction manner. Benefits of proposed scheme are as follows:

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1. It helps in achieving high PF and lower value of THD in input current. 2. There is no need of DSP as this scheme can be implemented in a microprocessor at large frequency. 3. Size of filter required is small as ripple in the input current is very little. Also, the design of the input filter is very simple. 4. This scheme provides lower stress on switch. 5. The conduction loss is also minimized. 6. Low values of ripples in output voltage during steady state. 7. Low transients in overshoot and undershoot. 8. Easy implementation of algorithm in control scheme.

3.6 Use of Metaheuristics in Regulation of Grid Voltage In distribution system, it is necessary to regulate grid-voltage with a quick response. In voltage-sensitive loads, it is desirable to get the fast voltage regulation. The causes of voltage disturbances in a grid are generally initiated by dynamic characteristics of consumer loads, intermittent sources of generation, voltage transients due to switching of capacitors and parallel connected loads etc. The duration of such voltage disturbances is very small and its nature is stochastic. To achieve fast voltage regulation, Mohamed and El saadany [20] presented a PSO based voltage control scheme for the distributed generation. The proposed voltage controller is capable of minimizing the voltage disturbances in capacitor-switching. Tuning the parameters of voltage controller requires a lot of time and quite difficult task also. For this purpose, the problem of controller tuning was expressed as a constrained optimization problem. The PSO technique is inspired by fish schooling, movement of swarms and flying pattern of birds. The proposed methodology allows fast voltage regulation, mitigation of harmonics, voltage flicker, sag, and swell in grid voltage. A simple methodology of tuning has been implemented in the study. The experimental results validate that proposed grid-voltage regulation technique enhances the reliability of voltage.

3.7 Control of Volt/VAr in Smart Grid In smart grids, the quality of voltage is maintained through voltage and reactive power (VAr) control. The optimization technique is applied in VAr problem nowadays due to various advantages of metaheuristics. However, the large computational time to reach the optimal solution is a major drawback of metaheuristics. This is due to the large search space. Thiago Saúde Medeiros et al. [21] presents a comparative study between different metaheuristics techniques applied to the Volt/VAr control. ACO, GA and memetic algorithm have been compared. Steps of GA are as follows:

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1. Initialize random population. The position of on load tap changer (OLTC), voltage regulator (VR), and switching capacitors are defined by the chromosomes. 2. Evaluate the fitness of each chromosome. In this process, fitness of chromosomes is evaluated. 3. Selection of chromosomes on the basis of fitness values. 4. Crossover is performed in the selected individuals. A point is chosen in random manner in parent chromosomes and values placed in individual vectors are exchanged between them. 5. Mutation is also performed to bring diversity in the population. 6. Step 2–6 are performed for new population until stopping criteria is met. Memetic algorithm is inspired by the evolution of individuals in martial arts. In this algorithm, knowledge is passed to next generation through masters. The important moves and motion sequences are called memes. It is similar to GA except of having an extra step called ‘local search’. In this step, the best neighbor is searched during exploration near an agent. Their fitness is compared. If the fitness of neighboring agent is found better than that of agent, then neighbor replaces the agent. In memetic algorithm, competition and cooperation steps are performed which are similar to the selection and crossover steps performed in the GA respectively. ACO is a promising metaheuristic technique which works on food foraging behaviour of ants. The ants release pheromone on route as they move from colony to source of food. The amount of pheromone is updated at each iteration. The longer paths become lesser attractive as compared to shorter path. This is due to the fact that the concentration of pheromone is lower in longer paths while the concentration of pheromone is higher in the shorter path. After certain iterations, the shortest path traced by ant represents the solution. These methods were implemented on a bus feeder (13.8 kV rating) and 6 shunt capacitors. Memetic and ACO algorithm converge to optimal solution quickly. ACO method performed better than other counterparts as it approaches the reference voltage level throughout the day.

3.8 Use of GA in Enhancement of Voltage Stability Voltage instability is a big problem in power systems over the last two decades. In the industrial applications, maintaining the stability of voltage profile is the key criteria to be met in industry. FACTS technology is very beneficial for the improvement in the voltage stability, reduction in cost and transmission losses. FACTs controllers are employed in maintaining the electrical quantities such as current, phase angle, impedance, and voltage values near to reference values. They also helps in damping out the oscillations. Thyristor switched capacitor (TSC) and static VAR compensator (SVC) etc. are placed in optimal location which help to maintain the desired bus voltage with improved voltage stability. V. A. Preethi et al. [22] presented an application of GA to locate the FACTS devices optimally. Objective function (USD/kVAR) for TSC is represented by Eq. (8).

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CTCSC = 0.0015s2 − 0.713s + 153.75

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(8)

where s represents the operational values of FACTs. The cost function consists of terms with maximization of stability index, minimization of losses and cost. The objective of implementation of GA is finding the optimal operating range and location of FACTS controllers in distribution network. For this purpose, IEEE-14 bus system is loaded with 140% of rated load. Simulation was performed for three different scenarios. In first case, FACTs devices were not installed. In second and third scenario, FACTs devices were installed. In case 1, voltage stability was found maximum but losses were found very high. In scenario 2 and 3, losses and cost of operation were found minimum. It can be concluded that the installing FACTs devices at optimum places can provide the benefits such as improvement of voltage stability, saving in economic cost and reduction in losses.

3.9 Harmonic Reduction in Line Current Drawn by AC/DC Converters Using Evolutionary Method AC to DC converters have find their usage in many industrial applications for example regulated power supply circuits, charging of batteries, and dc drives. Converters with thyristor control are used in HVDC and energy storage with superconductor material etc. applications. However, the disadvantage of using these converters in power system is that it yield poor PF and large harmonics injection in supply. To mitigate these problems, PWM scheme is used in the converters. [23] applied genetic algorithm (GA) for the reduction of line current in a buck converter. The aim of GA was solving for optimal switching instants for which harmonics are minimized [24]. Steps taken are as follows: 1. Generate the population of initial solution having firing angles within 0 to π/2. 2. Evaluation of fitness function. F=

10 (1 + |er |)(1 + I H )

(9)

where, er = V0 − V0∗ and IH- is defined as IH = I3 + I5 + I7 + ···+ In . 3. On the basis of best fitness values, selection process is done. By using elitism, the best agents are selected for the next generation. On the remaining agent the crossover and mutation is implimented. 4. Now replace the old generation with new population and jump to step 2. The GA is a very simple technique in coding and finding global optimum is often guaranteed in many cases [25]. Population size was chosen six and stopping criteria was 500 iterations. From the hardware and simulation results, it is deduced that GA efficiently reduce line current harmonics. Also, it provided excellent voltage regulation at output.

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3.10 Use of Metaheuristics in Finding Optimal Location of Power Quality Monitors (PQMs) In the power system, PQMs are installed to assess the power quality parameters for ensuring the high quality in power delivery. Since, cost of such PQMs is very high, it is not economically viable to install such equipments on each bus of power system. In this context, researchers have opted the use of metaheuristic techniques. These methods are used for determining optimal number of PQMs along with their location in distribution system. Ling Ai Wong et al. [26] presented a lightning search algorithm (LSA) for finding the optimal number of PQMs in grid. Steps are as follows: 1. 2. 3. 4. 5.

Generation of initial population Initialization of all quantum bits individuals Fitness function evaluation Updation in best fitness and find the best location for installation of PQM Check whether stopping criteria is met or not. If no, then go to step 3 and continue the loop. If yes, then store the optimum PQM location.

This technique was implemented on 118-bus IEEE system and comparative studies have been performed with other quantum algorithms. The results exhibit that proposed LSA performs better in obtaining the optimal positions of PQM for installation in distribution systems as compared to other algorithms.

4 Conclusion In addition to above-discussed works, [27] applied PSO based SHE technique for removal of detrimental harmonics present in output of MLI. In [28], GA was proposed for finding optimum location of capacitors in distribution network for reduction of harmonic distortion as per IEEE/IEC standards. [29] presented a comparative analysis between metaheuritic methods used in power electronics. In [30], CSA technique is used for optimizing the size of superconducting magnets in dispatching optimum reactive power. Jumani et al. [31] comprehensively reviewed the metaheuristics for enhancement of power quality of AC microgrid. In [32], heuristics were applied for improving the voltage security. Mahdad and Kamel [33] implemented the new algorithm salp swarm for planning reactive power in Algerian distribution system. In [34], chaotic whale optimization was applied to improve the transient stability of 39-bus system. Alomoush et al. [35] employed the Fractal search methodology to minimize the operational and fuel cost for economic dispatch of power in grid. Table 2 summarizes the contribution of various metaheuristics in many applications of power electronics. In this chapter, the application of metaheuristic algorithms in tackling power quality issues were discussed.. Simulations were performed in MATLAB/Simulink

Domain of publication

IEEE

IEEE

IEEE

IEEE

References and Years

[15] (2010)

[16] (2010)

[19] (2013)

[20] (2008)

PSO

Bee colony optimization (BCO)

Evolutionary Strategy (ES)

PSO

MHA technique used

Canada

Turkey

Brazil

Iran

Country of research implementation

Table 2 Contribution of metaheuristics in power electronics Advantages

Disadvantages

Research based on

1. Chattering problem 2. Degradation in transient response

1. Low cost 1. Performed on low processor, power converter 2. Not compared lower with other conduction loss 2. Compatible metaheuristics with lower frequencies

1. Lesser 1. Nonlinear simulation time characteristics 2. Error below 1% with frequency and ability to decoupling case solve complex was not studied problems

1. Mitigation of 1. Quick voltage flicker, sag, swell regulation of 2. Effective tuning grid of controller 2. Higher voltage reliability

1. Achievement of unity PF over wide range of duty cycles 2. Low THD value

1. Estimation of harmonic distortion

(continued)

Real-time simulator with MATLAB/Simulink

Simulation/experimental setup (sheppard-Taylor converter)

IEEE 14-Bus test network

1. Harmonics 5th, 1. Best results in 1. Comparison with Simulation and 7th 11th and 13th SHE with other experiment setup for minimized in unequal metaheuristics 11-level inverter 11-level inverter sources in MLI was not done 2. Fundamental 2. Easy to 2. Offline voltage was implement in implementation maximized software and hardware

Research outcome

Tackling Power Quality Issues Using Metaheuristics 79

Domain of publication

IEEE

IET

IEEE

IEEE

References and Years

[23] (2002)

[24] (2014)

[25] (2010)

[26] (2018)

Table 2 (continued)

Lightning search algorithm (LSA)

Differential Evolution (DE)

GA

GA

MHA technique used

Malaysia

Romania

India

India

Country of research implementation

1. optimum placing of PQ monitors was found 2. Superior to other quantum algorithms

1. Optimal location of DG found 2. Better reactive power dispatch with efficient penalty

1. Minimization of resonance, harmonics, operational cost and voltage sag

1. Harmonic minimization in line current of PWM converter

Research outcome

Disadvantages

Experimental setup of PWM converter

Research based on

(continued)

1. performed 1. Not compared IEEE 118-bus system better in finding with other swarm optimum optimizations locations

IEEE 30-bus simulation model

1. Analysis not done IEEE 33 -bus radial for unbalanced distribution distribution network 2. Recent meta

1. Power loss 1. Not compared minimized with other 2. Assumption not metaheuristics required in modeling

1. optimized size and placement of capacitors 2. harmonics reduced as per IEEE-519

1. Derivative free 1. Not applied on scheme MLIs 2. applicable to 2. High THD higher count of 3. Complexity rises pulses/cycle as pulses/cycle rises

Advantages

80 P. Kala et al.

Domain of publication

IET

IEEE

IET

IET

IET

References and Years

[27] (2017)

[30] (2019)

[32] (2017)

[33] (2019)

[34] (2017)

Table 2 (continued) Country of research implementation

Algeria

India

India

chaotic whale India optimization

Salp swarm

Harmony search

CSA

Modified PSO Australia

MHA technique used

1. Lack of experimental validation

1. Large computational time taken by algorithm

1. Improved 1. Complexity in convergence programming., and optimal Integration of location of renewable static controller resources

1. Improved 1. efficient transient stability algorithm to 2. Minimized fuel optimize cost transient stability

1. Reduced deviation in voltage 2. Reduced power loss

1. Used in conventional topology

Disadvantages

1. Improved 1. Higher dynamic operational cost voltage stability of 2. optimum superconducting solution for magnetic storage reactive power dispatch

1. Harmonic minimization 2. THD minimized

Advantages

1. Improved voltage 1. Less security computational 2. Increased voltage effort quality 2. Improved loading capacity

1. optimized the size of superconducting magnetic storage 2. Reduction in power loss

1. SHE problem solved for equal sources 2. superior to PSO

Research outcome

(continued)

New England 10-generator, 39-bus test

IEEE 30 bus and 118 bus system

69 node, 119-node MATLAB/Simulink

IEEE 118 bus system

CHB inverter Hardware

Research based on

Tackling Power Quality Issues Using Metaheuristics 81

Domain of publication

IEEE

References and Years

[35] (2020)

Table 2 (continued) Country of research implementation

Fractal search Jordan

MHA technique used

Advantages

1. Minimized 1. Little operational cost computation in nonlinear time economic 2. high accuracy dispatch problem

Research outcome

Research based on

1. Lack of Simulation model experimental data

Disadvantages

82 P. Kala et al.

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to solve SHE problem of MLIs using metaheuristic techniques. The merits of metaheuristics have enabled their applicability in tackling power quality issues. Many researchers have used these techniques in power quality problems. From the discussion presented in Sects. 3 and 4, it is found that the metaheuristics have found optimal results in many applications such as SHE problem, placement of PQMs, harmonic reduction, voltage stability enhancement, PF correction, tuning of DVR controller, and reactive power compensation etc. Further, their applications in renewable energy systems, smart grid and microgrid are also proposed owing to their numerous benefits.

References 1. A. Kusko, M.T. Thompson, Power Quality in Electrical Systems (McGraw Hill, 2007). ISBN 0-07147075-1 2. R.C. Dugan, M.F. McGranaghan, S. Santoso, H.W. Beaty, Electrical Power Systems Quality, 3rd edn. (McGraw-Hill, 2012). ISBN 978-0-07-176155-0 3. H. Malik, P. Kaushal, S. Srivastava, A Hybrid intelligent model for power quality disturbance classification, in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 55–63. https://doi.org/10.1007/978981-13-1822-1_6 4. M.H. Bollen, F. Fainan, Integration of Distributed Generation in the Power System (Wiley, Inc./IEEE Press, Hoboken/Piscataway, 2011) ISBN 978-0-470643372 5. R. Targosz, J. Manson, PAN European LPQI power quality survey, in Proceedings of 19th International Conference on Electricity Distribution (CIRED 2007) (Vienna, 2007) 6. J. Manson, R. Targosz, European Power Quality Survey Report: Leonardo Energy (2008). www.leonardo-energy.org 7. M. Mirjafari, R.S. Balog, Survey of modelling techniques used in optimisation of power electronic components. IET Power Electron. 7(5), 1192–1203 8. B.C. Neagu, O. Ivanov, G. Georgescu, Reactive power compensation in distribution networks using the bat algorithm, in International Conference on Electrical and Power Engineering, EPE, pp. 711–714 (2016) 9. S. Smriti et al., Special issue on intelligent tools and techniques for signals, machines and automation. J. Intell. Fuzzy Syst. 35(5), 4895–4899 (2018). https://doi.org/10.3233/JIFS169773 10. N.K.Nandan, et al., Solving nonconvex economic thermal power dispatch problem with multiple fuel system and valve point loading effect using fuzzy reinforcement learning. J. Intell. Fuzzy Syst. 35(5), 4921–4931 (2018). https://doi.org/10.3233/jifs-169776 11. T. Mahto et al., Load frequency control of a solar-diesel based isolated hybrid power system by fractional order control using particle swarm optimization. J. Intell. Fuzzy Syst. 35(5), 5055–5061 (2018). https://doi.org/10.3233/JIFS-169789 12. A. Khatri, et al., Optimal design of power transformer using genetic algorithm, in Proceeding IEEE International Conference on Communication System’s Network Technologies (2012), pp. 830–833. https://doi.org/10.1109/csnt.2012.180 13. H. Malik, et al., PSO-NN-based hybrid model for long-term wind speed prediction: a study on 67 cities of India, in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 319–327 https://doi.org/10.1007/ 978-981-13-1822-1_29 14. T. Mahto, et al., Fractional order control and simulation of wind-biomass isolated hybrid power system using particle swarm optimization, in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 698 (2018), pp. 277–287 https://doi.org/10.1007/978-981-13-1819-1_28

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15. H. Taghizadeh, M.T. Hagh, Harmonic elimination of cascade multilevel inverters with nonequal DC sources using particle swarm optimization. IEEE Trans. Industr. Electron. 57, 3678–3684 (2010) 16. E.F.D. Arruda, N. Kagan, P.F. Ribeiro, Harmonic distortion state estimation using an evolutionary strategy. IEEE Trans. Power Delivery 25(2), 831–842 (2010) 17. C. Benachaiba, B. Mazari, M.N. Tandjaoui, A.M. Haidar, Power quality enhancement using DVR based on ant colony controller, in 57th International Scientific Conference on Power and Electrical Engineering of Riga Technical University, (2016), pp. 1–4 18. O. Ivanov, B.C. Neagu, M. Gavrila¸s, Voltage profile improvement in electricity distribution networks—A genetic algorithm benchmark study, in 2017 International Conference on Electromechanical and Power Systems (SIELMEN) (Iasi, 2017), pp. 560–564 19. A. Karaarslan, The implementation of bee colony optimization algorithm to sheppard-taylor PFC converter. IEEE Trans. Industr. Electron. 60(9), 3711–3719 (2013) 20. Y.A.I. Mohamed, E.F. El Saadany, Hybrid variable-structure control with evolutionary optimum-tuning algorithm for fast grid-voltage regulation using inverter-based distributed generation. IEEE Trans. Power Electron. 23(3), 1334–1341 (2008) 21. T.S. Medeiros, N. Kagan, Bio-inspired metaheuristics applied to Volt/VAr Control optimization problem in smart grid context, in 2016 17th International Conference on Harmonics and Quality of Power (ICHQP) (Belo Horizonte, 2016), pp. 295–300 22. V.A. Preethi, S. Muralidharan, S. Rajasekar, Application of Genetic Algorithm to power system voltage stability enhancement using facts devices, in 2011 International Conference on Recent Advancements in Electrical, Electronics and Control Engineering (Sivakasi, 2011), pp. 333– 338 23. K. Sundareswaran, M. Chandra, Evolutionary approach for line current harmonic reduction in AC/DC converters. IEEE Trans. Industr. Electron. 49(3), 716–719 (2002) 24. S. Biswas, S.K. Goswami, A. Chatterjee, Optimal distributed generation placement in shunt capacitor compensated distribution systems considering voltage sag and harmonics distortions. IET Gener. Transm. Distrib. 8(5), 783–797 (2014) 25. C. Bulac, F. Ionescu, M. Roscia, Differential evolutionary algorithms in optimal distributed generation location, in Proceedings of 14th International Conference on Harmonics and Quality of Power—ICHQP 2010 (Bergamo, 2010), pp. 1–5 26. L.A. Wong, T. Jian Ling, N.A. Ramlee, Optimal power quality monitors placement using improved lightning search algorithm, in 2018 IEEE 7th International Conference on Power and Energy (PECon) (Kuala Lumpur, Malaysia, 2018), pp. 227–230 27. M. Etesami, N. Ghasemi, D.M. Vilathgamuwa, W.L. Malan, Particle swarm optimisation-based modified SHE method for cascaded H-bridge multilevel inverters. IET Power Electron. 10(1), 18–28 (2017) 28. J.H.D. Onaka, et al., Comparing NSGA-II and SPEA2 metaheuristics in solving the problem of optimal capacitor banks placement and sizing in distribution grids considering harmonic distortion restrictions, in 2016 17th International Conference on Harmonics and Quality of Power (ICHQP), (Belo Horizonte, 2016), pp. 77–82 29. C.S. Lee, H.C. Lin, Performance analysis of three evolutionary algorithms: the case for improvement on quality of power supply, in Proceedings of the 2002 International Joint Conference on Neural Networks, IJCNN’02 (Honolulu, HI, USA, 2002), pp. 1390–1395 30. S.B. Raha, K.K. Mandal, N. Chakraborty, Hybrid SMES based reactive power dispatch by cuckoo search algorithm. IEEE Trans. Ind. Appl. 55(1), 907–917 (2019) 31. T.A. Jumani, M.W. Mustafa, A. Alghamdi, M.M. Rasid, A. Alamgir, A.B. Awan, Swarm intelligence-based optimization techniques for dynamic response and power quality enhancement of AC microgrids—a comprehensive review, in IEEE Access 32. P. Kumar, I. Ali, M.S. Thomas, S. Singh, Imposing voltage security and network radiality for reconfiguration of distribution systems using efficient heuristic and meta-heuristic approach. IET Gener. Transm. Distrib. 11(10), 2457–2467 (2017) 33. B. Mahdad, S. Kamel, New strategy based modified salp swarm algorithm for optimal reactive power planning: a case study of the Algerian electrical system (114 bus). IET Gener. Transm. Distrib. 13(20), 4523–4540 (2019)

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34. D. Prasad, A. Mukherjee, G. Shankar, V. Mukherjee, Application of chaotic whale optimisation algorithm for transient stability constrained optimal power flow. IET Sci. Meas. Technol. 11(8), 1002–1013 (2017) 35. M.I. Alomoush, Optimal combined heat and power economic dispatch using stochastic fractal search algorithm. J. Modern Power Syst. Clean Energy 8(2), 276–286 (2020)

Meta-Heuristic Application in Suppression of Noise Rohun Nisa and Asifa Baba

Abstract Enhancement of Speech or Suppression of Noise from speech signal is considered as the practical and beneficial method for removing the unwanted disturbance and background noise from speech signal that results in the refinement of standards including quality and intelligibility of signal while communication from source to destination. Speech quality is a subjective performance measure which evaluates how fine the speech sounds and include the characteristics as naturalness and roughness of noise etc. and intelligibility is an objective performance measure which determines how much the signal is understood. Speech Enhancement aims at improving the communication system characteristics and performance with the input and output signals being degraded by unwanted noise that are encountered while transmission and reception of speech signal. Applications of speech communication requiring the noise reduction algorithms include answering machines, freehand communication, hard-of-hearing aids, localized and remote distance telecommunications, mobile and car phones, multiparty conferencing, noisy manufacturing and cockpits, teleconferencing systems, and Voice over Internet Protocol (VoIP). As the suppression of noise from corrupted speech signal brings in perceptible distortion to enhanced signal, causing impairment in its intelligibility. The main challenge in reducing the background noise from speech signal is to achieve Noise Suppression techniques suitable in enhancing the quality of signal except reduction in the intelligibility of signal. This involves a trade-off between speech distortion and noise reduction. Speech Enhancement techniques involve various methods for reducing the background noise from signal, providing an improvement in quality and intelligibility of speech signal.

R. Nisa (B) · A. Baba Islamic University of Science and Technology, Awantipora, Kashmir 192122, India e-mail: [email protected] A. Baba e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_4

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Keywords Noise suppression · Speech enhancement · Speech processing · Heuristics · Meta-heuristics · Stochastic optimization · Particle swarm optimization · Gravitational search

1 Introduction In this chapter, we try to analyze the effect of background noise on speech signal and the techniques for eliminating noise from speech with the meta-heuristic approach and its variants.

1.1 Noise Suppression As there is generally unwanted background noise associated with the signals particularly speech during communication that hinders the processing of signal in original form. Noise and unwanted disturbance affect human-human and human-machine communications and needs to be detected and removed from signal of interest. Speech Enhancement or Removal of Noise is an application of Speech Processing field [1] and provides the practical way of detection and elimination of noise from speech signal. Speech Enhancement algorithms thus suppress the impact of background noise from speech and therefore are termed as Noise Suppression algorithms.

1.1.1

Sources of Noise

Noise can be termed as undesirable signal that interferes with the speech signal during communication and alters the properties of speech, resulting in difficulty to perceive signal by listener and processing by communication system. Although, low intensity of noise does not affect the speech communication much but high intensity of noise causes absorption of sound signal and makes communication difficult to achieve. Thus, to frame the voice communication comfortable, natural, and practical, digital signal processing techniques are required [2] to remove noise from signal of interest and to ease the communication process. This process is termed as Noise Suppression or Speech Enhancement. As noise hinders the analysis and processing of speech signal in different way, it is desirable to classify the terminology into four basic subclasses of noise as: Additive Noise the interference that gets associated with the signal due to varied sources when transmitted via communication channel, interfering signals that arise when multiple speakers are communicating at a time, reverberation the effect of sound that remains after the sound is produced and is particularly due to multipath propagation, and echo the sound reflection that reaches the listener after delay and arises mainly because of mixed link among microphones and loudspeakers. To take into account the corresponding problems

Meta-Heuristic Application in Suppression of Noise

89

Background Noise

Speaker

Speech Signal

Suppression of Noise

Clean Enhanced Signal

Listener

Transmission Noise

Fig. 1 Impact of noise on speech signal

mentioned, numerous speech signal processing techniques are employed including Reduction in Noise or Enhancement of Speech, Separation of Source and Speaker, De-reverberation of Speech, and Cancellation and Suppression of Echo [1], further each of these relate to important research areas [3, 4]. The signal analyzed through microphone is usually a combination of the undesirable noise and clean speech signal resulting in corrupted signal and main challenge being to deal with background noise which results in the degradation of speech signal. The main consideration of suppression algorithms of noise is thus to recover and restore clean speech in original form given the superimposed signal to achieve the following essential goals: enhancing the perceptual quality of speech corrupted by noise, improving the objective performance criteria including intelligibility and Signal-to-Noise-Ratio (SNR) and, enhancing the robustness of remaining applications of speech processing techniques comprising echo suppression and cancellation, speech coding, speech recognition and synthesis, particularly to noise [5]. Figure 1 shows the impact of varied noise sources on the transmission of speech signal.

1.1.2

Real-Time Applications

The noise gets added to speech signal from the noise degraded location or when the signal is carried via communication channel. To detect and eliminate the impact of noise on signal and to enhance the quality of speech signal, there is need of Speech Enhancement. There are varied situations that require the application of noise removal algorithms. The communication system including cellphones experience background noise present in vehicles due to engine noise, street noise due to other vehicles, during the transmission of voice signal. Such systems require noise removal methods during the reception of signal to enhance the quality of received signal. This indicates that such method can be used before signal coding systems for improving standards of cellular telephone devices [6]. For systems involving recognition of speech, accuracy of the recognition rate suffers due to existence of noise. This requires the pre-processing of signal corrupted by noise using enhancement method before entering into speech recognizer system to recognize clean speech for conversion to text. In the situations involving communication between ground and

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air, and military communication, focus is on improving the intelligibility of speech signal rather than enhancing the quality of signal to better understand the voice signal. In the scenario of teleconferencing and videoconferencing, reverberation will result in transmission and broadcasting of noise to every point in room and thus needs preprocessing before the broadcasting operation to enhance the purpose of conferencing. In case of cochlear implant devices or hearing aids needed by people with hearing disability, communication is hindered in extreme conditions of disturbance and noise. The noise corrupted signal needs to be cleaned and preprocessed prior to the amplification in such devices with application of speech enhancement methods. Depending upon the application involved, speech enhancement algorithms can be applied for removal of noise from speech. A lot of research has been carried out in removal of noise, framed into different categories [7].

2 Speech Processing There are considerable number of approaches that lead to the interaction and communication between human and machine including words, symbols, pictures, displays and speech, among which most familiar and understandable method of communication is Speech. The method involving the analysis of speech signal is referred Speech Processing, a form of Digital Signal Processing (DSP). A speech signal is usually not stationary in real sense, but is typically considered quasi-stationary due to spectral characteristics for short period of 10–30 ms. For the analysis of speech, the waveform of speech signal is divided into small parts referred as segments, associated with varied sounds or words that are uttered. A speech sentence taken from the coded speech database of ITU-T P-series recommendations [8] is depicted in Fig. 2. In speech signal, there are different categories of speech segments including quasiperiodic, aperiodic, noise-like, silence, high-intensity segments and low-intensity segments that change according with the speaking style and expression of speaker.

2.1 Human Speech Generation Process The human speech is produced with the association of number of muscles and organs involving lungs, trachea (windpipe), larynx, pharyngeal cavity (throat), oral or buccal cavity (mouth), and nasal cavity (nasal tract), illustrated by the anatomy of human speech generating structure [9] in Fig. 3 as. The lungs form the basic purpose in the generation of sound and speech. During the inhalation and exhalation of air, pressure in the lungs decreases and increases and flow of air takes place among trachea and larynx. The larynx further manages the action of vocal cords or vocal folds that form three main characteristics of speech including breathing, voiced and unvoiced states. The glottis forms the opening between two folds. The opening and closing of the vocal folds characterize the glottal open phase

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Fig. 2 Speech signal for the sentence “I think it would be wonderful, there will be guests coming, she seldom listened to anybody” [8]

Fig. 3 Cross-sectional view of human speech generation structure [9]

and close phase respectively. The period associated with the glottal cycle is referred Pitch Period and its complementary form defined as Fundamental Frequency (in Hertz, Hz), designated as ϝ0 . Males are characterized by longer pitch period or low fundamental frequency compared to females. The variation in fundamental frequency in case of females and children is considered to be 200–400 Hz and 60–150 Hz in case of males [10]. The vocal folds include two main states that are associated with sound. The first one is Voicing state that comprise of the vowels such as /a/, /e/, and referred as Voiced sounds and second being voiceless sounds referred as Unvoiced sounds comprising of most of the consonants such as /p/, /t/ etc. The vocal tract including the oral cavity assumes various forms, subjected to the arrangement of lips, teeth, tongue and jaws together referred as Articulators. The

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male oral tract length is considered to be 17 cm and in females shorter compared to males. The vocal folds send the flow of air to the vocal tract. This makes vocal tract to form the linear filter by shaping the wave of air spectrally resulting in distinct sounds, frequency response of such linear filter being controlled by the articulators. This implies the nature of vocal tract relating closely with an Acoustic Resonator as the vocal tract collectively results in the vibration to sounds with resemblance to air natural frequency. Such frequencies or resonances of vocal tract are referred Formants and the resonating frequencies as Formant Frequencies. The first formant frequency is characterized by variations associated with small and wider opening of mouth, designated as ϝ1 , second formant frequency is defined by variations in oral cavity including movement of lips and location of tongue, designated as ϝ2 , and third formant frequency is related to the narrowing front and back position in oral cavity, designated as ϝ3 . The formant frequencies are generally measured and determined taking the spectral envelop of the associated speech signal into consideration.

2.2 Speech Generation Model As the vocal tract is considered to be treated as linear filter that receives the input of airflow from vocal folds resulting in varied sounds. An input in form of excitation, periodic or aperiodic, is supplied to vocal tracts by vocal cords providing the output in form of voiced sounds due to vowels and unvoiced sounds due to consonants. This implies that human speech generating system can be framed in form of engineering model, consisting of vocal tract as quasi-linear filter that receives the excitation from voiced or unvoiced source providing the response in form of Speech signal, as illustrated in Fig. 4. In the predicted model, the action of vocal folds results in periodic and aperiodic states taking the shape of switch, the vocal tract considered as filter is represented by time-invariant linear filter due to quasi-stationary nature of speech signal, and the attributes of linear filter are determined by incorporating linear prediction analysis procedure. The response from linear filter is provided to second filter that represents the speech transmission impact on lips and gives the speech signal response. The Vocal Tract attributes

Glottal Source Pitch Period

Switch

Noise Source

Fig. 4 Speech generation model

Vocal Tract Filter

Transmission Filter

Speech

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voiced state is modeled in terms of glottal source, vocal tract and propagation of lips, and for the unvoiced state the source associated is noise. The model deduced is referred Source-Filter model and finds application in narrow-band speech transmission due to dependence on three coefficients- fundamental frequency, periodic or voiced state of sound and attributes of vocal tract. Further, the model forms the fundamental method in the field of speech analysis, speech recognition, and speech synthesis.

3 Heuristic in Noise Suppression The application of noise removal and enhancing techniques vary according to the problem that depends upon numerous factors including number of microphone channels. Pertaining to single channel where signal is recorded by one microphone, and of multichannel where signal is recorded by more than one microphone, an optimal solution needs to be derived so as to remove as much noise as possible without degrading the standards including quality of speech signal and its intelligibility for purpose of communication. In general, noise reduction techniques become simplified with multichannel microphones. Consider the two-channel microphone system involving one microphone that selects the noise corrupted signal and second microphone estimating the area of noise. Here the second microphone is used as reference of noise and with the incorporation of adaptive cancellation removes the degraded nature due to noise in first microphone [11]. Nearly all communication systems are provided by single microphone that hampers the noise suppression process due to two reasons - in absence of reference of noise, pre-processing of clean signal cannot be achieved before the signal is affected by noise and the properties of noise vary drastically with and without time depending on the application. The reasons stated are demonstrated with the help of spectra considered for conference room noise signal and car noise signal as shown in Fig. 5. It is evident that periodogram spectrum of car noise signal is not identical with spectrum of conference room signal. In addition, the properties of noise that are processed at distinct instants of time are unrelated when considered for identical conference room. This reveals the non-stationary nature of speech signal that causes problem in measuring the dynamic properties of speech when affected by noise. Although, immense research has been carried out considering the single-channel microphone case, noise reduction problems gets more simplified when considered for multi-channel microphones.

3.1 Noise Suppression Performance with Meta-Heuristics Noise suppression techniques provide a practical method for removing the noise from corrupted signal and resulting in clean enhanced speech signal. The traditional methods involved in removal of noise include Spectral Subtraction [12],

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Fig. 5 Periodogram spectrum of a Car noise signal b Conference room noise signal [7]

Wiener filtering [13], Kalman filtering and Least-Mean-Square (LMS) algorithms to mention a few. The performance of reduction algorithms become easier with multichannel microphones involving the application of heuristics and meta-heuristics. Heuristics and Meta-heuristics are the general terms associated with stochastic optimization algorithms, the algorithms that work on random variables and deal with the maximization or minimization of functions involving randomness. Heuristic derived from Greek word εØρ´ισκω meaning—I find or discover, is a technique applied to noise removal method to achieve the desired speech signal rapidly in comparison to traditional noise removal methods and providing an approximate solution when traditional methods do not give exact solution. Heuristic technique involves completeness, accuracy and precision for faster speed. Meta-heuristic algorithms is an expansion of heuristic that means going beyond the simple heuristic approach with increased performance and involve randomization and local search. Thus all stochastic algorithms including randomization and local search are referred as Meta-heuristics.

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3.2 Application of Meta-Heuristic Optimization in Noise Suppression Consider the arrangement involving two-channel noise suppression system as depicted in Fig. 6. The two-channel microphones involve area of noise or reference signal of noise sr (n) in one channel and noise corrupted speech signal sd (n) considered in second channel, connecting these two signals by an Acoustic Path with transfer function P(z). The acoustic path transfer function is determined with help of a filter referred as Adaptive Filter with transfer function A(z). The performance of modeled speech enhancement system is evaluated by the application of Meta-heuristic algorithm. The two-channel microphone system possesses the signal sd (n) as the combination of clean signal sc (n) and noise signal sn (n) that is applied to the adaptive filter of transfer function A(z). The performance of adaptive filter are varied by the application of meta-heuristic algorithm to get the correlation among microphone signal sd (n) and filter output so (n). The application of Optimization technique, a form of programming method that choses the best element from a combination of accessible options is performed, referred here as Meta-heuristic Optimization technique. With the incorporation of optimization technique, a practicable number of adaptive filter coefficients that form the search space or population, each referred as Particle or Agent in population-based meta-heuristic algorithms are taken into consideration and checking the outcome of each agent in form of error signal se (n).

Fig. 6 Block diagram of two-channel microphone system with meta-heuristic approach

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Fitness Function and Objective Function in Optimization

There are two vectors associated with each agent namely Position vector and Velocity vector that are randomly achieved at the beginning and are updated as the iterations of algorithm are carried out based on the evaluation of a function referred as Fitness function. This function determines the standard features of each solution out of population or search space and arranges every solution according to a specified sequence that leads to a particular solution. This procedure is continued until an Optimal solution is achieved. In optimization, function required when minimization and maximization is carried out to choose particular solution as best one from given number of poor solutions for a definite problem is referred Objective function. For optimization involving minimization of function, objective function is termed as Cost function and for maximization categorized as Fitness function. The optimization technique is applied to adaptive filtering by considering the objective function as cost function that minimizes the mean square error among adaptive filter output and unknown system output. Enhancing the speech with the adaptive filtering method involves the segmentation and windowing of noise corrupted speech signal into short segments referred as Frames. The optimization technique involving objective function is interpreted as mean square error considered among input signal, that is, noise corrupted speech signal and noise signal estimation or spectrum related to particular frame. Mathematically, objective function may be expressed as indicated by Eq. 1, Oj =

N  2 1  (sd (n)) − so j (n) L l=0

(1)

Where O j refers as Objective function for j th agent, L as frame-length, l as frame-index, and N as number of frames. After predefined repetition of algorithm, the adaptive filter A(z) provides the best solution for minimum value of objective function, which implies when O j tends to minimization referred as Cost function. The convolution between reference of noise sr (n) and error signal se (n) provides an estimation or spectrum of noise signal. The subtraction of noise signal spectrum from noise corrupted speech signal results in enhanced clean speech signal.

4 Meta-Heuristics Optimization Algorithms for Noise Suppression The optimization algorithms form the most important part of machine learning techniques. Optimization means choosing the finest and desirable component depending upon a particular condition, out of a group of accessible components. In other words, optimization involves the maximization and minimization of a function of

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real elements or components through the selection of variable from a combination and determining its value. It includes determining the best solution of given objective function from a defined solution domain together with other objective functions with their respective domains. Mathematically, an optimization can be stated as [14]. Statement: a function f : S → R chosen from a set S and allotted to real numbers R. Conclusion: a solution z 0 in set S such that f (z 0 ) ≥ f (z) for all z in set S defining maximization and f (z 0 ) ≤ f (z) for all z in set S defining minimization. This forms the Optimization problem and are dealt for physical and conceptual world applications. The set S forms the search space and the components present in S forms candidate solutions of the objective function f . For maximization of objective function, f is referred Fitness function and for minimization as Cost function. The solution that yields the maximization or minimization for achieving particular goal is referred Optimal solution. The optimization can be applied to the field of artificial intelligence, computer science and many more fields. Related to physical world, optimization finds application in ant colony optimization, bee colony optimization, bird flocking algorithm, search algorithm, etc. Optimization problem can be dealt with either using deterministic approach or stochastic approach. The deterministic approach includes the numerical optimization that provides the global solution to optimization problem and referred as Deterministic Global Optimization. The stochastic optimization deal with the generation and application of random variables. In engineering field involving physical world applications, optimization of considerable features are required to work out on such problems with least calculating time. For such cases, deterministic approach is not feasible but requires the applicability of stochastic approach or random search that can resolve the problems accurately with simple implementation. Further, stochastic approach involves the solution to problem with heuristic and meta-heuristic algorithms. For the process of removal of noise from degraded speech, various meta-heuristic algorithms are employed, providing approximate solutions to number of optimization problems. These algorithms applied for suppression of noise are mentioned briefly as follows.

4.1 Particle Swarm Optimization This approach is based on stochastic or random search method and referred as Standard Particle Swarm Optimization (PSO) for enhancing the speech signal. It involves the arbitrary group of quantities referred as Swarm particles. The particle associated with swarm form a varied collection of unspecified attributes that need to be optimized. The specific particle in swarm is considered as a point in search space associated with a fitness value that is computed from the estimation of attributes relative to prearranged fitness function for desired optimal solution. The attributes

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of particle are taken either real variables or compressed variables owing to the situation of particle. For conventional PSO, the particles intercommunicate resulting in distinguishable paths during searching phenomenon [15]. Each particle j has an associated position vector p j and velocity vector v j with it. The position p j of the particle forms a definite solution to the optimization process. In the beginning, search space is formed by random generation of particles. During corresponding iterations, particle is associated with two position elements including deterministic element and stochastic element referred as current global best cgbest j and own local best olbest j , and possessing the random movement features. Considering the particle j of search space associated with position vector p j and velocity vector v j , new velocity at particular time t + 1 can be determined as,     = wi × vtj + γ .θ1 olbest j − p tj + δ.θ2 cgbest j − p tj vt+1 j

(2)

Where, wi refers as inertia weight that tends to manage the preceding velocity impact vtj on new velocity computed and usually varies from w less than 1 to 0 and makes algorithm to concentrate on cgbest, γ and δ refer as Learning attributes that determine the convergence speed of the algorithm, and θ1 and θ2 refer as random vectors chosen from uniform distribution. Also, the new position of the particle at specified time t + 1 can be determined as, = p tj + vt+1 p t+1 j j t

(3)

Where t refer as corresponding change in the iteration of algorithm. Here, the algorithm ceases depending upon the limit of maximum number of iterations or the achievement of optimal solution. Considering the adaptive filtering method, possessing Adaptive filter with transfer function A(z) for enhancing the speech signal degraded by noise, the mean square error (MSE) considered among the adaptive filter output and unknown system output is taken as the objective function referred as cost function. The respective cost function will determine the fitness value of corresponding particle in standard PSO process. For the two-channel microphone system employed for suppressing the noise from speech signal depicted in Fig. 7, the analysis involves taking the minimum mean square error (MMSE) in respective frame and is considered as the cost function for the optimization of the algorithm, given as Oj =

N  2 1  (sd (n)) − so j (n) L l=0

Steps in standard PSO for Noise Suppression For particle j Initialize position and velocity of particle j

(4)

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Fig. 7 Block diagram of two-channel microphone system with PSO approach

End Do For particle j Compute fitness value of particle j If fitness value is better than its own local best olbest Choose current value as the new olbest End Choose the particle with best fitness value among cgbest For particle j Compute particle velocity using Eq. (2) Update particle position using Eq. (3) End While maximum iterations achieved or minimum error criteria not attained The derivatives of Particle Swarm Optimization for enhancing the speech signal include improved PSO [16, 17], learning-based PSO [18, 19], and hybrid PSO [20] algorithms respectively.

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4.2 Accelerated Particle Swarm Optimization The accelerated PSO algorithm determines the objective function considering the modification in paths of respective particles that tend to form individual paths following quasi-stochastic approach. The swarming particle motion is associated with two components involving stochastic component and deterministic component. The position of the particle j achieves current global best cgbest j and own local best olbest j followed by random motion. After encountering an improved position compared to previous position, the position of particle j is renewed as new current best and current best is associated with respective particles following the iteration in time t. This algorithm focusses on determining the global best from the current best solutions of all related n number of particles in a specified number of iterations. Further, it takes into consideration the current global best only to enhance the convergence of the algorithm, giving the new velocity vector of corresponding particle j as,   = vtj + γ .θn + δ cgbest − p tj vt+1 j

(5)

Where θn refers as random vector considered for {0, 1} interval. The corresponding new position vector of particle j is given as, = x tj + vt+1 p t+1 j j

(6)

Here, the convergence rate can be enhanced by considering the renewed position of particle as follows, = (1 − δ) p tj + δ · cgbest + γ θn p t+1 j

(7)

In the accelerated PSO algorithm, γ is taken in the interval {0.1, 0.4} and δ in the interval {0.1, 0.7}. For the suppression of noise and enhancing the speech signal, the acoustic path is optimized by incorporating accelerated PSO algorithm that takes the concerned particle in swarm as feasible solution characterizing the filter coefficients with transfer function W (z) as shown in Fig. 8. The filter results in best solution in given iterations for minimum fitness value or minimum value of O j . The noise corrupted signal sd (n) is determined from the convolution of reference of noise sr (n) and error signal se (n). The speech signal in enhanced form is thus achieved by the elimination of noise spectrum from noise corrupted speech signal. Steps in Accelerated PSO for noise suppression Generate group of n particles Do Evaluate fitness for each particle using the objective function Eq. (4)

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Fig. 8 Block diagram of two-channel microphone system with APSO approach

Find best global particle cgbest for iteration t = 0 Update velocity vector of each particle using Eq. (5) Update position vector of each particle using Eqs. (6) and (7) While minimum error criteria not obtained or maximum number of iterations attained

4.3 Gravitational Search Algorithm The suppression of noise involving two-channel microphone system is achieved using conventional Particle Swarm Optimization (PSO) techniques and its derivatives due to simplified idea and implementation. In spite of the advantages of simple PSO technique, it encounters convergence of algorithm beforehand and confinement to local minima resulting from reduction in diversification of search space that causes stagnation in fitness value of swarm. To enhance the diversification regarding search space and upgradation in potential of local search, different algorithm is employed for suppression of noise referred as Gravitational Search algorithm [21]. The deterministic and random searching procedure involved in PSO algorithm and its derivatives depend upon the concept of bird flocking or fish schooling. The GSA algorithm involves distinct procedure regarding searching process by taking into consideration the separation among neighboring particles for renewing their position. The attribute concerned with inertia mass for renewing the position of particle related to GSA algorithm is independent on the movement of particle. The GSA algorithm provides a different approach contrary to conventional PSO technique and is employed in

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adaptive noise cancellation for removal of noise involving two-channel microphone system. The Gravitational Search Optimization algorithm depends upon the Law of Gravitation and Law of Motion [22]. This optimization algorithm is population dependent algorithm consisting of different particles referred as Agents and are regarded as Objects with respective masses. The objects involve direct form of interaction due to attraction by gravitational force with movement defined and concentrated to heavy mass object. The good solution is determined corresponding to the heavier objects as they involve slow movement than lighter objects. The corresponding agent in GSA is associated with four attributes as inertial mass, active gravitational mass, passive gravitational mass, and position. The agent defines a particular point regarding the search space, characterized by a fitness value and the position of particular agent forms the solution to problem together with inertia mass and gravitational mass adjustment. Consider the GSA process with the population of agents as a. In the beginning, agents are selected and arranged randomly to form the search space s. From Law of Gravitation, the force of gravitation acted on the agent k due to agent j for a particular time t, is defined as, (8) where, g(t) represents gravitational constant for time t that controls the accuracy of search, m ak (t) as active gravitational mass and m pk (t) as passive gravitational mass pertaining to agent j, Rk j (t) as Euclidean distance among j and k agents, and ϝ as small constant. The constant of gravitation is represented as,  g(t) = g0 × exp

−γg × t τ

 (9)

where, g0 represents initial gravitational value assigned to gravitational constant g that reduces with the number of iterations carried out leading towards optimized objective function, γg as descending coefficient, t as current iteration value, and τ as maximum number of iterations. The overall force associated with the agent k in search space s is given as, (10) where, rand j represents random number chosen for a period [0, 1]. From the Law of Motion, the acceleration of agents for a particular time t is represented as, (11)

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where, m k (t) represents inertia mass of agent k. The renewed velocity of the agent k is computed from the knowledge of previous velocity and acceleration of agent as, vks (t + 1) = rand j × vks (t) + Ask (t)

(12)

Also, the renewed position of agent k is computed from previous position and velocity of agent as, pks (t + 1) = pks (t) + vks (t)

(13)

Consider the two-channel microphone system for suppressing the noise as shown in Fig. 9. In this approach for enhancing the speech signal, the adaptive filter with transfer function A(z) is implemented using Gravitational Search Algorithm that modifies the features of adaptive filter resulting in the output of filter so (n) with the resemblance to sd (n). In the suppression of noise process, the speech signal is processed following the segmentation of signal into short windows as Frames. For adaptive noise cancellation using gravitational search method, fitness of the agent is defined from objective function taken as the average error computed among noise spectrum and noise corrupted speech signal related to particular frame and can be expressed as, Ok =

N  2 1  (sd (n)) − sok (n) L l=0

(14)

Fig. 9 Block diagram of two-channel microphone system with gravitational search approach

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where, L refers as length of particular frame, and sok (n) as filter output regarding the kth agent of search space s. The agents in the search space characterize the feasible solution, framed as the attributes of adaptive filter A(z). Following the corresponding iterations, the filter results in best solution for minimum value of objective function. The noise corrupted speech signal so (n) is obtained from the convolution of noise reference sr (n) and error signal se (n) and subtracting it from noise spectrum results in the enhanced speech signal. Steps in Gravitational Search Algorithm for Noise Suppression Do Generate search space of agents a forming adaptive filter coefficients Compute fitness of agent using Eq. (14) Generate initial velocity of agent randomly While condition is not satisfied Compute fitness of k-th agent for particular time using Eq. (14) For identification of good agent Compute g(t), Ƒk (t), and Ak (t) using Eqs. (9), (10) and (11) Update velocity of agent using Eq. (12) Update position of agent using Eq. (13) End

5 Conclusion This chapter includes the techniques involved in removal of noise from degraded speech including traditional speech enhancement methods. Further the application of optimization is included that reduces the mean square error between noise corrupted signal and noise spectrum to provide clean speech signal for communication. Heuristic and meta-heuristic optimization algorithms provide accurate results than traditional methods due to optimization technique involved and varied heuristic approaches are applied to carry out the research in noise suppression involving multichannel microphones. There is not any particular algorithm to all optimization problems that can achieve the optimal solution. Thus, finding new optimization algorithms is an open research area to expand the application of heuristic and meta-heuristic algorithms in suppressing the noise from degraded signal or in enhancing the signal corrupted by noise during communication.

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A Review on Genetic Algorithm and Its Application in Power System Engineering Vimal Singh Bisht, Navneet Joshi, Govind Singh Jethi, and Abhijit Singh Bhakuni

Abstract Genetic algorithm is a one of the frequently used soft computing technique which is used for optimization of real time problems. Genetic is gaining its popularity because of its robustness in finding the solution of a problem very close to the minima value. In this chapter we will briefly discuss basic concepts, functionality of GA and will learn that how it has been used in: Economic load dispatch, Unit Commitment problem, distributed generation and load forecasting of power system. A review work has been done to understand the usefulness of Genetic algorithm in above mentioned domains. The future scope of GA (genetic algorithm) is also highlighted in the chapter. Keywords Genetic algorithm · Economic load dispatch · Load forecasting · Distributed generation · Load forecasting · Power system

1 Introduction The four major areas of power system are its planning, designing, controlling and operation. For smooth operation of power system all these four departments need to be attended very carefully. If we talk about early time the classical methods used for solving the problem were not very efficient [1–6]. In using these classical methods V. S. Bisht (B) · A. S. Bhakuni Electronics Engineering Department, GEHU, Bhimtal, India e-mail: [email protected] A. S. Bhakuni e-mail: [email protected] N. Joshi Mathematics Department, GEHU, Bhimtal, India e-mail: [email protected] G. S. Jethi Department of CSE, GEHU, Bhimtal, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_5

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the probability of an output getting trapped at a local minima point was high, this is so because most of the power system problems are of non convex in nature. It means that problem will get tapped at local minima rather than going to a global minima point. However if the starting point is placed near to a global minima point then there is high chance of solution getting close to global minima, but again the probability to this is low. The other problem which researchers faced was that he most of the values of power system are having the integer value, for example: tapping position of transformer, capacitors placed at the bank etc. so it is always useless to go for a continuous solution. So in order to get the integer value of the output MIP (Mixed integer problem) or MILP (Mixed integer liner problem) methods are used. Though using of these methods increases the complexity of such problems [1, 2]. Genetic algorithm is one of the soft computing techniques which are gaining popularity these days. It can be applied to multiple areas of engineering, medical & management. It can solve the complex problems in very less time as compared to the classical methods. The main reason behind genetic algorithm popular is its robustness in searching the optimal solution near to the value close to global minimum. Genetic algorithm is based on the natural phenomenon of survival to the fittest i.e. the natural selection. In this method coding of real time parameters is done to find a solution near to global minima. It can easily solve problems having huge numbers of local optima. Genetic algorithm has been applied to various domains in power system. In this chapter we will review the application of Genetic algorithm for optimal power flow, economic load dispatch, load forecasting, distributed generation and load scheduling.

2 Genetic Algorithms Basic Introduction Solution of real word problem using a mathematical approach requires problem modeling with all the restrictions and then solving it for drawing any conclusion. But there is lot of complexity involved in this. Now we can see that there is a paradigm shift in way of solving a problem i.e. old fashion days when no math’s was known are getting back into trend. The reason behind this shift is the success that mankind have achieved in previous years when no mathematical modeling was known. These early inventions inspired mankind to develop methods which can be used to solve problems very easily and in a quick time. For example we have Fuzzy system which is based on human knowledge base, ANN which mimics human brain pattern, simulated technique a probabilistic approach. There is one more class of algorithm based upon natural evolution process of variety of creatures. Genetic algorithm is one such class of algorithm which was first discussed in 1967 by Bagley’s in his thesis “The Behavior of Adaptive Systems Which Employ Genetic and Correlative Algorithms” [7]. The algorithm was then strongly influenced by Holland who is also considered as father of GA [8, 9]. It was since then that this algorithm has attained researcher’s attention and has been applied for optimization process. Hybrid model of this algorithm were also developed by the researchers.

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Genetic algorithm is a soft computing technique with an aim to develop a system which mimics the nature. Hence the output was an algorithm that works on the principle of “survival of the fittest”. In genetic algorithm a random initial population is taken where each individual of the population is called as chromosome. These chromosome they represent the solution for the problem. Chromosome is the string of codes where each bit is called as gene and holds information of the problem in coded form. Once the population is selected fitness of each chromosome present in the population is calculate and the one which are found fittest are transferred to the next generation and the others are terminated [3]. Thus a new population is formed. GA differs from the other classical methods by the following characteristics: • Classical methods does not assure a global optimum solution, where as GA has a capability of converging to a global optimum point. • In GA the search is performed on a population (randomly generated) rather than at a single point which is done in the case of classical methods. • Constraints can easily be handled in GA as compared to classical methods. • In classical methods we work on actual parameters of the problem where as in GA we work on encoded form of information in form of chromosomes.

2.1 Basic Elements of Genetic Algorithm Genetic Algorithm consists of five basic elements also called as components of genetic algorithm. These components are: 1. 2. 3. 4. 5.

Coding of the problem Evaluation of the fitness Reproduction operators Selection Criterion Stopping Criterion.

2.1.1

Coding of the Problem

The parameters of the problem are coded in the form of strings called as chromosome [10]. The coding can be done using any numbers, characters or symbol depending upon the individual. But generally binary coding is used to represent the information in coded form as it is less complex. Each bit of the chromosome is called as genes and these genes are joined together to form a chromosome. Length of the chromosome depends up on the level of accuracy or precession required by the problem. Good coding is necessary to have an optimum solution therefore it is the most important factor in the performance of GA.

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Fitness Function

Through fitness function we can learn about the feasibility of a particular outcome Based on the value of fitness function a solution may be ranked over other. The higher value of fitness function [10] clearly indicates that we are very near to actual solution of the problem. All the populations having higher value of fitness function are transferred to the next generation and the remaining are terminated.

2.1.3

Reproduction

After fitness function value is evaluated, reproduction operators are applied to the entire population, [10] User can define the probability of these operators on their own keeping in mind that none of the operator can have value zero. There are two basic operators applicable in GA: • Crossover • Mutation. Crossover operator is applied randomly on the population having greater fitness value. Every time this Operator is applied a fresh new string (chromosome) is generated which may have a higher fitness value as compared to their parents. This crossover may be performed at a single point or more points. Crossover operator may be defined as: n-point, segmented, uniform, shuffle crossover. i.e. single point crossover, two point crossovers or uniform crossover. Based on the experiences of researchers it is said that a crossover probability of 0.7 yields better result. If crossover does not take place between two chromosomes than they are as it is transferred to the next generation, this phenomenon is called as cloning. In mutation entire gene of a chromosome is muted, thus resulting in a fresh new string (chromosome). It randomly selects a gene and flips its value. Mutation operator can be applied on a selected gene, randomly selected gene, or on the entire string (chromosome) According to the researchers the probability of this type of reproduction is very low i.e. 0.01 to 0.001. Use of this operator is highly risky but still it is applied so that the solution does not get trap at a local minima point.

2.1.4

Selection

Selection operator is applied on the population generated after the reproduction operators are successfully applied [10]. The two basic criterion of selection are Roulette wheel selection where selection depends on the fitness of the chromosome i.e. One having higher fitness will have more chances of selection and the other method of selection is tournament method where two chromosomes are randomly taken and selection is based on their fitness value.

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2.2 Basic Steps and Flowchart for Genetic Algorithm The working process of GA (genetic algorithm) can be understood from the flow chart drawn below. The basic steps of GA are: • • • • • • • •

A random population size depending on user choice is initialized. Fitness function is formed based on the problem type. All the constraints are defined which are used as stopping criterion. Selection criterion is applied, again it type depends on individual. Reproduction operators are applied whose probability is decided by the user. Again fitness of the survived population is evaluated using same fitness function. It all the constraints are satisfied then solution is achieved. And if not then all steps are repeated again (Fig. 1).

Fig. 1 Flow chart of genetic algorithm

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3 Problem Solving Using GA: Example In this section of chapter we will learn how actually a problem can be solved using Genetic Algorithm. For this we have taken the scheduling problem of thermal and hydro plants considering it over a short time horizon [11]. Scheduling of 10 (ten) thermal and four (4) hydro plants is done with an objective of cost minimization of thermal generation. Pdj Ghij Gtkl Vhij Dhij Hk x, y, z R1 − R6 NgT NgH

Demand in the Jth hour. Hydro generation by Ith reservoir in Jth interval. Power generation of thermal plant by Kth unit for Ith time Interval. Volume of Ith reservoir in Jth interval. Discharge from Ith unit at Jth interval. Thermal power generation cost for Kth unit. Thermal generation Cost Coefficient. Hydro Generation. Generation Coefficient. Total Thermal unit present in the system. Total Hydro unit present in the system.

3.1 Problem Constraints Balancing of the load with demand. That is the generation done by Hydro and thermal plant collectedly should be able to meet the demand at every time. Gt + Gh = Demand + Losses

(1)

Generation limit of Hydro and Thermal plant should be between its minimum and maximum limits. (Gh )min ≤ (Gh ) ≤ (Gh )max

(2)

(Gt )min ≤ (Gt ) ≤ (Gt )max

(3)

Hydro discharge from the hydro plant and the volume of water in the reservoir should be between the specified limit„ keeping in mind the generation to be done in upcoming hours or days. 

     Dhij min ≤ Dhij ≤ Dhij max

(4)



     Vhij min ≤ Vhij ≤ Vhij max

(5)

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3.2 Problem Formulation Using GA The entire focus of the problem is to minimize the cost of generation of thermal plant by changing the generation done by hydro plant. Thus our objective function is to minimize: Summation of: Hk (Gtkl ) over the entire time duration for all the thermal units. Thermal Cost =

Ng T  

Hk G tkl

(6)

T =1 K =1

where Hk is defined as: Hk (Gtkl ) = Xk + Yk (Gtkl ) + Zk G2tkl )

(7)

The population is initialized using the water discharge form hydro units on the hourly basis. Number of bits required for to represent population is calculated as:   − Dhmin × precession ≤ 2Bits req−1 2Bits req.−1 < Dmax h

(8)

where D is the discharge of the hydro plants. Taking value of precision as 10th up to the decimal place. The entire population will be represented as a matrix with of total number of hours x total units present. Fitness function of the problem is optimization of thermal plant cost. By replacing the values of the constant X, Y & Z total fuel cost is represented as: FK (Ptk ) = 5000 + 19.2 × Ptk + 0.002 × P2tk

(9)

where Gtk , the thermal generation is given by Gtk = Pdemand − Ghj Thus the Eq. (1) becomes   2  HK (Gtk ) = 5000 + 19.2 × Pdemand − Ghj + 0.002 × Pdemand − Ghj

(10)

Now Eq. (2) is the final fitness function need to be minimized by GA. Where in Ghj is given by the equation            Ghj = R1i V2hij + R2i D2hj + R3i Vhj Dhj + R4i Vhj + R5i Dhj + R6i (11)

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Reproduction operator is applied on the population initialized and fitness is evaluated using the Eq. 3. The probability of crossover may be taken as 0.8 and that of mutation to be 0.001.

4 Application of Genetic Algorithm Power system is one of the domains of real time system in which huge amount of accuracy is required. To achieve high level of accuracy in results lot many constraints are involved in the problem formulation which in turn requires lot of mathematical calculation and modeling. Thus traditional methods with lower ability to handle constraints and lower speed are g5enerally avoided for solution of such problems. Thus GA (genetic algorithm) one of the EA (evolutionary algorithm) is widely used for solving these problems. Researchers have widely used GA (genetic algorithm) for solution of ELD (economic load dispatch), DG (distributed generation), Load forecasting and Unit Commitment Calculation is involved. Review of few of their work in the above mentioned area is reported below.

4.1 Economic Load Dispatch For meeting the required load demand scheduling of the generators present in the power system is one of the most important concern of any electrical power system. ELD (economic load dispatch) is a process in which optimal combination of all the generating units in power station is done for minimization of the fuel cost, demand of the load and other operating constraints. Now that when we have transformed our power system as per the deregulated environment, network operator’s most important work is to optimize the load dispatch. Out of the many approaches applied for ELD solution Genetic Algorithm (GA) has its own importance in this domain and has proved it to deal well with all the constraints of the economic load dispatch (ELD) problem. A detailed review of work of few authors has been listed below which clearly shows that Genetic Algorithm (GA) can successfully deal with all the system constraints for giving an optimal solution to the problem. The author’s Susheel Kumar and Naresh [12] in this paper applied real coded genetic algorithm (RCGA) for solution of non-convex load dispatch problem. The ELD result obtained out of the proposed algorithm were compared with the BCGA and other already existing RCGA techniques and was found that RCGA provide better cost optimization, better implementation and easy computation of the problem. It was also reported that the proposed algorithm handled all the constraints and solved a large and complex system very effectively. This is the most recent work done by Rout et al. [13], in which GA is been developed to find out best solution for economic dispatch and unit commitment simultaneously to a MG (micro grid). To demonstrate the result three case studies

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are considered. In the first case cost minimization was obtained by minimizing the use of DE (diesel engine). In the second case allow mode detailed formulation as non-liner constraints are handled well by GA. fitness function took a higher value as compare to case I. in third case a new method is proposed which provided a reliable solution while MG(micro grid) is operating in islanding mode. Later on effect of ESS parameters were also analyzed. In this paper Jain et al. [14] applied Genetic algorithm to solve a multi-dimensional ED problem. Losses occurring in the transmission, cost of the fuel and environmental pollution were the main three constraints that author have considered. For the research work IEEE 5, IEEE 14 and IEEE 30 bus system are taken into account. It was found that this technique was very efficiently able to handle three objectives. Work also shows that if generation cost is increased then both transmission losses and environmental pollution can be controlled. Results also shows that by choosing a population of smaller size the computational part can be significantly reduced. Arif et al. [15] in this paper integrated genetic algorithm approach with the EMS (energy management system) of a micro grid enabled with multi facility on the daily basis. The applied algorithm works on: (i) to minimize he energy cost of grid and (ii) to make suppliers aware of the demand pattern. For showing the effectiveness of the proposed method it was applied on case studies and was proved to be a better approach. Practical validation of the current research work needs to be done. For better application of the work there is a need for this work to be applied to a larger micro grid. Calderon et al. [16] proposed vector search method for obtaining the lower cost of generation. The algorithm is applied in IEEE 14 and Wong networks. Using this method he met all the constraints of economic dispatch problem. It was also demonstrated that the average converging time was reduced to a significant level as the search space was reduced to single dimension. Author also stated that GA-V has to solve the vectors which meet at hyper cube edges with the hyper plane, which increases the complexity of the problem. By using this approach of real coded genetic algorithm it is very clear from the simulation results that the proposed method is very efficient as compare to other methods. In this paper Mishra and Das [17] used a hybrid model of GA for solving the ELD problem. Instead of clubbing both the algorithm directly together, the chemo effect of BFA (bacterial foraging algorithm) which is very different then the steps involved in GA was applied with BFA and a new hybridized model of GA was obtained. For the demonstration of the algorithm a non-convex ELD problem was solved for three different cases. The results obtained were compared with the other soft computing methods and was observed that CGAC is a much superior algorithm for solving ELD problems. Jain and Swarnkar [18], presented genetic algorithm approach for solving the economic load dispatch problem for the power plants having prohibited working zones. Author has included many cases in his studies to demonstrate that this technique provides a better result among all. It is claimed that it can be applied to real time ELD problems due to its characteristic of less convergence time. The only limitation

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of the method was that if a chromosome represents more number of variables then there will be difficulty in solving such problem due to the large search space. Shang at el [19] in this paper performed economic load dispatch using improved version of genetic algorithm and compared the result of studies with other dynamic programming methods. The study was done focusing the time, accuracy and stability of the system. The system taken for the study was a 26 turbine gorges hydro power station. The following three key points were reported (1) IGA provide better computational time when the units are less than ten, (2) for solving the same problem IGA will take less time and (3) convergence rate of IGA decreases with increase in the turbine numbers. The proposed method also shows that its application will reduce the vibration of the turbines, thus providing them better stability and life. It is also demonstrated that the proposed algorithm also provide better stability to smaller turbines. In this paper author Chiang [20], applied improved Genetic algorithm with a feature of multiplier updating (IGAMU) for solving practical non-convex dispatch problem. In IGAMU ICA increases the capability of the algorithm to proficiently search and search solution whereas MU helps proposed algorithm in managing constraints effectively. The first example taken for the study is 13 units considering the effect of valve point loading. The second example taken is POZs having non-convex cost functions. Using the proposed algorithm it was found that IGAMU has advantage of simple to understand, easy to implement, with better efficiency as compared with GA-MU. IGAMU also requires a small population and randomly assign the penalty at a suitable level which again makes it special smart algorithm. Comparative studies made in the paper shows that proposed algorithm have merits over other mentioned methods for PELD operations. Its practical application is also demonstrated on a real 40-unit Taiwan power system (Table 1).

4.2 Load Forecasting Prediction of electrical power requirement of a system for over a time horizon is called as load forecasting. Broadly load forecasting problems can be divided into two categories: Short Term load fore casting and medium or long term load fore casting. Any fore casting which is done for an interval of one hour to seven day is termed as short term forecasting and any forecasting done for the period of seven (7) or more days is termed as medium or long term forecasting. Load fore casting is one of the important studies of power system as through this we can increase the efficiency and revenue of distributing and generating entities. From the last few decades different methods have been proposed for the solution of load forecasting classified as: Conventional techniques and Artificial Intelligent (AI) techniques. As we know that convention methods are capable of solving linear problems only so they cannot be applied to non-liner case, hence there application is limited as most of the power system problem is nonlinear in nature. So for the solution of nonlinear problems AI techniques are used. One of such technique is genetic algorithm (GA)

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Table 1 Tabular form of above review work References Technique used Objective

Decision Main variable/constraints finding

Test case

[12]

Real coded genetic algorithm

Cost minimization and reducing optimization time

System load balance Limits of generation for thermal plants

RCGA is better than BCGA and other RCGA methods

Two test systems with three and six generators

[13]

Genetic algorithm

Finding economic dispatch for micro-grid

Power restrictions

GA gave feasible solution for all the three considered cases

Simulation frame work is developed

[14]

Genetic algorithm

Multi Load demand objective Losses economic load dispatch

Good IEEE 5, 14, 30 constraint bus system in handling 3-D space Fast computation is achieved

[15]

Genetic algorithm with EMS (Energy management System)

Reduced in operating cost for micro-grids

Operational limits of system Demand balance Generation limits

cost is minimized meeting there requirement

[16]

Real coded genetic algorithm GA-V

Minimization of active power generation cost

Active power generation limits Balance of active power

All IEEE14 and constraints Wong networks satisfied efficiently. Time of convergence reduced

[17]

Chemo-inspired genetic algorithm for constrained (CGAC) GA with Chemo effect of BFA (Bacterial foraging algorithm)

Solution on non-convex ELD problem

Balance in power CGAC Generator limit proved to be Rate of Ramp limit more reliable, accurate & efficient

[18]

Genetic algorithm

ELD with prohibited operating zones

Balance of power Algorithm Implemented on Limit of generators is applicable test cases to real time cases

[19]

Improved genetic algorithm

Minimization Turbine parameters Method 26 turbines in of water proved to be the three gorges discharge better hydropower applicable plant

Micro-grid with variety micro-generation and renewable resources of energy

Three test cases with 3, 13 & 40 units of generation

(continued)

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Table 1 (continued) References Technique used Objective

Decision Main variable/constraints finding

[20]

Power balance Due to realistic 40-unit generating capacity better Taiwan power searching system capability proposed algorithm is better than normal GA-MU

improved with a feature of multiplier updating genetic algorithm (IGAMU)

Non convex dispatch problem

Test case

which can handle all the system constraints very efficiently. Below is the review of work done by some authors using GA (genetic algorithm) showing its applicability and usefulness. Authors in this paper [21] author applied group-based chaos genetic algorithm for generating a diverse and active neural network for solution of a short term load forecasting. is developed to generate diverse and effective neural networks. In the study following points were concluded: (1) was found that partially connected neural network give better error testing results as compared to fully connected ones, (2) It was found that ensemble technique is more effective to overall increase the performance of the system and ensemble forecaster outclass other member forecasters and (3) Partially connected network may have greater tanning error as compared to fully connected network. For future work author also highlighted the extended version of the proposed algorithm. Lai et al. [22] in this paper load forecasting for a day is performed by using combination of GA and ANN. Author recommended the use of powerful computer for calculation if greater number variable are to be used. The training of the ANN waits is performed by GA and it was implemented on data provided by an Italian power company and was observed that a higher computational time was required for the solution. Author recommended using parallel computation of GA-ANN to reduce the computational time. Wang et al. [23] in this paper author developed genetic algorithm based ANN model using back propagation method. The results obtained by GA-BP were compared with the traditional BP network and it was reported that absolute error in GA-BP was 1.99% and in Traditional BP was 3.86%., i.e. Prediction precession was increased by 1.82%. The relative error gap was also reported to be 5.48% in GA-BP where as it was as high as 11.18% in traditional BP method. Author also reported that size of the sample space for GA should be large so that accuracy of the algorithm can be increased however the method to decide the solution space was not given by the author. In this paper author Upadhaya et al. [24] has applied Genetic algorithm along with ANN model for performing short term load forecasting. Ant colony algorithm is also used by the author for wait updating of the ANN model. For implementation of the

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work a load belonging to Shimla, Himachal Pradesh, India was taken into account and the parameters like precipitation, wind speed and temperatures were also considered. Fore casting was done for a period of six days and remaining 359 days were used for model training. The results obtained were compared with the ANN-ACO (ant colony) & ANN-BP (back propagation) models and was found that GA-ANN gave the much accurate results. In this paper Author Chaturvedi [25] has given solution for a long term load forecasting using improved genetic algorithm. In this algorithm population size, probability of crossover and probability of mutation are varied dynamically. The results obtained by the algorithm were compared with those calculated by CEA (central electricity authority) India and it was found that the curve obtained by the curve is very close to the calculation done by CEA. It was recommended by the author that using the above algorithm will save lot of time and man power. Ray et al. [26] in this paper combination of Artificial Neural Network (ANN) and GA was done to perform load fore casting. An ANN model was developed using back propagation algorithm and was used with the Genetic Algorithm (GA). The proposed model was demonstrated on Xingtai Power Plant in Hebei territory. From the result it can be concluded that GA base Back propagation algorithm is good for short term load forecasting. Sheikhan and Mohammadi [27] in this paper developed a hybrid model for load forecasting. Two models are discussed in the paper ACO (ant colony optimization) with GA (Genetic Algorithm) for selecting the features and MLP (Multi-layer perceptron model) for prediction of load on hourly basis. On application of the algorithm on the different five models for period of 24 h in advance load forecasted load, it was found that the proposed algorithm gives better results than other approaches. The MAPE (Mean Absolute percentage error) for the model was reported to be equal to 1.51, which is very good as compared to other existing method. Pai and Hong [28] in this paper a combination of support vector machines (SVMs) with Genetic algorithm was performed resulting in an RSVGM algorithm. It was for the first time in the history that this type of combination was proposed. This algorithm was proposed to forecast the load in an area. Genetic algorithm helped in finding the free parameters for the support vector machines and the algorithm was applied to the load data of electricity in Taiwan. From the result it was found the method has completely out driven the simple SVM and ANN models. Thus RSVMG was considered to be a reliable algorithm for providing load forecasting (Table 2).

4.3 Distributed Generation Distributed generation is a technique through which we generate power at or near a site where it is required. This setup may be used for lightning of a single building or it can be portion of micro grid. Distributing generation helps in delivering more reliable electricity by reducing the losses in transmission Lines and distribution lines. Thus we can say the in many situations distributed generation are capable of delivering quality

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Table 2 Tabular form of above review work References Technique used

Objective

Decision Main finding variable/constraints

Test case

[21]

group-based chaos genetic algorithm

Short term load fore casting

Distance between two groups

Proposed method significantly reduced the error and is better than ANN

PJM market dataset ISO New England dataset

[22]

Integration of GA & ANN

Short term load fore casting

Max-Min temperature Holidays

GA-ANN are preferred with highly efficient CPU

Italian power system

[23]

GA & BP Forecasting Error of the neural neural network load and network output error

Proposed method has high accuracy over BP network

Random neural network

[24]

GA-ANN-AC (Ant colony)

Short term load forecasting

Maximum generation Minimum error

GA-ANN is better that ANN-BP & ANN-ACO

Indian power system

[26]

GA with BP

Short term load fore casting

Fundamental Masses Chromosome size

GA-based BP should be implemented for STLF

Xingtai Generation Plant, Hebei China

[27]

GA-ACO and MLP

Load forecasting

Climate, month, season, day & time

Proposed method perform better in Mean absolute percentage error (MAPE)

Five (5) simulated models investigated

[28]

support vector Forecasting Forecasting period machines of regional Generations along with load genetic algorithms (RSVMG)

RSVMG outperformed ANN and regression model

Power load data of Taiwan

[25]

Improved genetic algorithm (IGA)

Results were comparable with those given by CEA India

Simulated model was developed

Long term load forecasting

Crossover and mutation probability Population size

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electricity at an economical price. Some common sources of distributing generators are wind, solar, natural gas, etc. which are very environment friendly. Due to the variable demand of the system it is difficult for the system operator to determine the size and location of the distributed generator. For solving such complex problem various algorithms are taken by the researchers which can very easily handle the parameters of DG as compared to conventional techniques. GA (genetic algorithm) is one such approach which has been used bye lot of researchers and has reported very feasible results. Work of few authors using GA (genetic algorithm) has been reported below. Pisic˘a et al. [29] in this paper studied how to decide the optimal location and the size of the distributed generator. A comparative study was made between genetic algorithm (GA) and other nonlinear optimization tools. The author varied the number of DG (distributed generator) units from one to three and found that as the number of units is made equal to three, GA completely outperformed the other nonlinear optimization tools used. The test system was taken as IEEE 69 bus with an objective of minimizing the loss in power and cost of generation and was found that the optimal location of the DG should be at 69th bus with a load of 1500 kw. By placing the DG at 69th bus the losses were transformed from 225 kW to 88 kW. Kashyap [30] in this paper author applied genetic algorithm for finding the optimal location for the distributed generator (DG). For performing the research work IEEE 33 and IEEE 69 bus system were taken into account. On application of GA it was found that optimal location of DG for 33 bus system should be 6th bus with active power loss reduced from 211 to 111.03 KW and for 69 bus system it should be 60th bus with active power loss reduced from 225 to 63.12 KW. Comparative studies were performed for IEEE 33 bus system by applying PSO, IA, repeated load flow & Hybrid approaches. It was found that the active power loss was achieved to minimum level (111.03 KW) when GA is applied. Soroudi and Ehsan [31] in this paper author applied non dominated sorting genetic algorithm (NSGA) for optimal location of DG in a distributed network. The study was performed in a deregulated environment where different demands level and there their duration was also considered in minimizing the loss in active power, cost of investment, cost of operation and environmental pollution. The comparative study was done among the proposed method, PSO, Simulated annealing, Tabu search and ordinary NSGA. From the study it was concluded that proposed algorithm is the fastest among the others (SA, PSO, NSGA (ordinary) & TS) as it took only 7240 s. It was also found that the proposed algorithm provided the highest number (430) of pareto optimal solutions. Som and Chakraborty [32] in this paper author evaluated distributed energy resources (DERs) including a microgrid infrastructure for power delivery in Indian power system by applying tuned genetic algorithm (TGA). Two power scenarios were considered for the study in the paper. Optimal power supply for these two cases was solved by TGA. In the case one, the consumer exclusively operated with optimal supply of distributed energy source where as in case two consumers formed a micro grid with ideal operation of distributed energy source. From the research work it was found that micro grid power distribution system having an optimal process of

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distributed energy source is cheaper. A total of 5.7% reduction in the total cost was reported as compared when the customers are independently operating optimally supplying the distributed energy source. The simulation result also showed that case two provides a total reduction of 19% in energy as compared with case one. A total cost saving of 8759 cost/103 rupees was achieved in second scenario. Sattianadan et al. [33], in this paper author proposed Genetic algorithm approach (NSGA-II) for solution of two objectives: (1) Cost minimization of distributed generator and (2) minimization of power losses. GA simultaneously provides the solution for optimal location of distributed generator and its optimal location. IEEE 33 bus system is taken for the study purpose and the results of GA were compared with VSI (voltage stability index) for different load models. Results were calculated for constant Power, Current & Impedance model and are represented in tabular form, proving that NSGA-II is better approach for all the three models. Ganguly and Samajpati [34] in this paper author used Adaptive genetic algorithm approach for allocation of DG and on load tap changer in a distributed radial network. Two adaptive AGA are proposed and are compared with some existing AGA approaches. For demonstration of the result they were tested on 69-bus DN and a 52 bus Indian network. Three different mode of DG were considered in study, considering it running at leading, lagging and unity power factor. In this Adaptive approach author varied the probability of crossover and mutation operator and was found that the new approach gave good result ac compare to other adaptive genetic algorithms. On multiple simulation runs were conducted to prove that the combined operation of DG with OLTC is better approach and also a cost effective one. Need of the expansion of the existing model was also proposed by the author as the future work. Yang and Chen [35] in this paper author studied the maximum capacity up to which we can connect distributed generators to the distributed power grid. For the solving the problem author applied dual genetic algorithm (DGA) approach. The results of the paper show that current methods will result undefined output because of various real time working conditions. The cases present in lower and upper range may result a bad decision regarding the interconnections. For solution of this DGA method is adopted by the author who responded well with the undefined problems of the system. It was also found that this method can very well be used for fast selection of the distributed generator and proposed efficient DG connections (Table 3).

4.4 Unit Commitment Problem It is one of the utmost complex and critical optimization problems of Modern power system with the constraints of forecasting of load and variable spin reserves. The main reason behind conducting unit commitment research is balancing the load demand with generation with optimization of available resources and its cost. Broadly the unit commitment problem can be categorized into three types: traditional UC problem, security based UC problem and UC problems considering cost minimization.

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Table 3 Tabular form of above review work References Technique used Objective

Decision Main finding variable/constraints

Test case

[29]

Genetic algorithm

Determining Size and optimal location of DG thus reducing cost and power loss

State variable and control variable Bus voltage Power limits

Distribution network of IEEE—69 bus system

[30]

Genetic algorithm

Minimization Voltage limit of active Thermal limits power loss DG limits

[31]

method Active loss Non-dominated minimization Sorting genetic algorithm (NSGA)

Available DG units Operating limits of DG Power demand level

Proposed Test Feeder algorithm is system fastest among PSO, SA, NSGA(ordinary) & TS

[32]

Tuned genetic algorithm (TGA)

Evaluation of DERs (distributed energy sources) of a system

Optimal planning of DERs Max-min limits of DG & BESS

Using proposed algorithm a reduction of 5.7% in Annual cost is achieved

[33]

NSGA-II

Optimal Size of DG Both objectives placement of Voltage at each bus of the problem DG for are satisfied reducing the power losses and DG cost minimization

Distribution system with 33-busses

[34]

Adaptive genetic algorithm

Planning of DG integration to distribution system

Bus voltage limit Thermal constraints Capacity of DG power Tap setting of OLTC

Combinational approach of DG & OLTC is beneficial

Indian 69 bus and 52 bus distribution system

[35]

Dual genetic algorithm

Study on maximum capacity of distributed generators

Feeder and transformer limit Limits of generation

Deterministic approach will give uncertain result so use of DGA is must

Taiwan power distribution network

The method proved to be valid for DG location

GA reduced the IEEE- 33 & active power 69 Bus loss to minimum system level

Indian micro grid delivery system

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Many algorithms have been developed by the researches and some are still working on it for developing feasible solution to unit commitment (UC) problem. In this section review of few paper in which UC (unit commitment) has been solved by the GA (genetic algorithm) has been listed. It can be seen that GA has taken care of all the system constraints well and have provided a reliable solution. Performance of hybrid versions of GA (genetic algorithm) are also been listed. Roque et al. [36] in this paper author applied biased random key GA for solving unit commitment problem. In BRKGA approach the encoding of the solution is done by random keys presented as vectors for interval between [0, 1]. The algorithm was applied to the system having 10, 20, 40, 60, 80 and 100 units having a scheduling time of 24 h. The results obtained shows that current algorithm is better than that of the other methods used for solving large commitment problems. The author also quoted that for avoiding low quality of solution the difference between best and worst solution should always be less that 0.30% and that between average and best solution should be below 0.11%. Paranjothi and Balaji [37] in this paper author incorporated hybrid genetic algorithm using priority order scheme for solution of unit commitment problem. The proposed algorithm along with simple GA and priority list commitment was applied to the different test systems having: 5 Units, 10 Units and 26 Units. From the results it was found that as the number of units were increased from 5 to 10 and 26 unit, a significant difference between proposed algorithm and to be compared algorithms is clearly visible. The cost comparison between all the three methods is also calculated by which it can be seen that proposed algorithm is the most economic one out of the three methods. Senthil Kumar and Mohan [38] in this paper author discussed OPF method for a Indian power utility system. author divided the study into two parts, here the outcomes of part one i.e. unit commitment studies are presented. The results were taken on considering 12 generation units and 96 lines for the transmission in an Indian system. Five units were taken into consideration with a total reserve of 10% of the total demand. Algorithm was run for 20 times with a population size of 50 every time. The results obtained were compared with the LR an GA (without line constraints) and was found that proposed algorithm is comparatively more efficient and reliable. Reddy et al. [39] in this paper author has solved unit commitment by dividing generating units into different clusters. A new Genetic algorithm approach in which feature of additive cluster and divisive cluster are incorporated with it has been used for solving the problem in the presented work. The additive cluster was used for the increasing load patterns and divisive cluster was used for decreased load. A thermal plant having 10 units was simulated in the paper and was found that the result obtained was effective and satisfactory. Swarup and Yamashiro [40] in this paper author has applied conventional Genetic algorithm for solving unit commitment problem. The programmed formed for genetic algorithm was implemented in “C” language. The constraints of up and down time of units were handled nicely by the proposed algorithm. A test system to 10 generators was taken in the study and was run for 300 iterations. Computational time of

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73.68 s was reported when probability of mutation was 0.03 and crossover was 0.8. Feasibility of solution at every stage is reported in the results with spinning reserves taken as one of the objective for the minimization. Senjyu et al. [41] in this paper author proposed a new genetic approach for solving unit commitment problem for large thermal units. The new algorithm is based up on unit integration arrangement and unit characteristic arrangement the simulation was done for the units 40, 60, 80 and 100 for a period of 24 h. 20 test trial were run with a population size of 20 every time. From the result it was reported that total calculation time was reduced up to 99% to 99.5% and the total cost was reduced to 0.2 to 0.13%. It was concluded on the basis of result that proposed algorithm provides satisfactory results in quick time. Kadam et al. [42] in this paper author proposed a hybrid algorithm having Genetic algorithm and fuzzy logic applied together for solving short term unit commitment problem for a thermal station. A comparative study between GA and Priority list method was made and it was found that GA provides better results as compared to the priority method. Results of solving the problem using fuzzy logic are also highlighted by the author showing its own importance. Bedekar [43] in this paper author developed a program in MATLAB for soling unit commitment problem considering a thermal power plant. The developed program was tested for different problems having various units and modified operating limits. Unit commitment problem which is full with constraints is reduced to non-constraint problem defining of new fitness function. Two different cases with three and two units were solved for showing the validity of the approach. Author also prepared a unit commitment time table for dissimilar plant load which helped in deciding shared load by each unit in priority (Table 4).

5 Some Other Application of Genetic Algorithm Apart from the above discussed topics, GA (genetic Algorithm) can also be used for the solving of: Congestion management: With a shift of paradigm from regulated to deregulated markets congestion in the power system has become a hot topic. To mitigate this problem of congestion various researchers have applied GA (genetic algorithm) and have reported good results, indicating its applicability. Anusha Pillay with the co-authors has developed a research work [44], indicating various power system problems that can be solved using GA and other methods. Author has reviewed more than 50 papers for this work. Energy management of Hybrid Vehicles: Genetic algorithm can be of great use when it comes to optimization problem. Optimization of hybrid fuel cell for management of energy in new electric vehicles is one such domain where it finds its good application. Lü [45] along with the co-authors has done a review work in this field

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highlighting the application and future scope of this algorithm. more than 120 papers are been reviewed by the authors. Load Shedding: In the last few decades the problem of black out in power system is been noticed around the globe. This has affected both generators and consumers Table 4 Tabular form of above review work References

Technique used

Objective

Decision variable/constraints

Main finding

Test case

[36]

Biased random key GA (BRKGA)

Schedule energy production of the thermal Units for cost minimization

Balancing poser and maintaining spinning reserves

Result shows proposed method is better than that of current state art

Large test System of 100 units for period of 24 h

[37]

GA using Priority list

Minimization of startup cost and shut down cost

Up- Down time of unit Satisfy demand Max-min capacity of units Spinning Reserves

Proposed algorithm provided optimum operating cost

Test systems with 5, 10 and 25 Units

[38]

Genetic algorithm in which only feasible solution were taken in sample

Minimization of fuel and startup cost

Min. Up- Down time of unit Spinning Reserves Power Balance Start & Shut down cost

Proposed GA 66- Bus produced Indian better result system as compared with GA & LR

[39]

GA with cluster algorithm

Minimization of fuel cost and Startup cost

Min. up-down time of unit Spinning Reserves Ramp rates Generators limits Demand

Proposed algorithm was effective and satisfactory

10 to 100 thermal generating units

[40]

GA program Optimization in C of spinning language reserves

Up and down time Startup cost Spinning reserve

Objective function is converged

10 Generating units

[41]

GA and fuzzy logic

Unit commitment of thermal unit for short term

Spinning reserve Load Balancing generation limits

Method guarantees the solution

8 thermal unit over a period of 8 h

[42]

GA, with new fitness function IC and Load balance

Cost minimization of generation

Power balance Generator limit

Program tested on various tests and gave accurate results

3 thermal units studied for two different cases

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causing a great monitory loss. Authors has also reported various major black outs of the history. Conventional load shedding techniques, their limitations and introduction of new AI methods are reported in the paper. Authors have done a review work [46] in which they have highlighted the application of GA along with other techniques. Optimal Power Flow: OPF is a very complex tool for control and optimal operation of the power system. Due to its high complexity it is very difficult to solve OPF problem by using traditional methods. So to handle the complexity of the problem researchers have used heuristic algorithms. Genetic Algorithm (GA) is one such technique which has drawn attention of the researchers. A Review work on GA application in OPF has been done by Ming NIU and co-authors [47], highlighting the contribution of researchers. Authors have reviewed more than 70 papers in the review work. Assigning Hybrid System for remote areas: With the continuous increase in demand of energy around the globe, the renewable energies have drawn great attention of the researchers. But before installing a renewable energy generating plant there are several decision that need to be made for so that it can supply easily to the target area. A review work on optimization of stand-alone hybrid energy system, working on renewable energy is done by Fadaee and Radzi [48], where they have used different evolutionary algorithms. GA (genetic algorithm) is one such algorithm which authors have reviewed in the paper, showing it application and future scope. More than 50 papers were reviewed by the authors.

6 Conclusion The paper presented a general review of Genetic Algorithm in power system, highlighting the importance of GA in various domains. It is clearly visible from the review work that GA (genetic algorithm) has regularly been applied by the researchers due to its robustness and constraints handling capacity. The GA (genetic algorithm) has constantly proved itself better that other traditional operating techniques and sometime even better that other EA (evolutionary algorithms). This work will help researchers to know about the application and opportunists present in GA (genetic algorithm) for its application in power system. Due to its large computational time GA (genetic algorithm) lags behind other approaches so by using better convergence modes computational time may be reduced. However the large computational time of GA (genetic algorithm) is constantly getting better with the advancements in the computers generations. As we know that in GA (genetic algorithm) the evaluation of fitness of each string (chromosome) is independent process it can be done in parallel for every string thus a reduction in operating time may be achieved. So researches may search for a technique through which this parallel operation is feasible. One of the current reproduction operators (Mutation) of GA needs to be modified or replaced with some other operator. As in case of mutation there is possibility of solution might lose

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some very important information. Some new notations may be used to represents the chromosomes in the population as binary representation some time finds difficulty in solution. Better constraint handling techniques may be introduced by the researcher so that more complex problems can be solved using GA. Furthermore emphases should be given on developing of a hybrid algorithm by fusion of GA with other algorithms.

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Different Variants of Particle Swarm Optimization Algorithms and Its Application: A Review Ayush Mittal, Amruta Pattnaik, and Anuradha Tomar

Abstract Particle Swarm Optimization (PSO) algorithm is an evolutionary development in the field of Artificial Intelligence and computational technique. This technique has grasped the attention of various researchers and scholars in a very short span in comparison to other old techniques, such as—Genetic Algorithm, Evolutionary programming, etc. existing since the 1960s or even before. The review chapter focuses on the brief information about how PSO has evolved since 1995 and the perception about the motivation behind the development of the PSO algorithm. The early modifications to the original form of the algorithm and alteration in the equation are also discussed along with the different types of PSO(s) and their hybrids. Also, the chapter gives an insight into various applications of the PSO and some of the application specified hybrid (or modified) PSO techniques. Based on the state-of-art, discussion on performance comparison of the hybrid (or modified) PSO is also presented in this chapter. It is concluded that the application of objective specific is more fruitful as compared to the implementation of standalone PSO. This chapter could present an interesting brief insight into the researchers working in the field of PSO. Keywords Artificial Intelligence (AI) · Optmization · Particle Swarm Optimization (PSO) · PSO Techniques

A. Mittal (B) HMR Institute of Technology and Management, New Delhi, India e-mail: [email protected] A. Pattnaik Dr. Akhilesh Das Gupta Institute of Technology and Management, Delhi, India e-mail: [email protected] A. Tomar Eindhoven University of Technology, Eindhoven, The Netherlands e-mail: [email protected] JSS Academy of Technical Education, Noida, India © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_6

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1 Introduction Unlike traditional search algorithms or techniques, the computational technique developed, Particle Swarm Optimization, abbreviated as PSO, has evolved enormously since 1995 and grasped the attention of various researchers and scholars in comparison to other popular techniques such as GA, present since the 1960s. The motivation for the development of four well-known algorithms or/and computational techniques—Genetic Algorithm (GA), Evolutionary Programming (EP), Evolution Strategies (ES), and Genetic Programming (GP)—is the evolution of nature, whereas the inspiration and inculcation of the idea for the development of PSO is the result of the nature, action, and behavior of the socially active biological creatures, such as—Animalia or/and birds [1, 2]. Thus, the two important methodologies that are inculcated in the PSO are—Artificial Intelligence and Swarming Theory related to a flock of birds, fish schooling, or ant colonies. The optimization and computational technique PSO is nearly equal and comparable to the 1960s GA. However, unlike GA, the process of selecting any single particle from the swarm is not carried out in the PSO and the accumulated particles during the process are held on and kept throughout the run (run is defined as the generations of evolutionary technique before termination) which makes it differ from other optimization and computational techniques mentioned [3, 4]. With numerous ongoing research on PSO, it has been modified tremendously and different applications are notified in various fields such as—medical, logistics, power system stability, hybrid and plug-in electric vehicles, processing of metals, scheduling of workflow, civil infrastructure, designing of the micro-grid system with an optimum generation of the electric energy and decreased cost of energy, etc. The review chapter is divided into various sections. Beginning with Sect. 1, which gives brief information about how PSO has been evolved since 1995. Section 2 gives the perception about the motivation behind the development of the PSO algorithm, followed by Sect. 3, which highlights the algorithm, along with the early modifications to the original form of the algorithm and equation. Section 4 deals with the study of different types of PSO(s) to improve the optimization process and especially focuses on the hybrid models of PSO. Finally, the chapter ends with Sect. 5, which depicts the various applications of the PSO and hybrid (or modified) PSO techniques.

2 Background of Particle Swarm Optimization An American Electrical Engineer, Russell C. Eberhart, along with an American social psychologist, James Kennedy, studied the behavior, actions, and nature of social organisms residing and/or traveling in the swarm (or flock) such as—birds, shoaling or/and schooling of fish, colonies of ant, etc. In the early 1990s, the researchers Eberhart and Kennedy first observed and studied the behavior and action of the birds searching for food and analyzed some unexpected changes in the flight, flying

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pattern, and velocity. Also, the flying group was often concentrated or scattered and changed the directions instantly without altering the positions in the group, thus keeping the flying formation intact [5, 6]. From the detailed analysis of the flying group, they concluded that - the flight of bird’s swarm has almost constant velocity, along with the reasonable distance between each bird. After studying and thoroughly analyzing the behavior and action of other socially active animals such as—fish, ants, etc. they summarized the rules and established the fact that the information has been shared continuously among the dispersed biological groups flying high in the air. After making the swarm analysis as a base, the researchers raised the concept of the PSO in 1995 and presented the first-ever research article [7]. The first research simulations of the PSO by Eberhart and Kennedy in 1995 was influenced by the 1990s work of Frank Heppner and Ulf Grenander [8]. However, the computational technique and optimization algorithm PSO is a relatively newer concept, and unlike a genetic algorithm (where a single individual is considered for computation), a group (or swarm) of individuals is considered for the computation.

3 Algorithm of Particle Swarm Optimization The PSO relatedness can be sourced from the basic model, Boid (Bird-oid) Model, developed by Reynolds [9] after studying the behavior of the birds [10, 11]. The effortless and elementary model of the PSO can be explained based on the bird’s swarm as—Each discrete and independent, a bird in the population (or swarm) flying can be assumed as a point in the Cartesian Coordinate System and each point is assigned a random place in the space, having their trajectories with two important vectors, namely initial velocity and initial position as well as it updates the trajectory constantly while moving in the search space. The methodology acquired by the birds in the swarm to reach the destination is the matching of the position and velocity of the nearest possible neighbor [12]. The PSO algorithm can be analyzed in detail using the Heppner’s “roost (a known place of birds) model” as a base. The Eberhart and Kennedy replaced the ‘roost’ with the ‘food’, presuming that there was food (cornfield) located on the plane and the birds were individually dispersed randomly in search of the food at the beginning. Also, it assumed that birds have the memory to retain the directions and the ability to memorize the best path traversed in search of food (or cornfield) to reach the destination. The ideology behind this variation was to let birds search for the unknown place through confidence in self and dependency on other’s knowledge. At this point, one of the important quantity is defined which will be used in further equations which are often termed as—Particle best (pbest), defined as the best possible position (fitness point) visited by the bird individually, since the beginning in the search for pbest (t). The next quantity is termed as—Global best the food. It can be denoted as xi (gbest), defined as the best possible position (fitness point) visited by the swarm (or gbest (t) [8, 13]. population) as a whole in search of the food. It can be denoted as X i

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The exploring area dimensionality, D, is used to define each bird (which is considered as a particle) in the swarm. Three D-dimensional vectors termed as—particle’s present (or live) position (denoted as, xi ), the former finest (or foremost) position of pbest the particle (denoted as, xi ) and the particle’s velocity (denoted as, vi ) are utilized to describe the particle. The movement of these particles is stochastic but is highly influenced not only by their memories but also with the memories of its peers. With each iteration, the particle’s new position (or present position), xi is computed and pbest . If the evaluated position compared to the former finest position of the particle, xi is loftier in contrast to the former finest position than the newly obtained value (or pbest [14, 15]. position) replaces the previous value stored at the vector xi The particle’s movement in the exploring area is determined and governed by the three major forces acting over it. These three forces can be defined as the three components of the iteration, which are termed as—momentum, cognitive, and social. The first force is Newton’s First law of motion, termed as ‘inertia’ and is defined as the tendency to remain unchanged and resisting any change in the direction or velocity if the object is moving. This keeps the particle moving in the same (or present) trajectory and can be termed as the momentum component. The second force which influences the motion of the particle and attracts towards itself is the gbest . This can be termed as the cognitive component. The Global-best, denoted as X i third and the final force which also attracts the particle towards itself is the Particle’s pbest , and the component which could be inferred from this is the best fitness point, xi social component [16, 17]. The initial mathematical equation can be derived by assuming that—at time t, the ith particle’s current position is xi (t), traveling with the velocity of vi (t). Also, let the pbest ith particle’s former finest position is xi (t) and swarm’s best location memorized gbest by the ith particle is X i (t). The following rules can be mathematically expressed as: pbest , then if, xi > xi

pbest

else if, xi < xi

vi = vi − (k ∗ α)

(1)

vi = vi + (k ∗ α)

(2)

vi = vi − (k ∗ β)

(3)

vi = vi − (k ∗ β)

(4)

, then

Similarly, gbest , then if, xi > X i

gbest

else if, xi < X i

, then

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where, k is the random number (or, constant) which lies in the range [0, 1] and both α and β are velocities adjusting constants for the particle velocity as individual and particle velocity in the swarm, respectively. Also, the system imitation results showed the importance of the ratio α/β, i.e. if it is relatively large, then the individuals will be attracted and gathered at the desired position (or a cornfield in this case) quickly, whereas if the ratio is small then the gathering will be slow and unsteady. Inspired by these outcomes, the following generalized form of PSO algorithm derived by Eberhart and Kennedy can be mathematically expressed as       pbest gbest v i (t + 1) = v i (t) + σ1 ∗ k ∗ xi (t) − xi (t) − σ2 ∗ k ∗ X i (t) − xi (t)

(5) x i (t + 1) = x i (t) + vi (t)

(6)

where, σ1 and σ2 are the constant parameters depicting the particle’s confidence in itself, which can be termed as cognitive coefficient and particle’s trust on the swarm, which can be termed as a social coefficient, respectively. Also, t denotes the time step (or, one can define it as iterations). Also, Eq. (5) showcases the three forces which were defined earlier as follows: Momentum Component (1st term) vi (t)   pbest Cognitive Component (2nd term) σ1 ∗ k ∗ xi (t) − xi (t)   gbest Social Component (3rd term) σ2 ∗ k ∗ X i (t) − xi (t) Performing numerous hit and trials method, Eberhart and Kennedy obtained the value of both the coefficients in Eq. (5), σ1 and σ2 as 2 (mathematically, σ1 = σ1 = 2) following which the original equation presented can be mathematically expressed as:       pbest gbest vi (t + 1) = vi (t) + 2 ∗ k ∗ xi (t) − xi (t) − 2 ∗ k ∗ X i (t) − xi (t) (7) x i (t + 1) = x i (t) + vi (t)

(8)

PSO algorithm was formulated based only on the particle’s velocity (or speed) and position as Eberhart and Kennedy assumed the individual particles to be without any mass, volume, or any other constraints. The basic and original PSO algorithm as defined above can be summarized as given below along with the flowchart [11] (Fig. 1).

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1. Initialize the particle(s) of the swarm with arbitrary and indiscriminate constraints—positions and velocities—on the D dimensions in the exploring area. 2. Loop a. For every single particle, evaluate the appropriate and best suitable optimization fitness function at a time ‘t’ in D variables consisting of the particle’s— pbest , and the velocity, present (or live) position, xi (t), former finest position, xi vi (t). b. Determine the constants—σ 1 , σ 2 and k pbest ; if the c. Equate the particle’s position determined in part (a) with its xi pbest calculated value, xi (t) is superior in comparison to xi , then dispose of pbest the previous xi and set it equal to the newly calculated value (xi (t) → pbest xi (t)) pbest d. Recognize the neighboring particle and equate all the xi and assign the gbest best success so far to the global best, X i . e. Modify the swarm’s particle constraints in obedience to the Eqs. 5 and 6 as depicted below:    pbest vi (t + 1) = vi (t) + σ1 ∗ k ∗ xi (t) − xi (t)    gbest − σ2 ∗ k ∗ X i (t) − xi (t) x i (t + 1) = x i (t) + vi (t) f. If the criterion is satisfied, i.e. relatively superior fitness is achieved or reached the ceiling of iterations, leave the loop. 3. End Loop The optimization algorithm and initial equation was new in the computational field but was not a very effective version of the algorithm and is still the subject of the amendment. In 1996, Eberhart et al., slightly modified the velocity expression by introducing the parameter V max , to bound the particle(s) velocity and increase convergence rate further preventing them from leaving the exploring area [18]. Later, in the year 1998, Shi and Eberhart presented the new modified PSO algorithm which was termed as canonical PSO algorithm. The introduction of a parameter termed as—Inertia weight, ω, was meant to eliminate the limitation of V max , i.e. restricting the global exploration capability. The widely used modified version of the PSO Algorithm is mathematically expressed as [19]    pbest vi (t + 1) = [ω ∗ vi (t)] + σ1 ∗ k ∗ xi (t) − xi (t)    gbest − σ2 ∗ k ∗ X i (t) − xi (t)

(9)

x i (t + 1) = x i (t) + vi (t)

(10)

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Fig. 1 Original particle swarm optimization algorithm flowchart Wang et al. [10]

It is found that if the value of the ω is slightly increased than 1, i.e. ω > 1, then the particles will resist the convergence to the finest positions known and will be inclined to traverse and explore the unknown. But, increasing ω beyond the considerable value will make the swarm unstable and oscillatory. On the other side, if the value of ω is slightly decreased than 1, i.e. ω < 1, then the particle will perform the exploration and it will remain inside the search space. However, decreasing ω beyond the considerable value will make the swarm deplete and particles will prefer their own previous best position, and the system will be more exploitative. Initially, Shi and Eberhart suggested the range of ω as [0.9, 1.2] appropriate and later found that the linearly reducing ω during the run from 0.9 to 0.4, has been efficient and giving an enhanced performance in several applications. Thus, the introduction of inertia weight, ω resulted in the escalated efficiency of the PSO algorithm. However, the value selected of the ω will determine the swarm’s capability of exploration (by increasing the global search space) or the swarm’s exploitation (by limiting and minimizing the search ability to local search space) along with the stability of the system. Also, the value of both the coefficients, σ1 and σ2 will determine if the pbest or towards particle will accelerate towards the previous particle best position, xi gbest the global best, X i , respectively. Later, in the year 2002, Clerc and Kennedy analyzed PSO convergence and established the fact that the constriction factor was necessary to ensure convergence but it was not necessary to bound the velocity with the parameter V max , as there were various other ways by which it could be implemented. In 2002, they proposed a modified version of the equation with a constriction factor, ψ and incorporated it as follows:     pbest vi (t + 1) = ψ ∗ vi (t) + σ1 ∗ k ∗ xi (t) − xi (t)    gbest − σ2 ∗ k ∗ X i (11) (t) − xi (t) x i (t + 1) = x i (t) + vi (t) where, σ = (σ1 + σ2 ) > 4 and

(12)

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ψ=

2 √ σ − 2 + σ 2 − 4σ

(13)

The constriction factor, ψ > 0 and prevents the explosion behavior thus divergence of the particles of the PSO without any bounding velocity factor, V max [20]. However, the experiments resulted in the fact that the constriction factor, ψ, didn’t eliminate the parameter, V max . The importance of the inertia weight, ω and constriction factor, ψ in the PSO is significant and can’t be neglected, but it is to be highlighted that both of the factors, i.e. ω and ψ are algebraically equivalent and can be used interchangeably with proper parameter setting. The equations can be modified and converted into one another by mapping ω ↔ ψ and σi ↔ (σi ∗ ψ). Thus, the optimal value for the parameter of PSO with inertia weight as put forwarded by Clerc are—ω = 0.7298 and σ1 = σ2 = 1.49618 [21].

4 Different Forms of PSO Techniques PSOs have their own merits such as easy to implement, robust, fast converge, and short computational time, and effective for solving problems. On the contrary, the demerits of PSO are as follows i.e. hard to describe initial design parameters, scattering issues, premature converge and optimization is difficult in complex problems. It is reported in one of the literature that PSO could be designed by keeping the particle position as well as velocity bounded within the area to be searched. In that case, PSO had only two variants, i.e. with and without the fastened velocity and three variants of the inertial weight, termed as—linearly decreasing, constant, and custom controlled. Controlled particle constraints—velocity and position—and faster convergence rate in comparison to standalone PSO are the two prominent advantages of this modified PSO algorithm [22]. To improve the local search capability, hybrid PSO was recommended in one of the literature [23]. PSO is the base for the improved hybrid PSO algorithm and also used to set the particle’s velocity and position. Tabu search approach was also introduced to avoid repeated access. It improved search efficiency. The tabu search algorithm uses the guided local search operation to control the plant position because it shuns the local optima and discards the swapping of points [24]. While dealing with multimodal optimization difficulties, PSO easily drops into local minima due to the integral arbitrariness of PSO. PSO performance is raised by using the adaptive parameter control technique on multimodal problems as presented by Wang [25]. It is to be noted that PSO performance is highly governed by its control parameters. So the use of adaptive technology can lead to lessen the dependency of the parameters. There are diverse types of techniques that have been designed for the optimization process based upon the particle velocity, design, sampling, and population to improve the performances [26].

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The following sub-sections give a brief insight into some of the modified PSO techniques.

4.1 Radius Particle Swarm Optimization (R-PSO) PSO’s premature convergence is one of the crucial disadvantages during the optimization of complex and complicated problems. Anantathanavit et al. [27] proposed Radius PSO (R-PSO), defined as an improvised PSO by reforming the agent particles inside the predefined diameter (or area) of the ring. It registers and prepares the record of particles, evaluates the suitability function along with the discovery of the finest particle in the prepared record. It also developed the group named swarm to save the range and progress of the swarm by the distribution of data from the agent particles which efficiently sustained the stability among the global exploration and the local exploitation [27]. The finest particle in the group named swarm is represented by abesti,j which was assigned by an agent as shown in Fig. 2a and among the agent best particles, the optimal solution found and named as gbest position is depicted in Fig. 2b. So, the distance among particles in the radius neighborhood was calculated by the below equations: 

d p i , p∅



  m  2 = p i, j − p∅, j ; d ≤ 2r

(14)

j =1

r = μvmax; μ[0.1, 0.9]

Fig. 2 Best agent particle abesti,j in swarm group (a) and finding of gbest by abest (b)

(15)

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where, d P Ø ji m r μ vmax

length between the particles, particle in exploring area; the dimension of a particle, key location in the particle (j = 1, m); size of the vector, radius of the area, constant (μ = [0.1,0.9]) the indicated maximum range of velocity.

The main aim of the RPSO was to discover the optimum answer by the agent particle abesti,j which was a radius local optimum as expressed in the below equation: abest i, j = minβ∅ f (β)

(16)

where f (β) is the function of fitness β: key of a particle in the radius neighborhood (β = 1, 2, …, f). So the velocity equation was  vi, j (t + 1) = w ∗ vi, j (t) + c1 ∗ R1 pbest i, j − x i, j (t)  + c2 ∗ R2 abest i, j (t) − x i, j (t)

(17)

R-PSO has the advantages of reforming the particles contained by a specified range and finds the agent particle (finest particle of the collection) for each local optimum. However, it was able to retain a proper swarm variety, seeking of the local optimum using the agent particle to accomplish the global optimum. As per the report, it was suitable to solve the optimization of complex problems.

4.2 Weighted PSO (WPSO) Algorithm According to Dhivya et al. [28], the Weighted PSO (WPSO) algorithm is capable to generate optimal test factors as well as reduce test size. It is useful to estimate the finest location of the particle by adding weight. The enhanced system efficiency accomplishes the high exposure of the units. The WPSO method was mainly applicable for multi-objective optimization in reported work [28].

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WPSO was a hybrid of the PSO algorithm with a weighting tool as reported by Hao et al. [29]. Three different finding techniques were introduced. Those are both non-uniform and differential mutation operator. The third one is a local arbitrary exploration technique. Those are utilized for mitigating the disadvantages of PSO as well as to mutate the global finest location. WPSO becomes cooperative to get a further better explanation. The behavior of WPSO is not only lessening the early convergence but also retain the stability among the local and the global exploration [29].

4.3 Hybrid Evolutionary Algorithm Based Particle Swarm and Artificial Bee Colony (PS-ABC) Wang et al. [30] presented a hybrid of PSO and artificial bee colony (ABC) optimization methods. The suggested PS–ABC algorithm was verified at IEEE-CEC 2014 race. It was a very effective and strong optimization method for resolving highdimensional optimization problems. There were three different phases in PS–ABC. Those are as follows: start, repetition, and last phase. At the start phase, values and keyspace were provided to several variables. The measurement parameter was adapted from an artificial bee colony algorithm i.e. pbest Measure, as well as two new control parameters were introduced i.e. Limit 1 and Limit 2 for the controlling process. However, a certain number (N) of keys were generated subjectively in the keyspace. During the stage of repetition, the iterations were executed until the terminating criteria matched. If the conclusion conditions achieved, the algorithm executes the last stage to yield the finest answer (gbest). Otherwise, the repetition phase was repeated. Following Fig. 3 depicts the PS-ABC algorithm: The PSO’s exploitation capability was used in the proposed algorithm to get the finest key as well as to increase the convergence factor of the algorithm.

4.4 Modified PSO Algorithm Using Uniform Design (MPSOUD) In 2016, AL-MTER et al, introduced an algorithm, termed as—Modified PSO using Uniform Design (MPSOUD) to resolve and curb the disadvantage of PSO’s randomness and time [31]. According to [32], the Uniform Design was the key to the randomness issues whose objective to distribute the searching points evenly in a test area AL-MTER et al. mentioned the particle’s velocity at its personal finest and global position is given by,

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Fig. 3 The PS-ABC algorithm. Adapted from Li et al. [30]

 (t) (t) v(t+1) = wv(t) p p + u1 ∗ c1 pBest p − x p  (t) + u2 ∗ c2 g Best (t) p − xp

(18)

where the p represents particle no., t: iteration number,w: inertial coefficient (0.8 ≤ w ≤ 1.2), and constants c1 and c2 whose value equals 2 (c1 = c2 = 2), particle’s and swarm’s best solution are p Best p(t) and g Best p(t) , respectively. The uniform designs are defined as u1 and u2 as follows:  u1 = iσ j −1 mod pBest (t) p +1

(19)

 u2 = iσ j −1 mod g Best (t) p +1

(20)

where i is the combination of the all j number of levels of pBestp .σ can be selected by the user.

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MPSOUD algorithm had four steps to execute the algorithm: Step 1: Firstly estimate the suitability for each particle Step 2: In the second step it informs individual and global particles for best fitness and positions. Step 3: Thirdly keep informed about the particle’s location and velocity. Step 4: Steps 2&3 are made to run in loop until terminating conditions found (or satisfied). MPSOUD provided good stability, global convergence as well as less execution time.

4.5 Adaptive Particle Swarm Optimization (APSO) One more disadvantage of PSO is the problem of clustering. So, Dashora et al. [33] recommended an adaptive PSO (APSO). It resolves the data clustering problem by scattering the preliminary swarm with a fuzzy function which makes the presentation in a better manner. The fusion of PSO with fuzzy logic could provide better outcomes. The clustering process is having the pre-knowledge of preliminary cluster centers. The clustering response becomes true and resourceful. The advantage of this method is to increase the convergence speed [33]. It was proposed to use fuzzy function and swarm optimization function in PSO data clustering which avoids PSO from early convergence. As a result, the final data was accurate. Figure 4 shows the flowchart of APSO:

4.6 L’evy Flight PSO (LFPSO) The stochastic approach of the PSO is utilized to resolve the complex non-linear optimization difficulties. But, this faces shortcomings like—sluggishness and slow convergence, which can be overcome by L’evy Flight PSO (LFPSO) as reported by Gupta et al. [34]. The two exploration methods, global search, and local search are utilized in this algorithm. Exploration of the area is performed by the former method and the exploitation is achieved by the latter. The algorithm proposed can be used to resolve difficult optimization issues. Hybrid of L’evy Flight local search (LFSS) and PSO improved the PSO’s local exploring capability. The suggested algorithm is depicted in Fig. 5. The strength, precision, and effectiveness of the suggested algorithm was verified over 10 well-known experiment complications and founds the effectiveness of PSO as matched to standard PSO 2011.

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Fig. 4 The flowchart of APSO problems. Adapted from Dashora et al. [33]

4.7 Krill Herd and Quantum Acted PSO [KH–QPSO] A unique hybrid of Krill herd (KH) and quantum acted PSO (QPSO), termed as— [KH–QPSO] was designed for optimization [35]. It helped to develop and improvise the capability of the local exploration along with premature convergence. It was helpful for discrete and continuous optimization problems. When the krill was involved in the local finest explanation, it was in the zero capability form of skipping out of local minimum in the typical KH method. To reduce the errors in optimization, the KH method was hinged with the QPSO algorithm to generate a fresh method named KH–QPSO. The location of a krill is divided into three sections such as: 1. Other krill involved with their movement; 2. Searching action; 3. Physical diffusion.

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Fig. 5 The LFPSO algorithm. Adapted from Gupta et al. [34]

Whereas that PSO can discover the absolute finest response if each particle could determine its local finest solution by trajectory study, pi = (pi1 , pi2 , …, piD ) defined as follows: p i (k) = ϕ p i (k) + (1 − ϕ) p g (k)

(21)

where, ϕ is an arbitrary number in (0, 1). The location in QPSO for an individual particle, is defined as x i (k + 1) = p i (k) ± α|C(k) − x i (k)|ln

  1 u

(22)

where, α is the narrowing–enlargement coefficient and u is an arbitrary number in (0, 1). Average best position C(k) can be calculated by the average value of Pi : C K = (C 1 (k), C 2 (k), . . . , C D (k))   M M M 1 1 1 p (k), p (k), . . . , p (k) = M i=1 i1 M i=1 i2 M i=1 i D

(23)

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Fig. 6 Steps to execute the KH-QPSO for optimizing the problem. Adapted from Wang et al. [35]

The steps are explained in Fig. 6 to execute an optimization problem. The KH–QPSO method provided a better way of control over convergence and performance. It can solve more difficult engineering optimization problems.

4.8 Memetic PSO Algorithm to Solve Multi-objective Optimization Problems (MoMPSO) Xin et al, reported in 2017 regarding a methodology to resolve and evaluate the multiobjective optimization problems. It expanded the searching for optimal answers like convergence speed, coverage, and uniformity [36]. So the algorithm is presented in Fig. 7.

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Fig. 7 Steps to execute the MoMPSO Problem. Adapted from Li et al. [36]

MoMPSO improved the restriction of particles dropping into local optimal solutions; discovering additional optimum keys in terms of convergence, spread, and consistency. It was useful for high dimensional multi-objective problems.

4.9 Hybrid PSO and Grey Wolf Optimizer (HPSOGWO) In 2017, Singh and Singh presented a combination of 2 techniques namely—PSO and Grey Wolf Optimizer (GWO) and termed it as—Hybrid PSO and Grey Wolf Optimizer (HPSOGWO). The aim behind the representation was to generate strong aspects of variants by improving the capability of both—exploitation of PSO and exploration in GWO. Twenty-three numbers of classical problems were solved by using this technique. The experimental data became reliable with less number of iterations as compared to PSO as well as GWO [37]. Both PSC and GWO were combined as two separate variants convoluted in producing last solutions to the difficulties. It improved the capability of manipulation in PSO with the ability of exploring in GWO to yield both variants’ strength. In HPSOGWO, the behavior of each agent calculated by the below equations:

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d α = |c1 x α − w ∗ x |

(24)

  d β = c2 x β − w ∗ x 

(25)

d δ = |c3 x δ − w ∗ x |

(26)

Where α, β, and δ are the potential location of variants. So the velocity and modified equations are as follows:     = w ∗ vki + c1 r 1 x 1 − x ki + c2 r 2 x 2 − x ki + c3 r 3 x 3 − x ki vk+1 i x k+1 = x ki + vk+1 i i

(27) (28)

The key objective of this method was to boost the capability of exploitation.

4.10 PSO Hinged with Local and Global Expanding Neighborhood Topology (PSOLGENT) The exploration of the local best neighborhood was noticed if the number of neighbors became match with the particle quantity. The current location of the particle was constantly changing according to the iterations. The variable neighborhood exploring algorithm is used to enhance the particle(s) location. It is the sequential exploration in a variety of neighborhoods of an explanation. A PSO algorithm with a neighborhood is defined as the topology of the group. VNS algorithm with a neighborhood is defined as the variety of local finding problems. Two methods of the VNS algorithm were selected. a. Classic version: Beginning of the VNS algorithm from a local exploration algorithm until the discovery of a local optimum to proceed with the next local search algorithm. b. A sequential version of the variable neighborhood search (SVNS): every local search is named sequentially per iteration. The reported hybrid PSO algorithm is given in Fig. 8. Firstly, a group of particles was formed arbitrarily where individual particle matches to a probable solution. Individual particles had a location in the area of keys and transfers with a specified rapidity. The VNS algorithm with a PSO was able to solve a controlled straight path problem effectively [38].

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Fig. 8 Steps to execute the PSO to solve a controlled straight path problem, adapted from Marinakis et al. [38]

4.11 Multi-vector PSO (MVPSO) Algorithm In the year 2019, Fakhouri et al, reported a new technique of PSO. It was an improved version of conventional PSO. It was an adding of three new rules in conventional PSO to find the global optimum position. An enhanced PSO stochastic meta-heuristic algorithm termed as—multi-vector PSO (MVPSO) algorithm is proposed for optimizing single-objective problems Fakhouri et al. [39]. According to Krawiec et al. [40], meta-heuristics algorithm was based on repeated tracing control based optimization algorithms. It could search the global optimum value at a high rate of finding. So that it was embraced with the properties of high consideration and manipulation and it could help to find more locations of search points in the search area [40]. Such type of algorithms was quite capable to depict an effective performance to reach the global best point, local minima prevention and high-rate of convergence. Some of the steps are as follows:

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1. It started with exploration feature; 2. Different areas of the exploration region were explored using the below equations at every step of the repetition. The location of the particle at each size is established by the following equations: (X 1t + 1)i = (1 + α) ∗ pbest − α ∗ pos

(29)

where (X1t + 1)i is the initial vector location of the existing key for ith size of the vector and tth number of repetitions, a constant value (α) = 0.2, and the location of the finest explanation in ith size of vector i.e. pbest. (X 2t + 1)i = γ ∗ X 1t + 1 − (1 − γ ) ∗ pbest

(30)

where (X2t + 1)i is the second vector location of the existing key in ith size of the vector and tth number of repetition. (X 3t + 1)i = β ∗ pos − (1 − β) ∗ pbest

(31)

where (X3t + 1)i is the third vector location of the existing solution in ith size of the vector and tth number of repetition 3. Promising areas of the inspection region were utilized between and around each of the freshly produced responses whereas affecting the global finest response. 4. The finest global optimum was throughout the optimization process. 5. Since the particles constantly inform their locations nearby the top explanation got during the optimization method; 6. MVPSO resolves optimization difficulties that are mentioned by mathematical equations; 7. The new search points enhanced the convergence to find the global optimum point to nullify the local minima issue. Such an algorithm boosts the PSO by the addition of three mathematical Eqs. (29 and 30) and MVPSO frequently modernizes the particle location concerning the global best explanation.

5 Applications Over time, several researchers have performed various experiments and simulations. They proposed numerous PSO algorithm based applications and proposed solutions to the existing problems [41–46]. Few of them are mentioned below in the tabular structure consisting of problem statements or objectives along with the application or/and solution proposed (Table 1).

The time taken by the PSO algorithm to determine the optimum Improvised PSO Algorithm has been proposed along with the parameters and constraints to optimize the low voltage distribution combination of the distribution transformer voltage regulation and network reactive power is not under considerable limits and is too large parallel capacitor. The improved PSO will help in classifying the particles, dynamically grouping them according to the difficulty and satisfy the constraint conditions. Constraints considered are—each node have qualified voltage, each node’s reactive power compensation capacity in within the pre-set value and system total reactive power is compensated rationally by roulette [48]

Utilization of partitioning technique to simplify and optimize the distribution network of two-echelon logistics

2.

3.

(continued)

Hybrid of PSO and GA, named—Extended PSO and GA (EPSO–GA) is designed to simplify and optimize the distribution network of the logistics using the partitioning model along with improvement of the logistic network economy. EPSO–GA enhances the exploring ability along with the reasonable design of convergence to an finest (or ideal) solution with the considerable number of iterations and reasonable rules [49]

The PSO and Genetic Algorithm optimized, adaptive and self-generating neural network, Radial Basis Function (PSO–GA–RBF) is designed to forecast the yearly required electricity. The proposed system has mixed-coded particle, each consisting of binary coded part (representing the GA optimized RBF configuration) along with real coded part (representing the PSO-GA optimized basis and weights parameters). The simulation results exhibited the simpler network configuration with lesser hidden neurons and accurate evaluation of PSO–GA–RBF model as compared with other ANN models [47]

The algorithms meant for learning the network are either single-coded or two-stage off-line learning. But, these have vital flaws like—slow rate of convergence, learning signals traversing in one direction, implementing hit & trials tactic to estimate the no. of hidden nodes, etc

1.

Proposed solution

Objective/problem Statement

S. No.

Table 1 Applications based on the PSO (conventional or modified) technique

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State of charge (SoC) is optimized in the plug-in hybrid electric vehicles (HEVs)

To determine the optimum configuration while designing a microgrid The proposed microgrid design with multiple energy sources is simulated system with multiple energy sources and services, exhaustive and employing the PSO algorithm for optimization. Outcomes exhibited that extensive search is performed which results in high computational cost the PSO generated optimal design solution converges with the solution obtained with the exhaustive search but with approximately 6 times lesser computational cost [52]

Online energy management system for HEVs engine/motor

Scheduling and lining up the workflow belongs to the NP-Complete problem and emerges as an important challenge in Infrastructure-as-a-Service (IaaS) clouds as demand for computing power is increased

5.

6.

7.

8.

(continued)

The proposed technique, named - Hybrid PSO (HPSO) is the combination of two algorithms namely—multi-objective PSO and Budget and Deadline constrained Heterogeneous Earliest Finish Time (BDHEFT). It is designed as a non-dominance sort based technique to supervise and manage the challenge of scheduling the workflow having multiple conflicts with increased demand for computing power on the IaaS clouds [54]

A five-step Improved PSO (IPSO), having 3 inputs and 1 output was developed for an online energy management system for HEV’s engine/motor HEVs. Also, the second-order dynamics-based vehicle simulator is integrated with the vehicle control unit, programmed based on IPSO. The simulation results verified that IPSO is quicker in finding the optimal solution as compared to traditional PSO [53]

In this, accelerated PSO is compared with the Standard PSO and was found that the APSO computational cost is moderate in comparison to SPSO due to additional acceleration parameters and also APSO is not too robust. But, APSO is highly efficient and resulted in a high-quality solution in comparison to SPSO [51]

Comparative analysis exhibited that GA or HOMER is inferior to the PSO method and latter is more economical for optimizing the hybrid energy system. Designed a hybrid energy model with PV/BGG/Diesel/BMG/Battery/MHG and also economically optimized the cost of energy using PSO Algorithm [50]

Development of Hybrid Energy System to electrify seven villages in Almora, Uttarakhand (India)

4.

Proposed solution

Objective/problem Statement

S. No.

Table 1 (continued)

152 A. Mittal et al.

Objective/problem Statement

Low-pressure fall and high heat transfer rates are among the plenty of parameters involved in the optimal designing of a plate-fin heat exchanger (PFHE). But, these two parameters have a direct relation

Among various types of NNs designed for the forecasting of rainfall, Radial Basis Function (RBF) Neural Network can estimate with an aspired degree of correctness. However, obtaining the appropriate parameters for RBF is highly complex

Designing of Static VAR compensator (SVC)

Removal of the brilliant green (BG) using the zinc sulphide nanoparticle loaded on activated carbon (ZnS—NP—AC)

Designing and planning of complex closed-loop supply chain system

S. No.

9.

10.

11.

12

13.

Table 1 (continued)

(continued)

An elevated hybrid algorithm is proposed using two meta-heuristic algorithms—PSO and GA. The PSO is hinged with GA and the strength of the former is used to improvise the latter [59]

The hybrid of the ANN and PSO (ANN-PSO) was used in contrast with the multiple linear regression (MLR) to forecast the eradication of BG using ZnS-NP-AC and the results exhibited that the hybrid model is highly efficient in forecasting the eradication rate of BG in comparison to MLR [58]

The algorithm suggested for the designing of the SVC controller is termed as—Bacterial Swarm Optimization (BSO), which is the hybrid of PSO and bacterial foraging optimization algorithm (BFOA). The results of the simulation validated that the BSO designed controller is superior to PSO and BFOA [57]

The technique proposed by incorporating adaptive optimization characteristic of PSO in GA is named as—Hybrid of PSO and GA (HPSOGA) and is meant for determining the parameters of RBF-NN (neurons number, their respective centers, and radii) automatically Wu et al. [56]

The algorithm named - Hybrid Chaotic Quantum behaved PSO (HCQPSO) is presented to model the optimal design of PFHE. Along with the local exploration mechanisms, the algorithm consists of the incorporating of the messy and disordered string created by the Logistic map into the Quantum based PSO algorithm, thus producing the technique called LQPSO. Results verified the algorithm’s precise and efficient convergence to the optimal design [55]

Proposed solution

Different Variants of Particle Swarm Optimization … 153

Objective/problem Statement

To minimise the energy cost and improve the potential of the plug-in HEVs, the solution for real-time energy management systems is needed but optimizing techniques can hardly be utilized for real-time

The logistics primary concern is the activities related to warehouse management, among which order pickup is the most costly activity because of repetitive and labor-intensive

Predicting and estimating the horizontal shift of the hydropower dams is difficult as it typically shows the non-linear and time-varying nature

System reliability, economical energy generation, and jolted environment are the major challenges faced during the assessment of the accomplishments of a standalone hybrid micro-grid system (HMGS)

S. No.

14.

15.

16.

17.

Table 1 (continued)

(continued)

Use of multi-objective PSO to estimate the optimal layout, schematic, design, and capacity of the HGMS for each location based on three conflicting objectives—system reliability, economical generation of electricity, and minimal jolted environment. The work helped the authorities of Sweden to look insight the project and also with the techno-economical aspect of HMGS deployment [63]

For the prediction of the hydropower dam shift, a hybrid AI system is proposed, termed as—swarm optimized neural fuzzy inference system (SONFIS). The NFIS is responsible for creating the model whereas PSO estimates the finest constraints for the aforesaid model. The results reveal that the high performance of the SONFIS makes it one of the efficient and prominent tools for modeling and predicting the horizontal shift of hydropower dams [62]

The presented technique is the hybrid of the two prominent algorithms—PSO and ant colony optimization (ACO). PSO helps in finding the optimum batch to be picked up and the latter finds the most effective traversing route for collecting each batch. The success of the experimental outcome revealed that the PSO-ACO model gives the best solution and is also computational efficient [61]

The presented technique for an energy management system is built on the PSO algorithm to reduce the combined energy cost of electricity and fuel in plug-in HEVs. The simulation results pointed out that the proposed technique can attain economical and superior energy efficiency in comparison to conventional algorithms, techniques, and strategies [60]

Proposed solution

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Objective/problem Statement

The roller’s surface is of great importance for precise rolling force in the metal rolling process and it should be in the considerable scope and limits. To achieve this, numerous abrasive passes have to be applied, which is typically leaned on the knowledge of the expertise and skill of the experienced engineers

Identifying the Bundle Branch Block (BBB) with the help of Electro-Cardiogram (ECG)

Determining the optimal maintenance schedule for the power system generating unit

Determining the ideal designing constraints for solar cells or/and Photovoltaic modules

The Traveling Salesman Problem (TSP), affiliated to the NP-complete problem, is a conventional benchmark problem to analyse the combinatorial discrete optimization algorithms. The realizable worst case of the TSP’s computational complexity can be the exponential rise of running time

S. No.

18.

19.

20.

21.

22.

Table 1 (continued)

(continued)

The proposed technique uses the PSO to discover and establish the ideal parameter values that influence the capability of the ACO. Alongside this, the 3-Opt technique is combined with the latter to enhance the local exploration capability. Thus, the proposed model is the hybrid of—PSO, ACO, and 3-Opt algorithm Mahi et al. [68]

In this, an algorithm named Nelder-Mead Modified PSO (NM-MPSO) is presented for determining the unknown parameters for the optimal design of solar cells and PV modules. The NM-MPSO is a hybrid of the Nelder-Mead (NM) simplex search method and Modified PSO (MPSO) technique Hamid et al. [67]

The technique put up here is the hybrid of two PSO influenced algorithms, namely—GA and Shuffled Frog Leaping (SFL), both of which are deployed to decide the finest and idea scheduling of the generating unit of the power system, considering the objectives of economic aspects and reliability of the system [66]

The following technique employs two independent methods—PSO and Firefly Algorithm (FFA), combined with the Levenberg Marquardt NN—to detect the BBB. The hybrid is termed as Firefly and PSO (FFPSO) technique, in which the local search is performed by FFA and global by PSO. The solution’s convergence speed and correctness prove the superiority of FFPSO over FFA or PSO individually [65]

The methodology presented for the grinding process involving the multi-pass is the use of hybrid PSO along with the evaluation of the surface roughness using a surface response model. The success and usefulness of the proposed method are experimentally verified with less than 16.53% error obtained between predicted and experimental roughness along with the improvement of grinding efficiency by 17.00% [64]

Proposed solution

Different Variants of Particle Swarm Optimization … 155

Objective/problem Statement

Image enhancement performed with commonly used methods like—linear contrast stretching (LCS) or Histogram equalization (HE), which has an excess of enhanced contrast which makes it inadmissible in the discipline where brightness is of critical importance

The incoordination in charging of plug-in electric vehicles (PEV) contributes to the strains on the power system which results in further undesirable drops in the voltage level along with the degraded (or low) quality of power

The hybrid standalone energy system, designed to cater to the area in Brittany, France makes the optimization a complicated problem, and obtaining a Global optimum solution becomes difficult

S. No.

23.

24.

25.

Table 1 (continued)

(continued)

The standalone system implemented to cater the area in Brittany, France is the hybrid of Wind/tidal/PV/Battery and the proposed solution using PSO algorithm is universally applicable to the problems of—optimal sizing and costing, energy management, reliability, and expansion of any standalone hybrid energy system. The traditional PSO is modified and the optimal solution is achieved with the 2 × speed at a rate better than 80% to conventional along with less than 20 repetitions only [71]

Two vigorous hybrid algorithms are proposed for the online coordination of the PEVs charging. The first hybrid is the Fuzzy Genetic Algorithm (FGA) which will help in the economical generation of energy, alongside minimising the losses in the grid and maximizing the power delivered to PEVs. The second hybrid is the fuzzy discrete PSO (FDPSO) which will ensure more precise, acceptable and quicker online coordination and will help in shifting the demand for charging from rush hours to minimum consumption hours, thus resulting in cutting of major cost and lessening the loading of the transformer Hajforoosh et al. [70]

The proposed hybrid is based on the artificial immune system algorithm, termed as Negative Selection Algorithm (NSA) and PSO algorithm. The presented algorithm intensifies the contrast and intensity of the grey-level in the images. The results unfolded the superiority of hybrid over other techniques like—LCS, HE, standalone PSO based image enhancement [69]

Proposed solution

156 A. Mittal et al.

PSO has below-par precision and time-consuming convergence rate and also local optimum deceives it while finding the solution to the complex functions related to optimization

Determining the power system’s finest and desired power flow

Overcoming the limitation of Stagnation effect in the conventional PSO The hybrid algorithm termed as—Hybrid Whale PSO Algorithm (HWPSO) is put up to overcome the limitation of the stagnation effect in the conventional form of PSO. The whale optimization algorithm’s (WOA) superior capability of exploration resulted in the hybridization of PSO and WOA along with employment of two techniques—“Forced” whale, which will guide the PSO to avoid local optima and “Capping” phenomenon, which will restrict the search mechanism and encouraging faster convergence to the global optimum value [75]

27.

28.

29.

(continued)

The combination of the PSO and Gravitational Search Algorithm (GSA) is designed to calculate and determine the Optimal power solution in the power system. The proposed hybrid uses the PSO’s social thinking and its capability to explore globally and GSA’s capability to explore locally to optimize the system in terms of—minimization of fuel cost, reduction in power loss, enhancing the reliability and voltage stability, and improving the voltage profile [74]

The proposed algorithm termed as—SA-PSO is the combination of Simulated Annealing (SA) and PSO. The SA allows the algorithm to avoid bad solutions initially and encourages it to escape the local optimum. Moreover, the hybrid algorithm elevates the capability of exploration in comparison to the conventional PSO [73]

For estimating and evaluating the Unconfined compressive strength The proposed hybrid uses the PSO algorithm and ANN. For the estimation (UCS) of rocks, BackPropagation ANN is used which faces drawbacks of the UCS of rocks (here, Granite and limestone) improvised version of such as—a slow rate of learning, getting trapped in the local minima the ANN prediction model is used, which is trained using PSO instead of Back Propagation. The performance comparison was made and it is found that PSO trained ANN is superior to the conventional ANN [72]

26.

Proposed solution

Objective/problem Statement

S. No.

Table 1 (continued)

Different Variants of Particle Swarm Optimization … 157

Objective/problem Statement

Determining the State estimation for 3 phase system in the power distribution network

S. No.

30.

Table 1 (continued) The method proposed to solve the State Estimation of the three-phase unbalanced system, combines the continuous state variables, such as—voltage magnitudes and angles with the discrete variables, such as—tap positions of On-line tap changers for voltage control and the Hybrid PSO (HPSO) is applied. The HPSO has overcome the limitation of weak selection process of PSO by hybridizing the tournament selection methodology of GA to PSO. Additionally, the outcomes demonstrated that the presented algorithm accurately estimates the discrete tap values in addition to the continuous state variables [76]

Proposed solution

158 A. Mittal et al.

Different Variants of Particle Swarm Optimization …

159

6 Conclusion In this chapter, the PSO technique has been reviewed successfully and it is found that the initial version of the algorithm is modified several times with various methodologies and parameters such as—design, velocity, dimensions, inertia weight, ω or constriction factor, ψ. It is also observed that the traditional PSO has the demerits of slow convergence rate as well as a large number of iterations. Hence various hybrid PSO designs are formulated to overcome the demerits of PSO. It has been discussed briefly in Sect. 4 of this chapter. It is also concluded that PSO finds a path to various applications, such as—medical, plug-in or/and Hybrid EVs, power system (power grid stability, maintain the voltage level), standalone or grid-connected micro-grids (optimum energy generation and minimum cost of energy), machining of metals, logistics, and tracking. After studying various applications of the PSO, it is also concluded that—PSO is better than other artificial neural networks or computational techniques. Also, the application specified hybrid PSO or modified PSO design is superior and gives optimum performance in comparison to the standalone PSO algorithm.

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Applications of Metaheuristics in Power Electronics Peeyush Kala, Puneet Joshi, Medha Joshi, Sanjay Agarwal, and Lokesh K. Yadav

Abstract The impact of power electronics in modern power system is profound. The grid integration of distributed generations (DGs) including renewable energy systems (RESs) employs the power electronic converters. For the economic operation of power system, the optimization is required to reduce its number of components, complexity, installation cost, running cost, electrical losses, and harmonic contents etc. Several conventional iterative methods were applied in these optimization problems. However, they suffer to a large extent from various drawbacks such as convergence to local minima, complexity in programming, large computational time, requirement of proper initial guess and intuition etc. Although there are various methods proposed to solve the optimization problem, the metaheuristics on the other hand have proven their capabilities in solving the problems related to optimization in many engineering fields. In power electronics, the optimization is required in circuit design, filter design, intelligent controllers design, parameters computation, modeling of new topologies, harmonic mitigation, losses evaluation, finding of safe operating areas of power electronic components etc. The evolutionary algorithms (EAs) and metaheuristics are very beneficial in solving these problems as these do P. Kala Department of Electrical Engineering, Women Institute of Technology, Sudhowala, Dehradun, Uttarakhand 248007, India e-mail: [email protected] P. Joshi (B) · S. Agarwal · L. K. Yadav Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar 224122, India e-mail: [email protected] S. Agarwal e-mail: [email protected] L. K. Yadav e-mail: [email protected] M. Joshi EED, SLSET Group of Institutions, Kichha, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_7

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not require intuition or past experience instead they work on the law of evolution and social behavior of groups. The advantages of metaheuristics over conventional optimization methods are saving in computation time, cost, ease of programming, lesser mathematical complexity. In grid-connected applications, metaheuristics have also shown their excellence, as they enhance the quality of power along with optimization of cost, size, and efficiency of power system network. In this chapter, EAs and metaheuristics proposed for the various power conversion applications such as FACTs controllers and devices, power filters, multilevel inverters, dc-dc converters, and PWM converters have been discussed. The merits and demerits of metaheuristics over conventional optimization methods are discussed. The detailed comparative analysis of various metaheuristics in power electronics systems is presented. The future perspectives of metaheuristics and EAs in power electronics is also discussed in this study. Keywords Evolutionary algorithms · Power electronics converters · Optimization · Metaheuristics

1 Introduction The contribution of power electronics has been immense on modern power system. The applications of power converters are not limited to control of conventional electric power but also extended to renewable energy systems, microgrids, industrial drives, harmonic filters and high voltage dc transmission (HVDC). There are numerous advantages of power converters such as fast operation, easy control, ease of programing, and high efficiency etc. There are some challenges in power electronics such as reduction in the cost of converters, reduction in installation space, determination of optimal placement of power electronic devices, tuning of controller, economic load dispatch, optimal sizing of harmonic filters, and minimization of switching losses etc. In order to solve these challenges, metaheuristic techniques are proposed and implemented by many researchers. In this section, various challenges in power electronics are discussed.

1.1 Challenges in Medium Voltage (MV) Industrial Drives The penetration of power electronics is huge in modern day power system. There are various challenges in power electronics applications. One of the application of power electronics lies in high-power MV industrial drives [1]. The drives are used in the various industrial applications such as petroleum, chemical, cement manufacturing, pumping, traction, transportation, and metals industry etc. The power rating of MV drives range can start from 400 kW and can be up to 40 MW with voltage of 2300 V to 14 kV. These MV drives have several concerns as discussed below.

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(a) Distortion in input current: The power converters introduce distortion in the input line current and voltage. As a result of distortion in current, overheating of transformers and interruption in automated industrial processes may occur. (b) Input Power Factor (PF): The MV drives draws power at low power factor which causes high copper losses. Therefore, reduction in input current and losses are obtained through improvement in PF. (c) Suppression of LC resonance: In the MV drives, LC resonance is usually caused by the harmonics introduced by the rectifiers on input voltage or currents. These may results in over voltages or severe oscillations. (d) High dv/dt stress: The high dv/dt stress in output of an inverter can lead to breakdown of insulation in motor owing to partial discharges. (e) Common-Mode Voltage Stress: These zero sequence voltages appear on neutral of motor and results in failure of motor. (f) The power converters generate harmonics in voltage and current. These harmonics cause heating in magnetic core and winding of machine. Therefore, motor is derated to operate at reduced capacity. (g) In the MV drives, the minimization of switching loss is essential. It reduces the size, operating cost, and cooling requirements of the drive. Apart from these issues, the drives should have optimization of efficiency, manufacturing cost, physical size, reliability, protection from fault, and dynamic performance.

1.2 Challenges in Transmission and Distribution Using FACTS In modern power system, the ever increasing electrical load demand has pushed the existing distribution and transmission networks to maximum limit. The use of FACTS and HVDC transmission system is preferred for ensuring dynamic and static stability. The FACTS controllers are conventionally used in regulation of voltage, steady and dynamic state control in power system, and optimization of power flow capability of transmission lines [2–4]. However, there are some issues as listed below: a. Low-voltage ride-through (LVRT) capability in PV systems and wind power conversion systems. b. Dyanamic stability of power system. c. Connection of converters to high-voltage network. d. The problem of balancing the voltage of dc-link capacitors. e. Precise control of active/reactive power for grid balanced/unbalanced conditions. f. Application of new converter topologies.

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1.3 Challenges in HVDC In HVDC systems, power converters play a major role. The advantages of HVDC over HVAC transmission are manifold and well discussed in literature [5]. The issues faced in the HVDC systems are as follows: a. b. c. d. e. f.

Reduction in very high cost of power converter. Independent control of reactive and active power. Requirement of reactive compensation equipment at converter stations. It requires use of converter transformers in HVDC system. The multilevel converter topologies are yet to replace the popular PWM inverters. It is necessary to eliminate harmonics by using harmonic filters. The cost of such filter is quit high.

1.4 Challenges in Renewable Energy Systems The renewable energy systems such as photovoltaic (PV) and wind energy conversion system (WECS) employ the power converters for conversion from dc to dc and ac to ac. Ocean energy, geothermal energy, nuclear energy, biomass, hydrogen fuel cells etc. are other major resources of renewable energy [6]. Following are the challenges in renewable energy systems. 1. 2. 3. 4. 5. 6. 7. 8. 9.

To attain efficient maximum power point tracking (MPPT) in PV and WECS. Intermittent nature of renewable energy resources. High cost of maintenance and operation. Injection of harmonics to grid. Issue of stability of grid during grid fault condition. Islanding effect. Optimal placing and sizing of power electronic converters. In ocean energy system, to maintain operation under harsh weather conditions. To optimize the requirement of energy storage devices.

1.5 Transportation Systems In our daily life, transportation system has become essential part. Nowadays, there has been focus on improving the reliability, efficiency, fault tolerance in operation, performance, and most of the above reduction in fuel demand, reduction in the CO2 emission, and cost of maintenance. To achieve these objectives, researchers have introduced the power electronics in the transport means such as in buses, trains, aircraft, ships, cars etc. [7]. The advantages of power electronics in transport system are as follows. 1. Reduced weight and volume of vehicle.

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2. 3. 4. 5. 6. 7. 8.

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To maintain reliability of system in fault condition. Reduction in fuel consumption. Reduction in cost of the system. Development of integrated transport system with power system. Simplified electrical circuit of aircraft. Design of optimized HVDC architecture. Improvement in plug-in hybrid EV (PHEV)/electric vehicle (EV).

1.6 Energy Storage Systems The examples of energy storage system are batteries, compressed air energy systems, fuel cells, flywheel energy storage systems, thermoelectric energy storage, and superconductive magnetic energy storage system etc. The power electronic converters are used in the energy storage systems [8]. The challenges in energy storage systems are as follows: 1. To facilitate the interconnected regional grids. 2. To match balance between load and generation. 3. The energy storage system should bring down the fuel cost in transportation sector. Also, environmental hazzards should be reduced. 4. To monitor the impact of energy storage on stability of grid. 5. Development of grid integrated/standalone EVs/PHEVs. 6. Optimized utilization of renewable energy sources.

2 Applications of Metaheuristics in Power Electronics 2.1 Microgrid The rising share of intermittent renewable energy resources into grid has propelled the concept of microgrid. It comprises combination of distributed resources such as wind, solar, fuel cells, micro hydro, combined heat and power (CHP) etc. with superior control and coordination [9]. There are several parameters of microgrid like efficiency, allocation of sources, scheduling, cost, size, and location of components etc. which have to be optimized. In this context, researchers have proposed the use of metaheuristics in microgrid application. Gamarra and Guerrero [10] have reviewed the different optimization techniques used in the planning of microgrid. In microgrid, the issues related to planning are as follows: • Selection of appropriate generation units and resources. • Sizing of generation units and energy storage system is done on the basis of economy and peak demand of load.

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Table 1 Metaheuristics used in microgrid issues S. No.

Microgrid problem

Method

1

Generation unit selection

GA, Simulated annealing

2

Optimal sizing

GA, PSO, EA

3

Optimal scheduling

GSA, GA, BFA, PSO, SCSS

4

Sitting of generation units

GA, PSO, AIS, SA

• The objectives of planning are: to attain reduction in cost, less adverse impact on environment and achieve high reliability. • Allocation of generation units and layout of distribution lines in a manner that will result in low power losses. • Scheduling of available resources is also an important parameter. • Economic load dispatch problem. Table 1 summarizes the metaheuristic techniques applied on abovementioned microgrid issues. Selection of suitable metaheuristic technique for economic operation of microgrid is also a challenging task. Khan and Singh [11] discussed this problem in their research work. In this study, the various configuration of microgrids comprising generation units such as PV system, diesel generator, fuel cells, electric vehicles, wind turbine, plug-in EVs have been considered. Several techniques like GA, PSO, TLBO, firefly algorithm, and whale optimization were considered in the problem. There are several constraint in the microgrid such as: electrical load demand, output power limit, battery storage constraint, constraint of grid and diesel generator output, constraint of rate of charging/discharging of battery in EVs and PHEVs and constraint of operating reserve which are to be taken into consideration while optimizing the cost of microgrid. Two cases were discussed. In first case, batteries were considered in charging mode i.e. acting as a load while in second case, batteries were assumed in discharging mode i.e. acting as sources. The firefly algorithm showed superior performance as compared to that of others for population size up to 100 for first case. For the second case, it was found that performance of TLBO, GA and PSO improved as the population size increased while performance of firefly and whale optimization were found excellent for population size up to 100. One of the desirable objective of RES based microgrid is the minimization of power losses and reduction in size of components while optimizing the power output of RES. To achieve this goal, Senthil Kumar et al. [12] proposed the use of hybrid cuckoo search algorithm (CSA) in AC/DC microgrid. In CSA, egg hatching behaviour of cuckoo birds was imitated. Further to achieve the faster rate of convergence, Nelder-Mead algorithm was combined with CSA. The proposed metaheuristic algorithm was able to obtain the following goals: • Optimum sizing of generation units in microgrid. • Minimization of power losses. • Improvement in the voltage levels in AC/DC microgrid.

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• Determination of optimum number and locations of RES generation units in microgrid. • Improvement in the performance of microgrid for 69-bus and 33-bus benchmark distribution system.

2.2 Renewable Energy Systems (RES) The contribution of RES in modern grid is increasing nowadays owing to their several environmental, technical, and economical benefits. Some of the benefits of RES to distribution networks are as follows: • • • • •

Reduced transmission loss. voltage profile improvement. Increased efficiency. Reduction in electricity bills. Reduction in greenhouse gas emission.

To achieve the abovementioned advantages of RES systems, it is desirable to optimize the sizing and allocation of generation units. Farh et al.[13] proposed the application of a crow search algorithm (CSA) based swarm optimization to solve for the objectives such as: • • • •

Minimization of cost and power loss, To find the optimum number of units required, To obtain the optimal allocation and sizing of RES, To find the optimum number of generation units.

CSA imitates the collective behavior of crows. These birds remember the location where the food was previously hidden. They follow the other crows to theft the hidden foods from the hiding locations once the other crows left the places. The crows also take care of their food from being stolen which is based on the probability. To obtain better results, CSA was hybridized with PSO and was implemented on IEEE-30 bus system to solve the problem of optimal power flow with RES. The proposed algorithm showed its excellent performance as compared to other metaheuristic methods for minimization of power loss and total cost of system. Askarzadeh incorporated the integration of tidal energy into a solar and wind energy based RES. For the economical operation of the proposed system, optimal sizing of generators, converters and other components is required. In this context, a novel CSA technique was proposed. The power extraction from the tides is more anticipated and can be extracted with the help of tidal barrage or ocean current. Its working is similar to that of wind energy system. The important outcomes of the research work are as follows. • CSA efficiently found the optimum size of components of PV/wind/tidal microgrid.

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• CSA holds the superiority in terms of better rate of convergence, accuracy, and time saving as compared to PSO and GA. • Optimum cost and high reliability of the system with battery storage. In Yahiaoui et al. [14], proposed the use of grey wolf optimizer (GWO) for the optimization of design and total cost of hybrid RES. The proposed RES consisted of diesel generator, PV panels and energy storage devices. GWO algorithm imitates the hunting behaviour of grey wolves. In the hierarchy, the α wolves lead the group followed by β, δ, and ω wolves. The hunt for prey is steered by α, β and δ wolves while ω wolves follow these wolves and change their positions according to positions of their leaders. The important findings of the proposed strategy are as follows: • GWO converges faster than the PSO. • The optimal size of hybrid RES was obtained using GWO. Number of components for optimal operation were as follows: PV panels = 33, batteries = 90, diesel generators = 2. These numbers were found lower than that obtained by PSO, hence GWO resulted in least cost of the system. • GWO minimized the annual cost of system. In the PV systems, the maximum power point tracking (MPPT) methods are widely used. Most of these methods are not able to find the global peak power during partial shading conditions and often converge to local minima. The metaheuristics techniques such as BA, PSO and GWO can solve the problem of finding global minima in such conditions. In Eltamaly et al. [15], proposed the application of new bat algorithm (BA) for MPPT considering partial shading in PV systems. In this study, the optimum number of agents were computed and found to be inversely proportional to the number of maxima in power-volt curve of PV system. The optimum size of swarm helps in reducing the convergence time and increasing the probability to find global minimum. The convergence time was reduced from 8 to 3 s. Ram et al. [16] emphasized on the mixture of conventional P&O and bio-inspired metaheuristic method. The author proposed this idea to effectively utilize the robustness and simplicity of P&O to enhance the reliability and efficiency of MPPT. Flower pollination algorithm (FPA) mimics the biotic and abiotic transfer process of pollens. Steps involved in FPA-P&O are as follows: 1. 2. 3. 4.

Initialization of variables such as duty cycle, increment in duty cycle, probability. Initialization of swarm position. Find the best duty ratio corresponding to the global maximum power. Update the duty cycle, if the criterion Gbest (t + 1) ≈ ±0.05 Gbest (t) is not met, continue with FPA else switch to P&O.

The simulation and hardware results validate the superiority of proposed method over PSO and enhanced leader PSO. The proposed scheme took only 0.45 s for convergence to global MPP. Also, other advantages of proposed scheme are higher power output, higher efficiency, and lower switching stress. Oshaba et al. [17] proposed the MPPT for PV system driven motor drive. In their work, authors implemented the use BAT algorithm for optimum tuning of parameters

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Table 2 Applications of metaheuristics S.No.

Problem

Metaheuristic applied

1

Charging of vehicle

Hybrid PSOGSA, GA, ACO

2

Modeling of load and planning of charging stations

ACO, GA

3

Route optimization

Modified GA

4

Allocation of energy for charging station

GSA

5

Integration of vehicle to grid

GA, PSO, PSOACO

of PI controller. Simulation results showed the better performance as compared to that of PSO. In PV systems, the problem of parameter estimation is multimodal and nonlinear. For solving this problem, use of optimization techniques is preferred. Nunes et al. [18] proposed the use of hybrid metaheuristic method. In the study, a combination of three metaheuristics namely wind driven (WD), whale optimization (WO) and PSO was tested on PV systems for various scenarios including partial shading. The advantages of this methodology is to utilize the beneficial characteristics of each algorithm for achieving global optimum solution. The proposed technique was applied in single diode and two-diode models considering partial shading and variation in irradiances and temperature. Results showed that the PV system’s parameter estimation were determined with excellent accuracy and consistency. Energy stored in the magnetic form in superconductors can be utilized for meeting peak load demand. However, the high operational and installation cost of superconductors limit their applications. In order to reduce the cost, Raha et al. [19] proposed the hybrid solution involving capacitors and superconductors together. CSA was applied for optimal sizing and optimal allocation of VAR compensators in the IEEE118 bus system. Simulation results suggested that economical benefits were increased by 1.39 times as compared with that of superconductor magnetic storage solutions. Apart from the above mentioned applications of RES, transportation sector is also experiencing the penetration of RES and battery energy storage systems. Rahman et al. [20] presented the review of metaheuristics used in electric vehicle (EV) and plug-in hybrid EVs. The metaheuristics were applied on the several EVs issues as listed in Table 2.

2.3 Power Converters The power conversion devices are principal component in power system which are used to interface RES to power grid. Koch et al. [21] presented a new procedure of designing current controllers in grid connected application. GA was used to automatically tune the parameters of controller, improve the dynamic response of controller and to reduce the time in design stage. In Singh et al. [22], applied the firefly algorithm on the problem of power system stability. The firefly technique minimized the

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oscillations, overshoot and settling time of power system controller. Convergence rate of proposed controller was faster than that of conventional controller. Duman [23] presented the application of new moth swarm (MS) algorithm for the optimum power flow control in HVDC system. The objectives achieved were as follows: • reduction in total cost of fuel, • improvement in the voltage regulation, • improvement in voltage stability. Mohapatra et al. [24] applied GA based compensation technique for voltage and reactive power control. In Li et al. [25], discussed the role of metaheuristics in the optimization of weight in aircraft’s power converter design application. GA, PSO and simulated annealing (SA) were applied in the weight reduction of 2 kW inverter and the minimum weight was found to be 420 g only. Shayeghi et al. [26] proposed the application of quantum PSO in UPFC for tuning the parameters of damping controller. The results showed the improvement in the transient stability, effective damping of low switching frequencies, and superior performance as compared to PSO based power stabilizers. Sarkar et al. [27] proposed an ACO metaheuristic scheme for the control of switched shunt capacitors. Results showed that the proposed technique was superior from the point of view of memory required, time of response, and dynamics. See et al. [28] discussed the application of ACO in wave energy conversion systems. The ACO reduced the computation time which helped to reduce the oscillations in output power. Abd-Elazim and Ali [29] applied the CSA for optimal design of STATCOM and finding their locations in distribution network. The proposed technique reduced the damped oscillations and improved the voltage profile. Another application of metaheuristics found in multilevel inverters where solution of selective harmonic elimination (SHE) problem is required. Solving the SHE problem requires complex methods such as algebraic method, methods of resultant theory, iterative methods and optimization techniques etc. Out of these methods metaheuristics based optimization techniques are becoming popular due to their several merits over conventional methods. GA, PSO, CCA, BA, GSA, and firefly algorithm etc. are the metaheuristic techniques that were used by several researchers in solving SHE problem [30–37].

3 Conclusion In this chapter, the applications of metaheuristic algorithms in the various areas of power electronics were discussed. The merits of metaheuristics have emphasized their applicability in various power electronics applications such as in microgrids, in RES, and in power conversion devices. In general, metaheuristics are used in sizing, allocation, scheduling, cost and loss reduction, harmonics reduction, MPP tracking, voltage profile improvement, economic load dispatch problem, fast charging of batteries and numerous other problems. In the future, it is expected that several

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metaheuristics techniques may be used in solving the various complex problems related to power electronics.

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Cuckoo Search Algorithm: A Review of Recent Variants and Engineering Applications Abhinav Sharma, Abhishek Sharma, Vinay Chowdary, Aayush Srivastava, and Puneet Joshi

Abstract Metaheuristic algorithms, in the field of engineering, have attracted researchers for problem-solving of complex and non-linear optimization. Many algorithms have been designed to address wide-ranging applications such as GSA—gravitational search algorithms (GSA), PSO—particle swarm optimization, GWO—grey wolf optimization, and various hybrid plus evolutionary algorithms. Hybrid algorithms also made for such wide-range application, but the drawback of such algorithms are convergence time is very high and challenging to implement for multiple wide range applications. Cuckoo Search (CS) is an optimization technique, developed in 2009, is a highly efficient algorithm. It is an algorithm that is based on population and is also a nature-inspired metaheuristic algorithm, which is easy to implement for such applications. The success of the algorithm has been fueled because of its characteristics, i.e. its simplicity, few parameter, ease of implementation. Cuckoos are delightful birds, which have attracted people not only because of their melodious sound but also because of their aggressive reproduction capability. The algorithm addresses two important behavioral aspects of some cuckoos i.e. brood parasitism A. Sharma (B) · A. Srivastava Department of Electrical and Electronics Engineering, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India e-mail: [email protected] A. Srivastava e-mail: [email protected] A. Sharma Department of Research and Development, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India e-mail: [email protected] V. Chowdary · P. Joshi Department of Electrical Engineering, Rajkiya Engineering College, Ambedkar Nagar, Uttar Pradesh 224122, India e-mail: [email protected] P. Joshi e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_8

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and levy flights. The two Ani and Guira cuckoo species will all lay eggs in a communal nest. The cuckoo can then remove the eggs laid by others to improve the probability of hatching the laid eggs. Cuckoo immigration along with environmental factors make the cuckoos to find an appropriate and also a place for reproduction and breeding. Cuckoos presents the random walk Levy flight behavior, which enables the algorithm to completely explore the search space. In CS algorithm fixed number of better fitness cuckoos survive in the environment. This chapter introduces with the mathematical concept of CS algorithm and summarizes different research articles where the algorithm has been explored in the field of engineering. Furthermore, the resent version of CS algorithm are addressed which mainly focuses on modified and hybrid versions. The novelty of this chapter is that it presents current trending research aspects of CS algorithm in the field of engineering, machine and deep learning. The chapter concludes with the future direction which can be investigated using CS algorithm in the field of science and technology. Keywords Metaheuristic · CS · Eggs · Brood parasitism · Levy flight

Nomenclature ACO ANN APO CBO CFO CS CSS DE FA FPGA GA GHS GSA GWO HS PCB PSO SA SVM TLBO TS WOA WSN

Ant colony optimization Artificial neural network Artificial physics optimization Colliding bodies optimization Central force optimization Cuckoo search Charged system search Differential evolution Firefly algorithm Field programmable gate array Genetic algorithm Global harmony search Gravitational search algorithm Grey wolf optimization Harmony search Printed circuit board Particle swarm optimization Simulated annealing Support vector machines Teachin learning based optimization Tabu search Whale optimization algorithm Wireless sensor network

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1 Introduction Optimisation plays a vital role in solving diverse issues in various fields of science and engineering. It is a method of changing a system that makes certain features more productive to operate or to find the alternative output in the sense of certain constraints by optimizing desirable parameters and reducing the unwanted parameters involved. Optimizing means trying to achieve good results in less time. The goal of the optimization process is to decide whether the problem solved has a maximum or minimum value, generally known as the target function. Metaheuristic natureinspired algorithm is the best example of optimization algorithms. Due to computer limitations of traditional numerical methods, researchers have a challenge where they need to focus on meta-heuristic techniques for solving complex scientific problems [1]. Over the last few decades, numerous metaheuristic (high-level search) algorithms have been successfully implemented for diverse problems in engineering optimization. These types of algorithms are mostly used to solve the nonlinear objective function. Research community have developed and are developing different types of metaheuristic nature-inspired algorithms. Most of the modern metaheuristics rely on the fact that it imitates the best aspect of natural biological systems, established over millions of years by natural selection. Fitness selection or environmental adaptation are two key features that can be mathematically translated into two important features of modern metaheuristics, i.e. intensification and diversification [2]. The first feature, intensification finds the best possible solutions and then selects the best candidates or solutions. The second feature, diversification, ensures that the algorithm is efficiently explored in search space. CS algorithm is based on the breeding technique of cuckoo birds for population increase. CS a nature inspired algorithm imitates the peculiar reproductive behavior of the cuckoo birds. Yang and Deb developed this algorithm on the basis of three principles [2], which are: a. Every cuckoo lays just one egg at a time and then dumps into a nest chosen randomly. b. Egg nests with highest fitness, termed as best nests will move to the next generation. c. A host bird discovers cuckoo laid eggs with a likelihood in the range [0, 1] from the set of available hosts nest. In such a scenario, a host bird throws away her egg or she may leave the nest to construct a new one. Cuckoo birds shows a unique behaviour, they always lays eggs in a communal nest and when the host bird discovers eggs in the nest, which are not its own, then the bird move the eggs down or leave the nest to create a new one. Cuckoos prefers the host nest for laying eggs which will be in the same color and shape as that of host eggs. This increases the chances of not only hatching of cuckoo eggs but also increases the chances of hatching cuckoos’ eggs faster than host bird eggs. The chicks then will imitate the sound of a host bird for food. The same method is made up of a mathematical equation and the quest principle for levy flights, which makes 90 degrees more accurate to the scale-free search.

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The chapter is organised as follows. In Sect. 2, a brief introduction of the metaheuristic algorithms is presented and in Sect. 3 introduction of the inspiration, mathematical model of the CS algorithm is presented. Sections 4 and 5 discuss the different modified and hybrid CS algorithm. In Sects. 6 and 7 artificial intelligence and engineering applications of CS algorithms are explored and discussed. Section 8 asses and evaluate the CS algorithm and Sect. 9 presents the conclusive remarks to summarize the chapter.

2 Metaheuristic Algorithms Metaheuristic optimization technique have shown massive growth in the last few decades. The wide applicability of these algorithms among researchers compared to conventional algorithms in diverse research domains is due to their simplicity, local optima avoidance and derivative-free mechanism. These algorithms search randomly for the solution inside the search space which shows their stochastic nature. Metaheuristic algorithms are categorized as a single-solution based and population-based algorithms. A single-solution algorithm begins from a single point and refines the solution through the successive iteration of the algorithm. An example of a singlesolution based algorithm is Simulated Annealing (SA). The population-based algorithm generates an initial population of agents and all agents explore the search space and discovers the global solution. Metaheuristic optimization technique based on population are of three types namely evolutionary-based, swarm-based, and other algorithms [3] as shown in Fig. 1. Genetic algorithm (GA), based on Charles Darwin’s theory, is a popular evolutionary algorithm. Swarm intelligence, on the other hand, is the collective

Fig. 1 Categories of metaheuristic algorithm

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behavior of a self-organized system which in nature is decentralized. These algorithms are inspired by nature and imitate a group of animals and species’ social behavior. The most widely used swarm intelligence algorithms are PSO, Cat swarm optimization, Bat algorithm, chicken swarm optimization (CSO), etc. Other algorithms are based on different aspects of our nature, some of them are inspired from natural physical phenomenon of our universe, and some are inspired from human behavior while some from the mathematical concepts. Ray optimization, Jaya algorithm, Magnetic charged system search, Harmony search, flower pollination algorithm, Big Bang-Bing Crunch algorithm, Tabu search (TS), firework algorithm and sine-cosine algorithm (SCO) are some of the examples of this category.

3 Cuckoo Search Algorithm 3.1 Inspiration of CSA Mother Nature have different species of birds, insects and fish which are brood parasites, i.e. these species rely on others to grow their own infants. This natural breeding parasite phenomenon inspires CS algorithms in which cuckoo birds lay their eggs in the host bird’s nest. CS optimization technique is also inspired from the random walk behavior of animals and birds, widely known as levy flight. For this the step-length is determined according to the strong tailed distribution of probability. The MATLAB code of the CS algorithm is open source and can be found from MathWorks using the following link: https://in.mathworks.com/matlabcentral/fileexchange/29809-cuckoo-search-csalgorithm.

3.2 Mathematical Model of CS Algorithm The following steps presents the mathematical model of CS algorithm [2]: Step-1: Initialize the cuckoo habitat, i.e. current position of cuckoo nest.   X = x1 x2 . . . x N , wher e N r eper sents the numbe o f variables Step-2: Each cuckoo randomly move by levy flights to the neighbour bird nest and lays eggs. The new position of cuckoo nest is defined as: xit+1 = xit + α ⊕ Levy(λ),

(1)

where α is size of the step and its value is larger than zero, ⊕ means entrywise multiplication. Levy flight is defined as:

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Levy ∼ u = t −λ ,

(2)

where λ is a variable that lies from 1–3. Step-3: Estimate the eggs quality over all the nest by finding the fitness of host nest. Step-4: Nest j are choosen randomly among N nest and find whether the fitness (fit), f iti > f it j

(3)

If the condition is met then replace j nest with new solution nest. Step-5: With a likelihood (pa), the laid eggs which are less similar to the host bird nest are discarded and thrown out of the nest. Step-6: Go to step 2 till the time minimum error criteria is achieved or the maximal number of iterations is reached.

3.3 Exploration and Exploitation Exploration pertains to exploring wide areas of search space for determining most promising solutions while exploitation refines the solution by searching round the promising regions of the exploration phase. In CS algorithm exploration phase is governed by levy flights while exploitation phase is governed by determining the stochastic solution inside the boundaries.

4 Modified Version of CSA In the research community, improving the performance of existing algorithms is an active area of interest. CS algorithm lacks balance between local and global search and has slow rate of convergence. Acknowledging these two limitations and improving the performance of existing algorithm, researchers that have modified CS algorithm. The modifications in the CS algorithm are categorized in three different categories as shown in Fig. 2.

4.1 Variation in Algorithm Parameters In [4] author improves the rate of convergence of the algorithm and proposed adaptive CS optimization technique, where the size of the step is adaptive and is independent of the Levy distribution.

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Fig. 2 Modified CSA

The adaptive CS algorithm step is modeled as: 



f it(t)− f iti (t)    bestbestf it(t)−wor st f it(t)  1 stepi (t + 1) = t

(4)

where t bestfit (t) worstfit (t) fiti (t)

generation of CS, Best value of cost function in the t-th iteration, Worst value of cost function in the t-th iteration, value of cost function of ith nest in t-th iteration.

Adaptive CS algorithm update equation is defined as: X i (t + 1) = X i (t) + randn ∗ stepi (t + 1)

(5)

The updating equation includes adaptive step size parameter which is initially high and decreases with the course of iteration. Since the adaptive algorithm has less parameters thus it has fast rate of convergence. In [5] author proposed advanced version of CS algorithm, in which α and Pa are dynamically changed over the course of iterations. These parameters are defined as follows: gn (Pa max − Pa min ) NI     αmin 1 ∗ gn Ln α(gn ) = αmax exp NI αmax Pa (gn ) = Pa max −

(6) (7)

where gn and NI are the present iteration and complete set of iteration. In [6] an enhanced CS algorithm is proposed which follows the Gaussian distribution random walks and is based on greedy selection approach. The updating equation is defined as follows:     X it+1 = Gaussian Best t , σ + r1 ∗ Best t − r2 ∗ X it

(8)

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Bestt represents the solution of t-th generation. X it+1 and X it represents the solution at (t +1) and t generation. The standard deviation is defined as:  σ = 

log(t) t



  ∗ X it − Best t

(9)



  decreases the Gaussian step size with generation, X it − Best t   preserves the best solution and r1 ∗ Best t − r2 ∗ X it adjust the search direction of Gaussian. The algorithm presents accurate results with fast rate of convergence. In [7] author proposed modified CS algorithm for dynamic optimization environment. In [8] author modified CS algorithm to overcome slow convergence rate and local optima avoidance. In the modified algorithm, author utilized coefficient function for altering size of the step and detection probability. In [9] the author proposed Cauchy operator to efficiently explore and leverage the search space in place of Levy flight. The Cauchy density function is defined as: The term

log(t) t

g 1 2 π g + δ2   1 δ 1 y = + arctan 2 π g f Cauchy (δ) =

(10) (11)

where y lies between [0, 1] and g is the scale parameter. The value of δ from above equation come out to be:    1 δ = tan π y − 2

(12)

The above equation generates the Cauchy random number distributed within the range [0, 1]. On the basis of this equation global search equation changes to   X it+1 = X it + α ⊕ Cauchy(δ) X it − X tj

(13)

The Cauchy distribution effectively explores the larger search space. In [9] author defined self-adaptive phase size parameter (α) for multimodal optimization problem, which changes during the iterations and is defined as:     f x best  ϕ   t α=   σt ∗ ω 

(14)

  where f xtbest is the best solution of iteration t, ϕ and ω are the constriction factors, σt is the mean fitness value of the current iteration.

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4.2 Division of Population and Generation Exploration and exploitation are two essential parameters that decide the algorithm’s effectiveness. In [9] author establishes the balance between exploration and exploitation by dividing the population and generations. Author divided smaller groups of population in and used different search equations in each group. Three different division strategies have been employed using multiple search equations. Similarly generations are divided in such a manner that for half of the generation equations having best exploration properties.

4.3 Modified Selection Strategy In [10] author modified the conventional selection strategy of CS algorithm. In this algorithm author replaced the random probability selection parameter with the threshold function. Based on this function the abandon solution is decided. The methodology of the proposed algorithm is follows: (i)

Evaluate the mean fitness (α) of entire population N αt =

f (xi ) M

i=1

(15)

where M represents the overall population and t is the number of iterations. (ii) Evaluate the difference function between mean fitness and best fitness at iteration t,    vt = C ∗ αt − f xtbest

(16)

(iii) Evaluate the threshold value,   βt = f xtbest + vt Ct,K = index( f (xi ) > βt )|∀i and K ∈ 1, . . . p Rt,L = B˙ t,K where, array B˙ holds the index of the solution which is abandoned, K is the array of single dimension of t-th iteration. In [11] author replaced the random selection scheme of CS algorithm with the tournament selection scheme. The simulation results shows that modified algorithm has fast rate of convergence with higher computational precision.

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5 Hybrid Cuckoo Search Algorithm With the development of number of metaheuristic algorithms, researchers are now focusing on hybridization of one or more algorithms. It basically exploits the best features of one or more algorithms and is best suited for different sets of optimization problems. In literature, CS algorithm has been hybridized with different algorithms. In [12] the author hybridized CS algorithm with GA to solve the route optimization problem for the printed circuit board (PCB) hole drilling phase. In this hybrid algorithm, every two parent cuckoo reproduce two cuckoo eggs followed by mutation operation. The hybrid algorithm is tested on different size of problems and the results presents that it is robust, efficient and have good rate of convergence. Ding et al. [13] proposed hybridized CS and PSO algorithm for optimizing complex problems. In this hybrid algorithm the Levy flight is deemed to replace the PSO algorithm random search process. The hybrid algorithm’s efficacy is validated on several mathematical functions. Author also analyzed the performance of the hybrid algorithm on parameter identification of the motor drive servo system and reactive power optimization of power system. The simulation result shows that the hybrid algorithm presents superior results compared with PSO and CS algorithm. In [14] the heating route selection problem has been considered and solved by hybrid ACO and CS algorithm. Hybrid algorithm finds the best route with greater efficiency and stability. A hybridization of CS algorithm with SA algorithm is presented [15]. The proposed hybrid algorithm exploited SA algorithm discovery mechanism and improved CS algorithm efficiency. In [16] author explores the protein-ligand docking problem using hybrid differential evolution (DE) and CS algorithm. This approach shows improved performance and presents proper balance between global and local optimization. In [17] author combines the great exploratory quality of CS and efficient exploitation capability of harmony search (HS) algorithm for calibration of ground water flow models. Furthermore, author modified the CS with a chaotic varying step size and modified distribution of HS. In [18] author efficiently solve 0-1 knapsack problem using hybrid CS and global harmony search (GHS) algorithm and the results presents improves search accuracy and convergence speed. In [19] author exploits the attraction mechanism of firefly algorithm (FA) and reproduction strategy of CS algorithm. The two approaches are applied in-parallel, which results in guaranteed search around the best location instead of random search. The proposed hybrid algorithm is evaluated on various benchmark problems and produces superior performance.

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6 Artificial Applications of CS Algorithm 6.1 Neural Networks A computational network that has a propensity of learning from the environment is artificial neural network (ANN). It finds wide applications in the field of manufacturing and engineering. The training algorithm plays a significant role in the network’s learning ability and efficiency. Back-propagation (BP) algorithm, a learning algorithm is mostly used to train feedforward neural network. BP algorithm is sensitive to initial weight and bias, has slow rate of convergence and get trapped in local optima. In [20] author proposed CS algorithm for optimizing initial weight and biases. The proposed approach trains fast and presents good generalization capabilities and find the global optimal solution. In [21] author explores the CS algorithm to estimate different parameters of neural network. In [22] author presented improved CS algorithm for training feedforward neural network. The improved algorithm demonstrates effective performance to train ANN. In [23] author explored the hybrid CS and PSO algorithm for feedforward neural network training. Hybrid algorithm makes use of PSO’s fast convergence speed and CS algorithm’s optimum global finding potentiality.

6.2 Support Vector Machines Machine learning is the subset of artificial intelligence. Support vector machine (SVM) is a supervised learning model of machine learning with learning algorithms primarily used for classification and regression problems. In [24] author explored CS algorithm for obtaining frequency which is tuned and damping ratio of tuned mass damper (TMD) system, that ultimately becomes the database for least square-SVM algorithm. The model forecasts TMD system’s tuning frequency and it’s damping ratio. In [25] a novel chaotic catfish effect based CS algorithm is proposed to improve the rate of convergence as well as for local optima avoidance. The author explored proposed approach in optimizing SVM model in applied petroleum engineering problem.

7 Engineering Applications of CS Algorithm 7.1 CSA Application in Wireless Sensor Networks In Wireless Sensor Network (WSN), CS algorithm finds application for locating a sensor node, data routing protocols for optimizing the lifetime of the sensor network,

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for creating node clusters and optimizing network energy efficiency, etc. For maximizing the energy efficiency CS algorithm is used to distribute the consumption of energy evenly across each node so that every node consumes balanced energy which there by increases the overall lifetime of the sensor network [26]. As a sensor node has limited amount of energy it may happen that one node, for example, a master node which has more computational duties than the normal node tends to eat up the available energy more rapidly than the normal node. As a result, these master nodes die quickly and there by creating coverage holes in the network which makes the entire WSN to be disconnected. Therefore, CS algorithm balances the energy consumption along with improvement in the overall operating lifetime of the network. Localizing a sensor node in WSN is an essential requirement as it identifies the health and operating condition of each node. Localization also helps in reducing the complexity of computation along with communication overhead which again helps in prolonging the lifetime of sensor nodes. CS algorithm has been effectively used and demonstrated for localization application in WSN [26]. In WSN, sensor nodes are usually divided into clusters after initial deployment. In most cases, random deployment is preferred over sequential deployment due to operating constraints of WSN. In random deployments, it is highly desirable to involve maximum number of nodes in communication. Clustering of nodes achieves the task of increasing the coverage by involving ample number of nodes in the network and CS algorithm have been extensively used in forming of clusters [27]. In [28] author proposed clustering based routing protocol using SA and CS algorithm. In [29] an adaptive CS based energy efficient algorithm was proposed for placement of nodes in wireless body area network.

7.2 CSA Application in Antenna Array Pattern Synthesis The method of evaluating the parameters of antenna array for obtaining the field pattern with reduced level of side lobes along with placement of nulls is known as pattern synthesis. Amplitude, phase and position are the three parameters that are optimized in antenna array pattern synthesis. In [30] author have utilized CS algorithm for optimizing the amplitude and phase in linear antenna array. In[31] authors optimized the position and amplitude of circular array for pattern synthesis. The simulation results demonstrates that CS algorithm presents better results than GA, PSO and DE algorithm. In [32] author explored CS algorithm for finding the optimum amplitude of antenna array so as to minimize the side lobe level with a constraint on beam width. In [33] author presents modified CS optimization technique for synthesizing the pattern of uniform linear antenna array. The simulation results showed improved performance than GA and PSO algorithm.

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7.3 CSA Application in Robot Path Planning In the area of robotics, estimation of optimal path for autonomous mobile robot is widely studied. The ability of swarm intelligence algorithms such as robustness, fast convergence rate and minimum computational time makes them suitable for the optimal path planning of mobile robots in unknown environment. Authors have implemented CS optimization technique for getting the shortest path from initial position to target position in unknown environment [34]. Simulation results are verified in real time by using KAPHERA III as the mobile robotic platform. Furthermore, authors have compared the results with PSO and GA.

7.4 CSA Application in Image Processing Recent work on the processing of images has increased exponentially because of its vital applications in various domains. CS algorithm has been explored in the areas of image processing viz., face recognition, satellite image processing, image segmentation, etc. In face recognition, approach CS algorithm was used to match the image with the most appropriate images from the available database [35]. CS algorithm achieved better results than PSO and ACO.

7.5 CSA Application in Design and Applications of Engineering Domain In engineering domain, the term design covers multiple domain such as electrical and electronics, mechanical and automotive, physics and chemical, civil and construction, etc. Main objective in each engineering domain will to be reduce cost, minimize energy requirement and consumption, reduce heat generated and to minimize the overall impact on the environment. Authors of [36], reported that CS algorithm is used in structures where the algorithm has given an acceptable performance and has solved many optimization problems with respect to structures. Use of CS algorithm in other design problems such as design of pressure vessel, parameters identification for structural designs and design of 3-bar structures also exists in literature.

7.6 CSA Application in Power and Energy In power and energy sector, maximizing the available power and minimizing the energy consumption while maintaining the balanced load has always been a challenging task. CS algorithm is used in maximum power point tracking (MPPT) in

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solar panels which uses photo voltaic cell [37]. In this article, authors reported that CS algorithm is capable of handling the partial shading effects and can perform the tracking of maximum power at the cost of a single photo voltaic cell. CS algorithm has also addressed few optimization problems such as reservoir optimization problem, optimal allocation of power capacitors for storage and distribution of voltage in the power sector. In distributed generation of power, CS algorithm aims at improving the power profile and thereby reducing the overall power loss. In [38] author proposed improved CS optimization technique to strengthen the energy extraction capability of fuel cell. A hybrid GWO and CSA was proposed for extraction of parameters of different solar PV models under different operating conditions [39]. The hybrid model was analyzed on different benchmark functions and presents optimum balance between exploration and exploitation.

8 Assessment and Evaluation of CS Algorithm The key factors examined for evaluating the performance of any optimization algorithm are their balance between exploration and exploitation, local optima avoidance capability, rate of convergence, and mathematical complexity. This section assess and compares the performance of CS algorithm with other metaheuristic algorithms. CS algorithm is known for its simplicity, less tuning parameters, ease of implementation, thus the algorithm adaptively solve wide range of complex science and engineering problems. CS algorithm explores the area under the boundaries randomly employing Levy flight. Since the size of the step of Levy flight is obtained from the Levy distribution. Therefore, CS technique has slow convergence rate as compared to PSO and GA, and didn’t find any control to reach the optimum result. To overcome this limitation researchers have modified the CS algorithm by incorporating different exploration strategy. Mathematically CS optimization technique is less complex in contrast to GA and PSO as the algorithm don’t require any crossover and mutation operator of GA and velocity update operator of PSO. Thus, CS algorithm has shown superiority in solving number of engineering problems as compared to older metaheuristic algorithms. Although the algorithm couldn’t be efficiently applied on diverse problems therefore researchers have hybridized CS with other algorithms to resolve this limitation. In the area of engineering many of the design problem are multi-objective and have multiple optimal solutions which forms the Pareto front. There are number of powerful multi-objective metaheuristic algorithms that deals with this kind of problems. In 2013, Yang and Deb [40] developed multi-objective CS algorithm by modifying some of the building blocks of single objective CS algorithm. Author analyzed the performance of proposed algorithm by solving design problems in structural engineering. Exploitation is another important parameter in the field of optimization. CS algorithm presents good exploitation capability to address a particular problem. Although,

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Table 1 Assessment of CS algorithm

CS algorithm

Computational complexity

Search technique

Convergence speed

Exploration capability

Exploitation capability

Less complex

Mutation

Slow

Poor

Good

researchers have employed some modification to existing algorithm for improving its exploitation capability. Table 1 outline all assessed parameters of CS algorithm. In literature there are number of metaheuristic algorithms for solving single and multi-objective problems. No Free Lunch (NFL) theorem [41] states that there is no single optimization algorithm that can find the solution for all optimization problems. Therefore, some modifications need to be incorporated in the algorithm to suits it to a specific problem. Researchers have modified and hybridized CS algorithm for solving real world NP-hard problems.

9 Conclusion In this article, inspiration, mathematical model and exploration and exploitation capability of CS algorithm is discussed. Different modified and hybridized versions of CS algorithm are explored and analyzed. The artificial intelligence applications of CS algorithm, more specifically in the area of training ANN and in SVM are analyzed and briefly discussed. A detailed discussion of engineering applications of CS algorithm such as WSN, antenna array pattern synthesis, robot path planning, face recognition, satellite image processing, MPPT under partial shading conditions are presented. Discussion of these diverse applications of CS algorithm ranging from current engineering research domain to machine and deep learning are the key points of this chapter. At the end the CS algorithm is accessed in terms of mathematical complexity, exploration and exploitation capability and rate of convergence. The research gaps of the CS are as follows: • CS algorithm can be explored in 4G/5G communication for optimizing weights of antenna array in adaptive beamforming in FPGA boards. • CS algorithm can be explored in raspberry pi for solving complex engineering problems such as PID controller, robot path planning, etc. • The algorithm can be hybridized or enhanced to improve the exploration capability and convergence rate. • Complex problems in the health sector can be optimized using CS algorithm.

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Energy Management System for Hybrid Energy System: Renewable Integration, Modeling and Optimization, Control Aspects and Conceptual Framework Geeta Kumari, Akanksha Sharma, H. P. Singh, R. K. Viral, S. K. Sinha, and Naqui Anwer Abstract In developing Countries like India, the interest of energy has been expanding surprisingly because of the speculation of the agricultural, modern just as residence exercises. The rising an Earth-wide temperature boost marvels and an expansion in the consumption of petroleum derivatives has been the most crucial main thrust towards the thoughtfulness regarding misuse of Renewable Energy Sources. Alongside different favorable circumstances of these sources, there comes a heap of complexities connected to them because of their irregular and variable nature. Consequently, to maintain a strategic distance from these vulnerabilities it is important to give these assets appropriate planning and proper energy management. This work here a detailed study of different optimization techniques which can be applied to the renewable energy resources including the multi-agent solution as well as the Artificial Intelligence and Micro-grid controller which can offer a clear vision for the researchers in this field. Certain recommendations considering the challenges in renewable energy (RE) development are also been provided. In the proposed framework, the smart grid is optimized by the use of different optimization methods. G. Kumari · A. Sharma (B) · H. P. Singh · R. K. Viral · S. K. Sinha Department of Electrical & Electronics Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh, India e-mail: [email protected] G. Kumari e-mail: [email protected] H. P. Singh e-mail: [email protected] R. K. Viral e-mail: [email protected] S. K. Sinha e-mail: [email protected] N. Anwer Teri School of Advanced Studies, New Delhi, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_9

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Keywords Energy management system · Renewable energy sources · Integrated renewable energy system · Hybrid energy system

1 Introduction Developing vitality request and deficiencies of vitality supply, just as energy use and ecological security, are turning out to be basic thought. Specifically, satisfying the vitality need in some remote areas (creating towns, islands and sign stations, and so on) is a provoking issue to be tackled as it isn’t financially savvy to stretch out the force framework to cover it. Building up the utilization of sustainable power source right now to be increasingly encouraging on the grounds that the energy wellspring of Renewable Energy (RE) plentiful in these districts [1]. The cross variety framework, formed by interconnecting little, explicit age (wind turbine, PV gathering, little degree turbine, full cell, etc.) and limit gadgets (battery bank, flywheel, and so forth.), has end up being the best methods for satisfying the essentialness need with high immovability, adaptability and cost sufficiency. By and large, Micro lattices created power using oil subordinate red joined warmth and force and reacting engine generators. Microgrid scale networks can run on renewables, vaporous petroleum filled start turbines, or creating sources, for instance, vitality parts or even little particular atomic reactors, when they become monetarily available [2]. The joining and amassing of DER (Distributed Energy Resources) makes the necessity for Distributed Energy Resources Management Systems (DERMS). In the course of the most recent two decades, more consideration has been pulled into environmentally friendly power energy age the world over. Here, the general force age is diminished because of the high infiltration of the various RESs. To satisfy this force diminishment the petroleum derivative age frameworks are utilized, yet the natural outflow brought about by this non-renewable energy source age frameworks [3, 4]. Among any place all through the RESs progressions the PV arrangement furthermore, the breeze vitality frameworks are the world’s snappiest making RESs which is work in structure tied. Using these two RESs, the power age and the framework security are improved and the creation expenses of the framework are limited [5–8]. The normal limit of earth for providing fossil energy isn’t ever enduring. Along these lines, notwithstanding the expanding energy requests, the dangerous global warming, exhaustion of conventional energy sources and because of the persistent increment in oil costs have been occupying overall consideration for the improvement and usage of sustainable power sources [9]. To deal with the variable weight request, the breeze remain solitary structures are used to flexibly separated loads requiring essentialness amassing. For such frameworks, during the shakiness of wind and weight request, the force the board is performed by the dynamic and responsive force, rehash, and strengthen organize voltage during deficiencies are obliged by the force electronic inverters. To satisfy the enthusiasm of intensity, the vitality inequality of sun oriented and wind vitality frameworks used the limit system with the satisfactory limit. The results of the examination of Energy Information Administration shows that the world essentialness uses increments with

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2.3% dependably. It is evaluated that by the year 2035 the essentialness use will move by over half showed up contrastingly comparable to the present circumstance. 2015 being the first year when the extent of imperativeness passed on by hydro power plant was over taken by the essentialness made by wind power, sun arranged and other viable force assets [10]. The hybrid system that joins sun oriented and wind creating units with battery reinforcement can weaken their individual changes and decrease energy stockpiling prerequisites fundamentally. A few issues come from the expanded unpredictability of the system in correlation with single energy systems particularly when it is supported by and productive capacity framework. This multifaceted nature, realized by the utilization of two unique assets consolidated, makes an examination of mixture frameworks progressively troublesome [11].

2 Energy Management Systems A vitality framework that joins numerous vitality resources is known as a hybrid renewable energy system (HRES). By and large, utilizing such frameworks prompts higher unwavering quality and lower activity cost than on account of utilizing just a single vitality source [12]. An Energy Management System (EMS) gives the procedures and frameworks expected to fuse vitality contemplations just as the vitality the executives into everyday tasks as a feature of an authoritative methodology for improving vitality execution [13]. A power the board controller for a DC Micro-grid within sustainable power resources, stockpiling components and burdens are introduced. The controller guarantees energy equalization and lattice dependability in any event, when a few gadgets are not controllable as far as their capacity yield, and ecological conditions and burden shift in time [14]. The present world has gotten a total subject to vitality world where power is of prime significance. Power has made life simple and hence its utilization is expanding enormous sum step by step. An intelligent energy management system (IEMS) for keeping up vitality supportability in sustainable power source frameworks is presented here. This comprises of wind energy and photovoltaic (PV) sun powered boards are built up and used to experiment the proposed IEMS. Since the breeze and sun-based resources are not dependable as far as manageability and force quality, an administration framework is required for providing the heap power request [15].

3 Need of Energy Management System Creating economy and land changes has driven majority from everywhere throughout the world to go to various types of vitality resources to satisfy their vitality needs [16]. The prudent, continuous and consistent inventory of power is basic and required by the customers however unfortunately in numerous nations; because of absence of vitality creation and as a result of the national offices being driving provider of

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power the circumstance of vitality showcase is very basic. In this way, to meet the prerequisites clients are utilizing interchange sources rather than regular sources however the absence of joining between these sources is the most significant factor to be considered so as to address the vitality issues [17]. The basic objectives for the proposed system are given below: 1. To deal with association and disengagement occasions of batteries. 2. To give low need stacks each time heap request is more prominent than age limit. This control activity envisions at all hurtful activity of the system through foreseeing model, which identify voltage burden uneven characters. 3. To keep the voltage greatness with a most extreme variety of ±5% [18].

4 Modeling and Optimization Techniques Used for RESs While arranging, structuring and building a hybrid energy framework, the issue gets complex through unsure sustainable supplies, load request, non-linear attributes of segments and the way that the sizing and operation methodologies of hybrid framework are autonomous. This requires an advanced hybrid energy framework with a goal to limit the life cycle cost while ensuring reliable framework activity. As the segment sizes and activity are related, diverse arrangement of segment design is dissected in every hybrid combination to get an ideal optimal hybrid system [19]. Approved an ideal structure of HRES for a remote town in Pondicherry, India utilizing Artificial neural network (ANN-BP) feed-back propagation and LevenbergMarguardt (LM) information preparing ideal procedure. The work proposed demonstrates that HRES in remote areas is a financially savvy answer for the maintainable advancement of the rustic zones [20]. A system was built to give complete investigation on the new structures of AC as well as DC frameworks, to decide limit and ideal plan with HRES in a smart micro grid to expand the accessibility and to reduce organize costs utilizing multi objective PSO strategy [21]. The combination of at least two advancement systems is known as hybrid procedures which are utilized to conquer the issues and impediments of the single calculation. There are different such procedures including artificial neural fuzzy interface system (ANFIS), artificial neural network/GA/monte carlo simulation, hybrid iterative/GA, monte carlo simulation (MCS)—PSO, simulation optimization [22]. To introduced an ideal arranging of PV-Wind-Biomass hybrid vitality framework including the reinforcement power sources like battery bank and diesel generator. GA and PSO are uses for the cost of energy minimization [23]. There are four calculations in particular subterranean ant lion optimizer algorithm (ALO), grey wolf optimizer algorithm (GWO), krill herd algorithm (KH) and JAYA calculation for the foundation of rules and the instruments for vitality the executives enhancement and furthermore the measuring of a wind and sun oriented creation framework utilizing an electrochemical stockpiling gadget [24]. The way toward advancing the control, measurement and selection of segments for the hybrid system is to give it a practical solution for the general public. The

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fundamental target of the paper is diminishing the Total System Net Preset Cost (TNPC), Cost of Energy (COE), neglected burden, CO2 discharges utilizing Genetic Algorithm (GA) and HOMER Pro Software. The after effects of the two techniques are contrasted and four mixes of hybrid sustainable power source frameworks [25]. An energy-based administrators unit including a disconnected unique programmingbased advancement orchestrate and continuous standard based controller is planned to in a perfect world control the force stream in the structure as showed by the gave energy plan. The framework is planned by required guidelines of the grid associated residential RES [26]. New equal and parallel hybrid genetic algorithm-particle swarm optimization algorithm [P-GA-PSO] is created to fathom in estimating the energy of the board issues for small scale frameworks. The considered smaller scale grid is made for four diverse RE innovations and energy stockpiling framework. The destinations of both enhancement issues are to fulfill regular burden request, to limit energy creation cost, to amplify RE combination, to maintain a strategic distance from energy misfortunes and over-burden [27]. These days, the control gear for the power quality generally uses a voltage source converter (VSC) or a current source converter (CSC). The yield of converters is encouraged for controlling the power quality depending on the voltage or the current reference. This control strategy used for the converter basically influences the impact of the control of power quality. A variety of works like delineating control strategies, which are the hysteresis control, bum control, model farsighted control, comparing essential control, relative full control, dull control, and nonlinear solid control are there [28–34] (Table 1).

5 Control Aspects With the broad use of arbitrary loads and the huge scope opportunity of disseminated vitality ages dependent on power gadgets types of gear, power quality issues in the conveyance arrange are progressively genuine with new attributes. Further inside and out research is of incredible centrality in principle and practice. It gives a review of intensity quality examination, compensators and control innovations under the recent circumstance of a smart grid. It depends upon the physiography and various control procedures for conditioning of power quality, especially late properties of force quality and suitable control progresses in miniaturized scale matrices and spread force plants. Finally, examples and possibilities of the control development of power quality are introduced, basically to achieve security and compelling movement of the shrewd structure (Table 2).

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Table 1 Comparison of various optimization techniques used for RESs S. No. Techniques/approach Objective function

Merits

Demerits

• Reorganisation • Simplify the • and behaviour • optimisation and situation of EMS reorganisation

References

1

Multi-agent solution in four case

2

Micro grid controller • Grid services and participating in markets

3

Optimization algorithm

• Optimal sizing • A minimum • Annual costs [4] of hybrid life cycle notably grid-systems cost lower

4

Genetic algorithm (GA) and Pareto optimality concept

• Effectiveness of the proposed models

• Maximizing • NPC analysis [6] the power condenses all supply the costs reliability (positive) • Minimizing and revenues the system (negative) lifecycle cost

5

Dynamic decision strategy

• Supervisor control • To check storage and grid constraints to prevent blackout

• Reducing the energy costs • Greenhouse gas emissions • Extending the life of flywheel

6

Intelligent energy management system (IEMS) with fuzzy logic decision

• Maintaining • Tracks the the energy maximum sustainability power in renewable energy systems (RES)

7

Numeric Iterative Algorithm

• Minimum life cycle cost

• Flexibility in complex grid

Small in size Complex energy management

[1]

• DER outside a boundary

[2]

• A possibility to select the optimum control scheme

[8]

• Wind and PV [15] sources are not reliable in terms of sustainability and power quality

• Reliability • Require • Economic diesel power generator supply to the backup for village peak hours • Applicable to any village area

[19]

(continued)

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Table 1 (continued) S. No. Techniques/approach Objective function

Merits

Demerits

References

8

Artificial Neural • Minimization Network Feedback of total cost Propagation (ANNBP) Algorithm

• Estimate load forecasting

• No practical system used

[20]

9

Particle Swarm Optimization (PSO)

• Minimization of total cost

• Reduce losses • Increased efficiency

• Risks related [21] to renewable sources uncertainty

10

GA Hybrid Iterative Technique

• Minimization of system cost • Loss of Load Probability (LPSP)

• Lowest cost • Applicable [22] optimization only when average wind speed is available

11

GA PSO

• Minimization of Energy Cos

• Reliability • Low green house gas emission

12

Ant Lion Optimizer • Minimization • Reliability • Does not (ALO) of Energy cost • Reduction in have a much Grey Wolf Optimizer cost optimal (GWO) solution Krill Herd Algorithm (KH) JAYA Algorithm

[24]

13

Genetic Algorithm (GA) and HOMER Pro Software

• Total System • cost Net Present effective Cost (TNPC) power • Cost of Energy solution (COE)

[25]

14

2D Dynamic programming optimization

• Optimal energy management of residential HEES

• Performance • Complex is increased model by 4% • Cost is reduce

15

GA-Particle Swarm Optimization

• Sizing • Energy management problem

• Minimizing • Cost of [27] the energy energy close production to Fossil fuel cost cost • Maximizing the RE energy integration • Avoiding energy losses (continued)

Not more efficient than P-GA-PSO

• Homer is more CO2 emissions

[23]

[26]

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Table 1 (continued) S. No. Techniques/approach Objective function

Merits

Demerits

References

16

• Security • Efficient operation of the smart grid

• Harmonics generated by power electronics converters

[28]

Active and Passive control technology

• Power quality analysis • Compensate

Table 2 Comparison of various optimization techniques used for control S.

Control strategies

Parameters

References

1

• Multi-agent solution

• Battery and power grid

[1]

2

• Battery-based storage Asymmetric • Power quality cascaded H-bridge multi level inverter (ACMI)

[5]

3

• Energy management control strategy

• Cycle-charging batteries

[12]

4

• Power management controller

• Power balance • Grid stability

[14]

5

• Intelligent power management system (IEMS)

• Power management during critical [15] peak power instances • Fast power demand changes

6

• Feed-forward compensator

• Reduce low frequency ripple

[26]

7

• Active and Passive control technology

• Power quality analysis • Compensators

[28]

No.

6 Conceptual Framework The inspected work show that the scheme procedure demonstrating and enhancement for energy the board framework for hybrid energy framework ought to be altered considering the conveyance arrange properties. In the proposed structure, the keen lattice is advanced by the utilization of various streamlining strategies. The proposed technique offers a chance to play out an ideal techno monetary assessment of energy the executive’s usage in dissemination systems. The cost/advantage examination of streamlined strategy application and its capacity to sustainable power source settlement will be done later on works. The total applied structure depicting a mixture sustainable power source framework is appeared in type of a flowchart in Fig. 1.

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Start

Estimate the load, Demand and SOC of the Battery

Suggest the optimal design for the hybrid system model using simulation

Using simulation to calculate the power generated from different sources used for the hybrid model

Power generated is AC?

Yes

Convert to DC power ( P wind , P hydro )

No Calculate the total Power P t generated

No

P t ≥ P lo ad

Depending on the maximum power obtained from different sources of generation

Yes Using sensors to obtain the voltage value from each system Adjust the voltage using the buck – boost circuit and controller

No

Same Voltage

Yes

Integrate the whole system using the buck – boost controller circuit then, connect to the load End

Fig. 1 Conceptual framework for a hybrid renewable energy system

7 Recommendations In nations like India, which are wealthy in sustainable assets, the influence age utilizing RES will be on appeal due to the declining non-renewable energy sources and it gets essential to focus on different provokes joined to these assets and relying upon these difficulties there are sure proposals which can be remembered: 1. Technical limitations like-power quality, solidness, voltage and force changes ought to be considered appropriately because of the multifaceted nature of the framework. 2. Various improvement methods like—ANFIS, ANN, GA ought to be utilized to locate an ideal answer for the unpredictability engaged with the procedure.

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3. For keeping up the solidness of IRES, the transient examination of framework ought to be done in a legitimate way by changes in the parameters like solar irradiance, speed of wind, load request and so on.

8 Conclusion The chapter gives an exhaustive investigation of the most recent research improvements in the field of advancement of sustainable power sources. The outline gives about different streamlining strategies included and utilized in the arranging, plan and control of sustainable power source. Different optimization techniques are discussed like multi-agent solution, CPLEX solver, intelligent energy management system, Genetic algorithm (GA), Pareto optimality concept, Optimization algorithm, Dynamic power management controller, simulation optimization, etc. Various improvement methods like—ANFIS, ANN, GA, GA-Particle Swarm Optimization are also used for optimization of hybrid sources. The examination shows that a few specialists have utilized heuristic enhancement techniques and others have tackled multi objective issues utilizing Pareto advancement strategies. In this way, it very well may be reasoned that multi objective enhancement strategies utilizing different hybrid procedures is a promising field in sustainable power source advancement.

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Recent Advances and Application of Metaheuristic Algorithms: A Survey (2014–2020) Neha Khanduja and Bharat Bhushan

Abstract Metaheuristic optimization is a higher-level optimization that uses a simple and efficient procedure to solve optimization problems. Metaheuristic can understand higher-level algorithmic framework which is problem independent and equipped with a set of strategies to develop heuristic optimization algorithms. Metaheuristic can be defined as a method to get a solution that is “good enough” in “small enough” computing time. MHA gives a better trade-off between exploration (global optima) as well as exploitation (local optima) along with solution quality and computing time. The characteristic which makes MHA more reliable and efficient as compared to exact methods are (1) adaption according to the need of realtime optimization problems (2) better solution quality in lesser computation time (3) non-problem specific, approximate and non-deterministic. The literature of the last three decades clearly shows that there is an explosion in the field of MHA from different sources of inspiration. This literature review consists of some of the metaheuristic algorithms which come in existence from 2014 to 2020. The review describes algorithms and modifications done so far. Keywords Metaheuristic algorithms · State of matter search · League championship algorithm · Bird mating optimizer

1 Introduction Optimization is all over, be it building structure or mechanical structure, business arranging or on the other hand occasion arranging, and so on. We use optimization methods to take care of issues intelligently by picking the best from a bigger number of accessible choices [1]. In some real-time optimization issues, no definite solver can be applied to unravel them at a moderate computational expense or inside a sensible time, because of their multifaceted nature of the measure of information to utilize. In N. Khanduja (B) · B. Bhushan Delhi Technological University, Delhi 110042, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_10

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such cases, the utilization of conventional systems has been broadly demonstrated to be fruitless, in this manner requiring the thought of alternative optimization draws near [2]. Optimization is the process that is used to deal with real-time problems having high nonlinearity, complexity, large solution space, etc. These increased complexity results in need of a process which can give good quality solution in a reasonable amount of time by using available resources. Metaheuristic algorithm is such a technique that has become an integral part of all optimization process. An optimization process consists of several steps like the mathematical definition of the system which is termed as an objective function (a function which is used to evaluate the nature or quality of generated solution), variable identification, specify the constraints, define system properties and then find an optimized response. In a broader, way the optimization process can be characterized in two categories (1) exact method (2) approximation method [3, 4]. The exact method guarantees the optimal solution whereas the approximate method results in good quality of solution in a reasonable amount of time but it doesn’t guarantee optimality. The Exact methods of optimization include branch and bound technique, dynamic programming, and approximate method include Local search, cut and plane, genetic algorithm, scatter search, etc. Further Approximate methods can be categorized into approximation algorithms and heuristic methods. The previous plan gives provable arrangement quality and provable run-time limits, while the last includes finding sensibly great arrangement in a sensible time. Heuristic calculations are exceptionally problem specific. Metaheuristics act like guiding mechanism for the elemental heuristics. They are not problem or area explicit and can be applied to any optimization. The term metaheuristics was presented by Glover [3, 5]. Meta-heuristics are refined logically to locate an ideal arrangement that is “adequate” in a figuring time that is “sufficiently little”. Metaheuristic optimization helps to settle wide scope of ongoing issues because of its (i) effortlessness and simple to actualize; (ii) needn’t bother with slope data; (iii) keep away from neighborhood optima; (iv) can be exploited in a sufficient scope of issues wrapping various controls [6]. Dismissing their wellspring of motivation, there is away from the expanding fame and reputation picked up by nature-and bio-inspired optimization calculations over the most recent decade. This energy discovers its explanation in the ability of these calculations to learn, adjust, and give great answers for complex issues that in any case would have remained unsolved. Numerous outlines have gained by this range of calculations applied to a wide scope of issue trick, from combinatorial to large-scale optimization, evolutionary data mining, and others the same. Thus, practically all business divisions have utilized this achievement as of late [2]. Notwithstanding the accomplishments of the old style or classic metaheuristic calculations, new and novel transformative methodologies additionally developed effectively in the most recent two decades. Exploration of Metaheuristic calculations in amid of present time gives an incredible statistic of new methods propelled by behavioral or evolutionary forms. In numerous cases, this new rush of metaheuristic approaches yields the best answers for a portion of the unsolved benchmark issue sets [7].

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From 2014 to 2020 more than 1214 research papers are published in different journals, magazines, conference papers and books etc. are shown in Table 1. In this chapter an attempt is made to show that how emerging and popular metaheuristic optimization Algorithms are. In this survey only some esteemed journals are considered. Figure 1 shows the Number of papers published on metaheuristic optimization in different publishing domain from 2014 to 2020 and Fig. 2 shows total number of publication year wise from 2014 to 2020. In this study only some major publishing domains are considered. This chapter is expected to be a targeted manual for the most well-known naturemotivated metaheuristic optimization algorithms in the last five years. It is not the main paper to audit this region, yet it is the first to introduce these calculations in quite a while that will be commonplace to the more extensive advancement, metaheuristics, developmental calculation, and swarm registering networks. In contrast to some past surveys, it doesn’t plan to advocate for this region of examining or offer help for framing algorithms dependent on perceptions of characteristic frameworks. It just expects to report and outline what as of now exists in additional open access terms [8]. Key challenges and direction of future advancement are also discussed in the chapter. Table 1 Year wise publications on metaheuristic optimization in different publishing domain Year of publications publishing domain

2014

2015

2016

2017

2018

2019

2020

Springer

347

322

415

549

616

1004

730

Elsevier

180

212

227

261

301

337

286

27

25

43

57

81

102

62

Taylor And Francis

IEEE Xplore

145

135

155

151

194

282

182

ACM

117

154

173

166

167

166

38

Wiley

105

83

148

153

233

276

137

1200

SPRINGER

1000 ELSEVIER 800 600

IEEE

400

TAYLOR AND FRANCIS

200

ACM

0 2014

2015

2016

2017

2018

2019

2020

Fig. 1 Number of papers published on metaheuristic optimization in different publishing domain from 2014 to 2020

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N. Khanduja and B. Bhushan 1400 1200

2014 2015

1000 2016 800 2017 600 2018 400 200 0

2019 2020

Fig. 2 Total number of publications in different esteemed journals from 2014 to 2020

Figures 1 and 2 reveals that each year hundreds of research papers are publishing in this area and these numbers are increasing with each passing year. In this chapter an attempt is made to give an easy and simple way of reviewing the recent advances and applications of metaheuristic algorithms by keeping the references limited. A straight forward approach is used for this survey; only papers related to recent algorithms and recent reviews are cited here. This chapter is organized in the following sections: Sect. 2 gives an overview of some recent algorithms. Section 3 focuses on challenges in the development of new metaheuristics. Section 4 describes future directions for advancement in the field of metaheuristic and Sect. 5 concludes recent metaheuristics along with issues and future of metaheuristic algorithms.

2 Recent Metaheuristic Algorithms There are two different ways to direct scan for efficient literature survey: Automatic and manual. This literature survey favors the later methodology, as the earlier approach presents scarcely any disadvantages since as of now accessible automatic search engines are not viable for this sort of study. The manual pursuit is commonly utilized for looking through essential examinations from the most important sources [1]. A proportional representation of surveyed performed on different categories of metaheuristic algorithms has been presented in Fig. 3. In the most recent decade, metaheuristics algorithms are developing as the feasible mechanism and optional tool for increasingly customary continuous applications. Among the numerous metaheuristics calculation, a few of the main algorithm developed in last 5 years has been explained with their year of evolution, Developers, control parameters, domain specifications, exploration and exploitation capability,

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Fig. 3 Proportion of surveyed algorithm by its classification [2]

advancement is done in an existing one, hybridization, etc. are presented in Table 1 (Table 2).

3 Challenges in the Development of New Algorithms We are frequently perplexed and regularly shocked by the fantastic proficiency of metaheuristic algorithms. Straightforward algorithms can do something amazing ‘extraordinary’, in any event, for extremely intense global optimization issues [37– 42]. Many detailed and modern ordinary calculations frequently don’t function admirably, despite the way that ordinary calculations have been all around tried for a long time. New metaheuristics regularly work much better by and by, even though we may not comprehend why these calculations work. Experimental perceptions, immense writing, and some fundamental combination investigation all recommend that metaheuristics accomplish function admirably. Freely, the achievement and fame of metaheuristics can be ascribed to the accompanying three variables: calculation simplicity, ease for execution, and diversity in solution. Regardless of the expanding notoriety of metaheuristics, numerous urgently significant inquiries remain unanswered. There are two significant issues: hypothetical structure and the hole among hypotheses and applications. Right now, the act of metaheuristics resembles heuristic itself, somewhat, by ‘experimentation’. Numerical investigation lingers a long ways behind, aside from a couple, restricted, concentrates on intermingling examination and security, there is no hypothetical system for evaluating metaheuristic optimization algorithms [43]. In a broader way challenges in the development of metaheuristic algorithms can be characterized as follows.

Name of developer Erik Cuevas1 Alonso Echavarria, Marte A. Ramirez

Ali Husseinzadeh Kashan

Name of algorithm and year of evolution

State of Matter Search (SMS) Algorithm, 2014

League Championship Algorithm (LCA), 2014

Table 2 Review on metaheuristic optimization algorithm

(continued)

The main concept of LCA is sport driven and has a good convergence rate for global minima. To get better convergence and exploration-exploitation balance LCA can be used with self-adaption methodologies. Testing results on benchmark functions conclude that it can be used for real-time optimization problems [11] LCA is modified by employing “between two halves analysis” instead of post-match analysis because it results in a variational operator and which further results in improved convergence. This modification makes LCA more realistic so it is named RLCA i.e. realistic league championship algorithm [12]

SMS algorithm is based on the thermal energy motion mechanism which results in a diversity of population and also prevents the particles to trap in local optima and results in a good balance between exploration and exploitation capability of the algorithm [9] SMS algorithm is modified so that its application can be extended to solve multiobjective optimization problems, for this, the whole algorithm works in two different stages first objective function is obtained by using Pareto strategy and then in later stage fuzzy decision making is implemented to get final solution [10]

Main features of the algorithm and advancement done in the existing algorithm

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Name of developer Alireza Askarzadeh

Name of algorithm and year of evolution

Bird Mating Optimizer (BMO), 2014

Table 2 (continued)

(continued)

Main characteristics of BMO are: • capable of exploiting the best-searched regions • adequately analyze the search space • different approaches are used to analyze the search domain • using platonic birds for both explorations as well as exploitation • the beauty of BMO is that new solution can be produced by weak quality solutions [13] BMO suffers from the limitations of finding the global minima for complex multiple minima types of functions and slow convergence. To overcome these limitations of BMO further improved versions of BMO are proposed. BMO is embedded with random search and diversity measurement to solve the problem of locating global minima [14] and it is hybridized with TLBO (teaching-learning based optimization) also to form TLBMO i.e. Teaching-learning-bird mating optimizer (BMO). This hybridization gives a better exploration-exploitation balance fast convergence and good quality solutions [15]

Main features of the algorithm and advancement done in the existing algorithm

Recent Advances and Application of Metaheuristic Algorithms … 213

(continued)

Seyedali Mirjalili, Seyed Mohammad Mirjalili, Andrew Grey wolf optimization algorithm is inspired by grey wolves and it Lewis shows good exploitation capability for unimodal functions and superior exploration capability for multimodal functions [16]. Grey wolf optimization (GWO) is hybridized with variable weights (VW-GWO) so that it doesn’t get trap in local optima and a result proves the superiority of improved algorithm [17]. GWO is hybridized with quasi oppositional based learning [QOGWO] to decrease the computational complexities and give gives a better dynamic performance in terms of time response specifications [18]

Grey Wolf Optimizer (GWO), 2014

Main features of the algorithm and advancement done in the existing algorithm

Name of developer

Name of algorithm and year of evolution

Table 2 (continued)

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Name of developer Rasoul Rahmani, Rubiyah Yusof, Nordinah Ismail

Name of algorithm and year of evolution

Radial Movement Optimization (RMO), 2015

Table 2 (continued)

(continued)

The main features associated with the radial movement optimization algorithm are very few parameters that need to be adjusted, fast speed, robust, highly reliable, require less memory, consistent, and not trapped in local optima [19]. Since the RMO algorithm avoids the particle’s feedback which leads to loss of particle information and results in less precision and stability. In 2016 a new modified radial movement optimization algorithm [MRMO] is proposed which uses the self-feedback of particles by modifying the data structure of RMO [20] in continuation of research on the Radial Movement Optimization Algorithm, a further improved form of RMO is presented in [21] which concluded that proposed MRMO has fast convergence, requires less space, few parameters to adjust and can be applied to solve complex problems of optimization

Main features of the algorithm and advancement done in the existing algorithm

Recent Advances and Application of Metaheuristic Algorithms … 215

Name of developer R. Venkata Rao

Name of algorithm and year of evolution

Jaya Algorithm, 2016

Table 2 (continued)

(continued)

The main benefits lie with this algorithm are: parameters are not explicitly defined for such a particular algorithm, and optimized results can be obtained in a lesser number of evaluations which results in fast response [22] Limitations with the JAYA algorithm [22] are premature convergence and trapping into local optima easily. To resolve the issues with the Jaya algorithm [22] some modifications are proposed in chaotic JAYA [23] and self-adaptive JAYA [24] In the modified Jaya algorithm [MJAYA] solution is updated by changing the equation and a member having the best fitness value is used to update these equations [25]. Another modification is done by embedding chaotic maps into Jaya algorithm, i.e. C-JAYA. This hybridization is used for two purposes (1) to develop the initial population (2) control of the search equation. But, this hybridization doesn’t affect two fundamental attributes of JAYA i.e. integrity and no algorithm-specific parameter. C-Jaya or chaotic Jaya gives faster convergence and the best quality solution. Further another modification is made in Jaya by incorporating integer, discrete-continuous variables i.e. this improved Jaya can be used to solve mixed variable type problems of optimization. This algorithm gets the optimal solution briskly and the worse solution is to get updated in every iteration [26]

Main features of the algorithm and advancement done in the existing algorithm

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Name of developer Seyedali Mirjalili

Name of algorithm and year of evolution

Sine-Cosine Algorithms, 2016

Table 2 (continued)

(continued)

In SCA a mathematical model which is based on sine cosine function is developed and then numerous initial random candidate solutions are generated arbitrarily to oscillate towards the global optima. Further to get a good balance between exploration and exploitation some random and adaptive variables are also unified with the algorithm [27]. The success of any metaheuristic lies in the good balance between global exploration and local exploitation and to achieve this for SCA algorithms, some modifications have been made: To select the value of the control parameter an exponential decreasing nonlinear control strategy is adopted so that this modified form of SCA works well in nonlinear search space along with great population divergence in less number of iterations [28] literature [29] reveals that the SCA algorithm is hybridized with opposition based learning [Elaziz et al.], differential evolution [Nenavath et al.], and results in speedy convergence Reddy et al. proposed new development in SMS i.e. binary variant of sine cosine algorithm. Further, this sine cosine algorithm is modified by applying the elitism method [Sindhu et al.]. Kumar et al. develop a new hybridized variant of Sine cosine by hybridizing it with Cauchy and Gaussian mutation. Bureau et al. P proposed an adaptive differential sine-cosine algorithm for structural damage detection problem. a multi orthogonal sine-cosine algorithm (MOSCA) is proposed by Rizk-Allah et al. which is based on a multi orthogonal search strategy (MOSS). This new development in sine-cosine algorithm results is solving the problem of quicker exploitation and trapping in local optima easily Further improvement in sine cosine is done by hybridization it with the greedy Levy mutation which results in prevention from premature convergence and higher stability

Main features of the algorithm and advancement done in the existing algorithm

Recent Advances and Application of Metaheuristic Algorithms … 217

Name of developer Long Cheng, Xue-Han Wu, and Yan Wang

Name of algorithm and year of evolution

Artificial Flora Optimization (AFO) Algorithm, 2018

Table 2 (continued)

(continued)

The AFO algorithm is motivated by the movement and propagation conduct of flora. It follows three primary practices, in addition to evolution conduct, spreading conduct, and select conduct. In evolution conduct, the proliferation separation of posterity plants is developed depending on the engendering separation of the parent plant and grandparent plant. Spreading conduct incorporates autochory and allochory. Autochory gives the chance to the first plant to investigate the ideal area around itself. This conduct gives neighborhood search ability to the calculation. Allochory gives chance to unique plant to investigate more noteworthy space, and worldwide inquiry ability of the calculation is acquired from this conduct. As indicated by the normal law of natural selection the more noteworthy the endurance likelihood of a plant with higher wellness, and in this manner, the common law is called select conduct [30]. It can be applied for unconstrained multivariable, multiobjective, and combinatorial type optimization problems To overcome the problem of reduced population diversity and reduced uniformity of solution set distribution knee point-driven multi-objective artificial flora optimization algorithm is proposed which uses the elite approach to solve these issues along with this addition of adaptive neighborhood, control strategy results in enhanced algorithm development effectiveness [30]

Main features of the algorithm and advancement done in the existing algorithm

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Name of developer Amir Shabani, Behrouz Asgarian, Saeed Asil Gharebaghi, Miguel A. Salido, Adriana Giret

Name of algorithm and year of evolution

Search and Rescue (SAR) operations based Optimization Algorithm (2019)

Table 2 (continued)

(continued)

The SAR is proposed for tackling single-objective persistent improvement issues. SAR is enlivened by the investigations completed by people during exploration (search) and recovery (rescue) tasks execution of SAR was assessed on fifty-five optimization functions including a lot of exemplary benchmark optimization functions, also to assess the utilization of SAR on real-time optimization problems, it is applied to cantilever beam design and spatial 25-bar truss structure design and the outcomes uncovered that sar can discover progressively precise solution arrangements with fewer capacity assessments in correlation with the other existing calculations. Proposed calculation comprises two stages including the social stage and the individual stage, and its execution is generally straightforward. aftereffects of the tests done right now have indicated that consolidating these two stages alongside the utilization of memory prompts a harmony among intensification and diversification [31]. In future works, the presentation of SAR on different sorts of optimization issues, for example, combinatorial and huge scope optimization issues will be examined

Main features of the algorithm and advancement done in the existing algorithm

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Name of developer S. Shadravan, H.R. Naji, V.K. Bardsiri

Name of algorithm and year of evolution

The Sailfish Optimizer, SFO (2019)

Table 2 (continued)

(continued)

The sailfish optimizer is influenced by a set of hunting sailfish and mimics the attack-alternation approach. Two types of the population exist in this algorithm one is the sailfish population which is used for exploitation of best observed in the entire search space and another one is sardines population used for exploration of search space Some major attributes of SFO are: • Utilized two gatherings of prey and predator populaces to mimic the group chasing act • Utilizes the rotation of intervention to separate the system barrier of collection prey • The prey developments can be refreshed over the entire search area, and hawker is permitted to get the fitting prey to get fitter than the past SFO calculation additionally indicated critical outcomes for non-raised, non-distinguishable and adaptable test capacities [32]

Main features of the algorithm and advancement done in the existing algorithm

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Name of developer Hamza Yapici, Nurettin Cetinkaya

Name of algorithm and year of evolution

Pathfinder Algorithm

Table 2 (continued)

(continued)

This technique is roused by the aggregate development of creature gathering and mirrors the administration’s pecking order of multitudes to discover the best food region or prey The motivation of PFA is influenced by the hawking act of animals headed by a leader entity and other members chase it PFA attempts to search for the best food location, and this best food location can be considered as global optima. Due to ambiguity in optimization problems, it is a tough task to calculate global optima. So the best solution obtained so far is considered as global optima and recognized as the food area which is to be intensified by the gathering. The algorithm begins with initialization of the location of gathering randomly, further fitness is computed for each individual, and which individual has the best fitness is preferred as pathfinder which is to be pursued by gathering [33]. This algorithm employs an integrated adaptive strategy which makes it easy to use for multi-objective optimization problems

Main features of the algorithm and advancement done in the existing algorithm

Recent Advances and Application of Metaheuristic Algorithms … 221

Name of developer Paweł Pijarski, Piotr Kacejko

Vahideh Hayyolalam, Ali Asghar Pourhaji Kazem

Name of algorithm and year of evolution

Algorithm of the Innovative Gunner (AIG) (2019)

Black Widow Optimization (BWO) Algorithm (2020)

Table 2 (continued)

(continued)

BWO is motivated by the remarkable mating conduct of dark widow insects. This strategy incorporates a restrictive stage, in particular, savagery. Because of this phase, breeds with improper wellness are discarded from the circle, along these lines prompting early union. The proposed calculation has various focal points in various perspectives, for example, early convergence and accomplishing optimized value of fitness function contrasted with different optimization algorithms. Additionally, it can give competing and promising outcomes [35]

AIG is influenced by the decision of mounted gun parameters that assigns a shot accurately to an objective. The enforced revision of the gun’s setting parameters contrasts from that characterized by exemplary mounted guns hypothesis. The AIG is portrayed by high productivity and speed in taking care of different advancement issues having nothing to do with ballistics. The AIG acquires different arrangements, which gives it high productivity in staying away from neighborhood optimum point. As appeared by the tests, it very well may be utilized effectively to settle target elements of different shapes and with numerous optima, too as multidimensional capacities [34]

Main features of the algorithm and advancement done in the existing algorithm

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Name of developer Amir Mohammad Fathollahi-Fard, Mostafa Hajiaghaei-Keshteli, Reza Tavakkoli-Moghaddam

Name of algorithm and year of evolution

Red Deer Algorithm (RDA) (2020)

Table 2 (continued)

It is a population-based algorithm that emerged from the crossbreeding behavior of Scottish red deer in a mating season. Similar to other population-based metaheuristic algorithms, this RDA also starts with some arbitrary population. The whole population is divided into two categories: best RD’s are termed as “male RD” and other than male RD’s all are termed as “hinds”. The algorithm has a different exploration-exploitation ratio at each step. The algorithm is implemented on some benchmark functions along with some real-world problems [36]. This investigation opens a few new headings for future considers. Like a discrete model of RDA can be developed, also single and multi-objective version can be evolved. As needs are, the means of the proposed RDA may require a set of adjustments and hybridizations with different streamlining agents to upgrade the properties of the proposed calculation in the intensification and diversification phases

Main features of the algorithm and advancement done in the existing algorithm

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3.1 Optimal Intensification and Diversification Toward the start of a search procedure, ordinarily, exploration, or diversity is high, and it diminishes as the populace may move towards the global optima. Immense diversification may give better insurance to locate the optimal solution with better certainty, however, this will, for the most part, lead to moderate convergence, and therefore there are a few tradeoffs between certainty and convergence. Then again, low exploitation variety may prompt quick convergence while relinquishing the assurance to discover global optimality and with poor solution certainty.

3.2 Mathematical Structure There is no consolidated structure yet that can give a more full image of an algorithm, information about convergence, pace of convergence, strength, ergodicity, repeatability, and adaptability [44].

3.3 Control and Tuning of Parameters The setting of algorithm parameters can influence the calculation altogether, however, a few parameters may have a frail impact, while others may have a solid impact. In principle, these parameters ought to be tuned to boost the exhibition of the calculation, be that as it may, such parameter tuning is anything but an insignificant task [45]. The issue of premature convergence outcomes in the absence of exactness of the final solution. The final solution is a possible solution near the global optima, frequently viewed as good or near-optimal results [1].

3.4 Scalability of Algorithms Contrasted with real-world applications, the dimensionality tried is generally low. In any case, it isn’t clear if these metaheuristic algorithms can be legitimately applied to huge scope issues. The genuine scalability is yet to be tried. It is profoundly expected to test issues with the number of factors over a thousand or even a lot higher [44].

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3.5 Premature Convergence Convergence rate can rely upon numerous elements, for example, the inherent parts, structure, values of parameters, and introductory design of an algorithm and such reliance can be unpredictable, circuitous, and nonlinear. Indeed, even for the situation, it might be conceivable to make sense of the convergence rate, it might be hard to control it to expand the searching efficiency. It very well may be normal that such control can be interlinked with the control and tuning of parameters [44].

4 Future Directions for Advancement in Metaheuristic Algorithms After witnessing a grand success of metaheuristic algorithms in dealing with complicated optimization problems, this question is yet to answer mathematically “what makes metaheuristic algorithm so competent”. Although research is going on to get maturity in this field. A vast literature on a survey of metaheuristic shows that researchers are continuously working on addressing the gap between the theoretical and experimental framework of the algorithm [1]. Another main field that requires the attention of the researcher is intelligent sampling and surrogate modeling. Through intelligent sampling, the limits of issue space are diminished for confined looking to best neighborhoods, while surrogate techniques help metaheuristics in work assessments of profoundly computationally costly capacities through approximating the real objective function. This area is not fully explored to date so it has vast potential of research. One more research area which needs to give emphasized by the researcher is to blend exact algorithms with metaheuristic algorithms. Some researchers have done work on the combination of these two and results show that it results in accelerated convergence rate [46]. Another modern technology which must be emphasized with metaheuristics is parallel computing [47]. Some Other emerging points which must be associate by researchers with metaheuristics are a hybridization of two or more metaheuristic in such way that benefits of two individual algorithm results in a new and stronger algorithm [44]. Along with this self-tuning, self-adaptive are tools which may lead for better future for metaheuristic. Whenever any researcher associate these new techniques with metaheuristic it must be taken care that it has clear structure along with ease of application [48].

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5 Conclusion In this chapter, many new algorithms of the last five years are examined along with the inspiration for their development and advancement done till the date. First, some recent metaheuristic algorithms developed in the last five years have been described. Then, some key challenges in the development of new metaheuristic algorithms are discussed, followed by future directions for the development of new metaheuristic algorithms. literature review of recent these metaheuristic algorithms reveals that Adaptable metaheuristics to be structured that can self-tune, self-adaptive, or selfadvance to adapt to complex and exceptionally imbalanced scenes of complex optimization issues with huge decision variables. It is seen that presentation investigation of metaheuristic techniques has been generally performed dependent on the basic norm of the fitness function, standard deviation, and some fundamental statistical tests on certain test functions; which is a specially appointed methodology. All the more entrenched and usually concurred execution approval criteria are required to build up firm decisions about the proficiency of any strategy being presented.

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Introduction to Renewable Energy Market and Metaheuristic Algorithms for Condition Monitoring of Photovoltaic Parameter Estimation Pradeep Kumar

Abstract For the growth of renewable energy in Indian modernized power zone, several efforts have been made in this chapter. This chapter précis the availability, existing status, key achievement and future potential of renewable energy, tradable REC certificates, and their consequences on the aspects of promoting renewable energy. It attempts to review a variety of plans and assesses commenced by administration of India for encouraging of renewable energy, the current policy mechanisms. Hence to explore the opportunity of a solution to the inconvenience of drastically decrement in renewable market, some comprehensive study and their future steps have been performed in this work. Highlighted power exchanges trading including which areas continue to need additional research in India. Role of ANN and Metaheuristic algorithms in renewable energy sector have been stated. This chapter also discusses about the role of private and public sector in energy sector in India and represents a brief discussion on market scenario of renewable energy especially solar energy. Keywords Government of India (GOI) · Solar radiation resource assessment (SRRA) · Market clearing price (MCP) · Renewable energy (RE) · Metaheuristic algorithms

1 Introduction In India, renewable energy has been stared in 1980 under the purview of the MNRE firstly in the world. In this chapter an analysis of the Indian renewable market in terms of how it’s varying over the years and their future implementation and capacity have been studied. This chapter also discusses about role of Metaheuristic algorithms in RE environment. Figure 1 illustrates escalation of established capacity from 1947 to 2015 for India. With a power production capacity of 273 GW, India has achieved of P. Kumar (B) EEED, NIT Sikkim, Ravangla, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_11

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fifth biggest power production in all over the world [1]. During 1990s the focused was basically on increasing the capacity since after twenty-first century due to the increasing demand of power we started shifting to generation rather than capacity but since after 2013 the world is more concerned about renewable energy sources since due to depleting sources of fossil fuels [2–4]. For the enlargement of RE, diverse plans are provided much thrust such as EA 2003, NTP 2006 and NAPCC, 2008 etc. In the Indian Renewable Energy position information 2014, the whole RE prospective from different resources in India is 249,188 MW. The unused market prospective for largely RE in India is 216,918.39 MW that illustrates a vast enlargement potential for RE in India [5]. Figure 2 represents Cumulative established capability of Wind and Solar till March 2015. The MNRE, Govt. of India has put a goal to achieve over all RE established capability of 41,400 MW till 2017 and 72,400 MW till 2022. In order to accomplish 30000 3877.8

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these targets by 2017 and 2022, already some of the policy and steps are taken and to make a successful India will have to spend approximately US$46.22 billion. The chapter is systematized as follows. After starting with Introduction in Sect. 1, Sect. 2 gives pictorial view of State-wise disintegrate of upcoming Renewable power goal in India. With the help of suitable graph, present scenario of established RE capability in India has been mentioned in Sect. 3. Section 4 shows Solar Map of India, Sect. 5 gives some idea about Renewable Purchase Obligation. Section 6 discusses Renewable Energy Certificate Mechanism. In Sect. 7, Advisory and Trading process of REC/RPO have been explained. Section 8 depicts growth timelines of renewable energy as RE Policy is increasing. Section 9 illustrates role of ANN in renewable energy. Section 10 share application of Metaheuristic algorithms in RE. Section 11 discusses about both private as well as public sector responsibility in energy sector and also represents a brief discussion on market scenario of renewable (Solar) energy and finally Sect. 12 concludes the chapter.

2 Future Renewable Power Goal (Till 2022) Provisionally State-basis disintegrate of RE goal accomplished till 2022 so that collective attainment is 175,000 MW by introducing new policy and regulatory support, MNRE Schemes, Govt. of India affords a combine of tax and non-tax profits to encourage these technologies [6–12]. Figure 3 indicates state-wise disintegrate of Renewable power goal in India.

3 Present Scenario of Installed Renewable Energy Capacity Figure 4 shows division of total energy and renewable energy established capability within India. There is maximum power generation in thermal power station but less power production by the nuclear power station. Almost 13% power is generated by RE. In RE installed capacity, maximum power production is by the wind farm.

4 Indian Solar Map and Current Scenario of Renewable Energy Installation Solar energy in India is a new trade that is taking off speedily. Till 31st July 2016, the country’s solar gird has a cumulative power of 8062 MW (8 GW). In the month of January 2015, the GOI drastically extended its solar strategy, aiming US$100 billion of deal and 100 GW of solar power till 2022. The faster development in latest employments of solar power are traced and reorganized monthly on the GOI’s MNRE

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Fig. 3 State-wise disintegrate of renewable power goal

website. Figure 5 depicted high-resolution solar maps for India as of September 2015 [13]. This high-resolution solar map was constructed by climate satellite records built-in into a spot-period precise solar mapping process. Figure 6 indicates Present Scenario of Installed Renewable Energy Capacity in India (As on 31st March 2015). Till 31st March 2015 entire established capacity in India is 272,502.95 MW and the entire renewable energy sources (RES) established capacity is 35,776.96 MW. Here the above graph shows the installed capacity and the vast RE potential to harness

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since in current status we are mainly dependent on thermal, above graph which clearly indicates that there is a long way for future growth of renewable and large potential to be harness.

5 Renewable Purchase Obligation (RPO) Renewable Obligation in UK was the first policy of its kind which serve demanding the power suppliers to include renewable power sources in their function which was introduced in April 2002. About 11% of the power produced in UK in 2010/2011 is contributed by Renewable Energy. The US Govt. was targeting a 3% production from non-hydro renewable energy sources by the years 2011–2013. India took discriminative stimulus steps by seeing the economy’s growth and adopted this policy in 2010 as Renewable Purchase Obligation (RPO). However the regulation, mandating a policy framework was made way back in 2003. During last decade this is one policy that has been accepted and implemented worldwide. RPO was implemented in India with a challenging target of supplying 15% of the energy demand in the national grid by renewable by 2020. By 2010 the very first target was set to be 10% (since it was figured out that by 2013 it has been reached) and an annual increase of 1–15% is reached by 2015. Similarly like US, India enforced this rule state-wise but the state independently wreaked policy framework for the implementation (Fig. 7).

6 Renewable Energy Certificate (REC) Mechanism A market supported mechanism known as REC, initiated in India on 18th November, 2010 [14–22]. The function of REC is to tackle the distributed availability of RE

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Fig. 7 Map for policies in different Indian states (numbers of RPO obligation is minimum at FY2009)

sources in different region of the Country splits the ‘green’ element from the ‘electricity’ element and assists meeting of the RPO by the obligated entities. Figure 8 indicates the REC Process.

Fig. 8 REC process

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7 Consultative and Trading of REC/RPO A roadmap has been afforded by the Electricity Act and National Action Plan on Climate Change to develop the RE in whole production [23–28]. RPO is the obligation authorized by Central/State Regulatory commission and is appropriate for allocation Licensee: distribution companies (DISCOMs); Open Access customer: those obtaining power from power exchanges (IEX/PXIL), from traders, through bilateral contracts etc. [29]. The REC method gets to deal with the inequality among accessibility of RE sources and the prerequisite of obligated things to assemble with RPO. Distribution corporations, open access customers and captive customers have the choice of procuring renewable power or RECs as per their obligations [30].

8 Historic Trends and Growth Enablers of Renewable Energy Figure 9 indicates RE Policy Enabler and development Timelines. This figure depicts development of renewable energy as no. of RE Policy is increasing with time. The growth timelines have been plotted for the period of January, 2002 to January, 2015. According to the Stakeholder consultations and worldwide skill key out where the new policy can boost this includes the need for

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A complete National Policy structure for RE. Keen and Credit precious purchasers (i.e. Discoms) for RE. Smoother RE Project growth situation. Modernized Grid arrangement and function.

Current policy and regulatory sustain for progress of RE have been described beneath.

8.1 Electricity Act 2003 It was started in June 2003, and is one of the most vital parts of legislation for the electricity segment and invalidates the entire previous acts that ruled the electricity trades [31–36]. EA 2003 affords information and allow for plan preparation by the Indian administration and commands SERC’s to contribute and encourage RE sources in their region of authority.

8.2 National Electricity Policy 2005 It intends for accomplishing the following purpose such as access to electrical energy, to utilize possible potential of renewable energy sources, decrease capital costs, and encourage contest and confidential zone involvement. The percentage for procure of power from renewable resources have been prepared appropriate for the tariffs to be decided by the SERCs [32, 36–38].

8.3 National Tariff Policy 2006 It tracking the National Electricity Policy 2005, has also been important legislation for renewable energy growth [39–41]. It creates that a least percentage of RE acquirement should be prepared appropriate. Moreover, a desirable tariff has been decided by SERC’s to facilitate RETs to compete.

8.4 NAPCC 2008 The NAPCC, Indian Government recognizes eight centre nationalized tasks operation during 2017, predicting numerous assesses to deal with worldwide warming. It has been mentioned that a dynamic minimum renewable purchase standard must be

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situate; with acceleration every year up to a pre-defined stage has been achieved. It covers a range of assesses [42–45].

8.5 Incorporated Energy Policy Details (Planning Assignment) 2006 It advises a track to assemble energy requires of the nation in an incorporated way till 2031–2032. This also proposed particular attention on non-conventional energy growth [46].

8.6 Other Planned Initiatives 8.6.1

Solar Park Plan

Solar parks have been focused regions of growth for solar power production schemes, isolating a region which is fine characterized, appropriately infra-structure and where the plan threats are reduced and approvals are facilitated. According to the National plan on Sketch Solar parks, MNRE will group 25 no. of solar parks of capability ranges 500–1000 MW [47, 48].

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National Offshore Wind Policy

The MNRE in order to switch this prospective is presently working on a policy for employment of offshore wind energy plans in the Exclusive Economic Zone (EEZ) of the nation [49]. The plan suggests addressing matters, for example resource appraisal and inspections, seabed allotment and hiring agreement, sanctions and migration of power produced from offshore wind power plans [50, 51]. Initial movement towards enlargement of offshore wind segment in India a MoU was signed on 1st October 2014.

8.6.3

RE Resource Estimation Catalogues

To establish potential RE wealthy spots in the nation during ground measurements, India has expanded records for renewable energy resource evaluation [52, 53]. The above task has been performed in a tender to encourage growth of consumption of RE in the nation. The NIWE has build up the wind plan of India. NIWE also assembles information from Solar [54, 55].

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Renewable Energy Associations

A proposal is developed to encourage the awareness of renewable energy by the preparation of RE organizations in AICTE Organization of the nation to teach youthful and upcoming scientists on diverse phases of novel RE [56–62].

9 Role of ANN in Renewable Energy The growth of renewable energy necessitates employ of complicated methods to exact assessment of the existing energy prospective with efficient control of process. Currently, Artificial Intelligence (AI) method is rapidly available in diverse area of renewable energy. They are capable to hold noisy and unfinished information, and previously trained, permit execution of complex tasks for prediction, modeling, identification, optimization etc. Amongst the diverse methods of AI, ANN is commonly employed. The idea of neural network study has been realized almost 67 years back, but its applications software has been build up in the previous 37 years back for carrying out practical tasks. An ANN can be described as a complicated system containing interlocked basic processing elements i.e. neurons. Neurons are systematized in the form layers and attached with diverse approaches. The application of ANN for MPPT in PV system has been discussed in [63] and depicted in Fig. 10. To enlarge effectiveness and consistency of PV systems, condition supervising and fault recognition approach may be selected. Since PV system is a static device and its preservation is less still they are affected with diverse faults. For big PV arrays, fault detection is critical and operation of PV system may be stopped during such faulty situation. Moreover, several faults in PV systems are unknown and if it

Fig. 10 PV system using ANN based MPPT [63]

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is not detected for long time, consequence is failure. Hence diverse literatures have employed soft computing techniques for fault identification [64–70].

10 Metaheuristic Algorithms in Renewable Energy The preamble of novel methods to crack linear programming problems initiated a novel wave for enlarging estimation algorithms that established and saw fabulous development in the 1990s. To deal, in a realistic logic, by the inapproximable dilemmas, there were a few techniques commenced in the 1980s and 1990s. These methodologies have been known as metaheuristics and comprise simulated annealing (SA), ant colony optimization (ACO), evolutionary computation (EC), tabu search (TS), and memetic algorithms (MA) etc. [71–76]. Nowadays, the vicinity of metaheuristics has found itself as a vital research part. The objective of metaheuristics is to afford the greatest probable results and to assure that such results satisfy definite significant properties. Here the purpose is to represent metaheuristic algorithms application in renewable energy areas. Numerous studies are intended about the wind power. Long term wind speed prediction bear on hybrid support vector regression (SVR) and whale optimization algorithm (WOA) has been discussed in [77]. A time series prediction model has been intended by Jiang et al., in [78] at which Bayesian principle and structural split for short term wind speed prediction and analysis with real wind speed data have been elaborated. A mixed model of Artificial Bee Colony algorithm-supported Relevance Vector Machine (ABCRVM) has been intended for wind speed evaluation to develop the evaluation capability of Relevance Vector Machine for wind speed [79]. Lastly, a combined PSO with Twin SVR has been discussed in [80] for wind speed prediction. Moreover, some meta-heuristic algorithm applications in renewable energy have been depicted in [81, 82]. A single diode PSO based PV system to recognize the unidentified factors have been proposed by Soon and Low in [83]. Also diverse MPPT based PSO have been shown in [84]. Literature [85] has discussed numerous PV forecasting supported with PSO. Moreover, a novel control technique is intended by PSO to extort MPPT from PV board has mentioned in [86].

11 Market Scenario and Role of Private and Public Sector in Field of Energy Market As the growth of Indian Energy Market, the most important role play during auctions are by Private Sector project developer which in turn increases as demand increasing mostly Indian companies and attracting the International companies as well. With increase competition the bidding for tariff bids slipped to new levels. As we will see the previous 5 years, biased average bids for Solar PV Power plans have dropped

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by more than 50% and now compete with the price of power production from novel firewood supported power plants. This insistent protest towards network equivalence has been possible only because of major involvement of national and international private corporations. Some of the corporation leading the Indian solar power sell comprises SunEdison, First Solar, and SkyPower Global etc. From above 5 years of public sales, it has become obvious that, without the insistent involvement of the private sector, the sudden increase of India’s renewable energy market would not have been achievable. Private Segment corporations have also played a vital task in enlarging India’s wind energy capability. Suzlon Energy appeared as one of the biggest wind turbine producers in the world tracking its achievement of Europe-based Repower [87]. India’s favourable wind energy market attracted international corporations comprising Vestas and Gamesa. To establish India’s primary offshore wind energy plan now these corporations are competing each other. Suzlon Energy has previously spent millions to establish a project in western India, while numerous other corporations are also expected to join in the first-ever auction of offshore wind energy plans in India. The nonstop involvement of private segment corporations will recover the upcoming of renewable energy goals attaining the apparently impossible capacity addition goals situate by the Indian government. Insistent involvement by private corporations shall put a strong base for the low-carbon development of India’s wealth. Make in India also took strong steps to support the Indian RE and boost the growth by involving investors from different countries and sectors [88–90]. Table 1 indicates market scenario of renewable (Solar) energy in terms of forbearance price and floor price at different periods under Non-solar and Solar REC mechanism [91]. Since CERC took some steps coming forward and reduces the solar certificate price range is Rs. 5800–3500 (Rs. 5.8–3.5/KWh) ordered on 31st December 2014 and implemented from January 2015 onward. There it was also seen how tariff rate decreases as the new policy and the trade variation occurs. Figure 11 indicates Buy/Sell Bids of Non-Solar market for the period of March, 2011 to October, 2016. Figure 12 indicates Buy/Sell Bids for Solar market in the IEX and PXIL on the period of March, 2011 to October, 2016. Figure 13 shows MCV/MCP of Non-Solar market in the IEX and PXIL on the period of March, 2011 to October, 2016. Figure 14 shows MCV/MCP of Solar market in the IEX and PXIL on the period of April, 2012 to October, 2016. Table 1 Market scenario Up to 31st March 2012

From 1st April 2012 to 31st Dec 2014

From 1st Jan 2015

N-Solar REC Solar REC N-Solar REC Solar REC N-Solar REC Solar REC in Rs. per in Rs. per in Rs. per in Rs. per in Rs. per in Rs. per kWh kWh kWh kWh kWh kWh Forbearance 3.9 price

17

3.3

13.4

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12

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1.5

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N-Solar 1200000 1000000 800000 600000 400000 200000 0 Mar '11 June '11 Sep '11 Dec '11 Mar '12 June '12 Sep '12 Dec '12 Mar '13 June '13 Sep '13 Dec '13 Mar '14 Jun '14 Sep '14 Dec '14 Mar '15 Jun '15 Sep'15 Dec '15 Mar '16 Jun '16 Sep '16

12000000 10000000 8000000 6000000 4000000 2000000 0

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Fig. 11 Buy/sell bids of non-solar (IEX and PXIL) 3500000

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years Fig. 12 Buy/sell bids of solar (IEX and PXIL)

From January 2015 when the forbearances prices and floor prices for solar certificate were cut down a huge growth was seen in solar market, IEX stated that on 28 January, 2015 it was recorded the highest ever trade of both Solar and Non-Solar RECs since the inception of the market. The whole deal quantity is enhanced by about 140% as contrast to last month. This jump in deal quantities can be attributed to better RPO compliance in the last quarter. A recent amendment in the REC regulations introducing Vintage Based Multiplier has also prompted obligated entities to purchase Solar RECs to fulfill Solar RPO. Figure 15 represents growth of No. of Participants in Non Solar and Solar market for the Indian Energy Exchange Company. In Feb 2015 there was a huge growth of

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Fig. 15 Growth of No. of participants (IEX March 2011–October 2016)

Oct '16

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Fig. 13 MCV/MCP of non-solar (IEX and PXIL)

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no of participants; one of the causes for optimistic consequence on the REC dealing could be characteristic to the government’s shift of cutting down the solar REC costs in a tender to enhance demand. The records had been trading at the floor stage of Rs. 1500 since August 2012 as a consequence of the inequity among supply and demand. IEX also stated that further volume is expected to increase in the remaining months because better RPO conformity in Solar by the obligated things. A recent amendment in the CERC regulations introducing Vintage Based Multiplier in solar REC has also prompted obligated entities to purchase Solar RECs to fulfill Solar RPO. In the article which was on solarquarter.com stated about the trade volume of Exchanges company [92] as given below: Power Exchange India Limited (PXIL) The market share of PXIL for the month of February was 53.06% and the whole cleared quantity on the trade was 420,446 RECs. The clearing ratio was 8.24% which was low because of the less demand on the participation [93]. India Energy Exchange (IEX) The REC market in February 2015 witnessed increased trade volume as the compliance year 2014–2015 is nearing to an end. A recent amendment in the CERC regulations introducing Vintage Based Multiplier in solar REC has also prompted obligated entities to purchase Solar RECs to fulfill Solar RPO. The buy demand for non-solar RECs cut down from 393,081 previous month to 345,184 in February and 6,025,638 vend bids were acknowledged and the entire purchase bids were cleared at floor cost of Rs. 1500 per REC. The buy demand for solar has decreased from 30,650 previous month to 26,726 in this deal session and vend bids of 987,764 RECs were acknowledged and the entire purchase bids were cleared at floor cost of Rs. 3500 per REC (solar quarter). Figure 16 shows variation of Market Clearing Volume (MCV) during March 2011–October 2016 of Non-Solar and Solar market in the IEX and PXIL. As from Fig. 15, it has been seen clearly that every year a huge growth was seen in the month of March. IEX stated the reason that it was last month of the compliance year and every State is supposed to successfully fulfill the RPO requirement [94]. The REC market trading session held on 25th March, 2015 witnessed trade of 279,205 N-solar and 39,385 Solar RECs. The market saw a decrease in trade vis-a-vis the previous month even though it was the last month of the compliance year 2014–2015. In the non-solar division 279,205 purchase bids and 5,311,670 vend bids were obtained and the entire purchase bids were cleared at floor cost of Rs. 1500 per REC. In the solar division purchase bids of 39,385 RECs and vend bids of 1,013,725 RECs were obtained and the entire purchase bids were cleared at floor cost of Rs. 3500 per REC. With the introduction of vintage multiplier there has been an increased buying of Solar RECs by the obligated entities due to reduction in floor price from Rs. 9300– 3500. Out of total 1.63 lakhs Solar RECs traded this year, 1.46 lakhs were traded in last three months after implementation of vintage multiplier.

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900000

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Fig. 16 Variation of MCV during March 2011–October 2016 of non-solar and solar (IEX and PXIL)

Huge drop can be identifying in the month of April when the REC market trading session held on 29th April, 2015 witnessed trade of 38,481 non-solar and 6721 Solar RECs. The market saw a decrease in trade volumes, mainly due to the fact that April is the first month of the compliance year 2015–2016. The fiscal year 2015 started with increased volumes and low prices on IEX [95]. The average Market Clearing Price (MCP) for April 2015 was 2.68 per unit, almost 5% less than 2.82 per unit last month. The average area clearing price across most of the bid areas was almost same as last month. Surprisingly, the Southern States especially Andhra Pradesh and Karnataka saw drastic reduction of 38% in price. Increase in generation capacity within the region along with reduction in demand due to rainfall was key reasons for reduction in price of power. In April, about 83 MUs were vanished owing to Inter-State transmission system blocking, a drastic reduction of 387% above the earlier month when 400 MUs were lost stated by IEX. In Business Standard article was there on April 13, 2015 which states the reason for drastic reduction in the month of April, sell financiers lose out on REC bid for sale. The majority sell financiers failed to acquire any allowance in the Rural Electrification Corp (REC) offer for sale (OFS) carried out previous week. A large amount sell bids were made about the floor cost of Rs. 315, while the allocation cost was almost Rs. 330. The sell division for the initial time happened insistent bidding and was assured nine times. From the above volume trade graph we analyze that in the month of May 2015 again gain in the market was seen, IEX 28th May 2015 REC Market observers enlarge in quantity and maximum yet solar REC deal. The REC trading assembly held at IEX

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in month of May observed deal of 2.92 lakh RECs (21,153 Non-Solar and 80,867 Solar REC) 55% increase on the earlier month’s dealing session when 45,202 RECs (38,481 Non-Solar and 6721 Solar) were traded. Last year, in May 2014, a total of 2348 MUs was traded. The everyday common cleared volume in month of May 2015 was 93 MUs. Enlarge in traded quantities on the earlier month was mainly due to enlarged purchasing by open access customers who received benefit of the competitive costs realized on the trade. IEX in a declaration shown the increase in the quantity was mainly due to the current decision of the Supreme Court which expressed the captive producing companies to comply with RPO as authorized by SERC.

12 Conclusion India has 5th worldwide ranking of huge prospective for renewable source sources. Currently, Govt. of India is enforcing the new policies for the growth of RE market in India. In this chapter, we have predicted and examine the energy trading market and scenario of the process variation that happen during the period from March 2011 onwards till October 2016 and determining the proper precautions for the future aspects. This was confirmed that during the month of March, huge growth was seen; reason seems to be the last month of the compliance year during the period. It has been also analyzed the fall and growth especially in 2015, how renewable market grow and have given a reasoning for successful growth and fall. The strategy for achieving this enhanced goal of developing renewable energy which will help for future long term energy supply and environmental benefits. Moreover, role of ANN and metaheuristics in wind and solar energy have been incorporated.

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Single and Multi Objective Optimization Studies of Metaheurestic Algorithms in Engineering and Systems

Applications of Meta-heuristics in Renewable Energy Systems Manoj Kumawat, Nitin Gupta, Naveen Jain, Vivek Shrivastava, and Gulshan Sharma

Abstract The utilities are facing many problems with the conventional electrical system. Moreover, the electrical demand of the system is exponentially increasing since the last decade. The traditional framework is not able to address the demand of the end-user with environmental, technical, and economic concerns. Though, some counties have adopted the liberalization in power distribution systems. In addition, renewable energy systems can compensate for the demand of the utility. The renewable energy systems have contributed to minimize the economical and technical losses of distribution and transmission networks, support aggressive policies and decreases the cost of ancillary services. In the current competitive liberalization scenario, the utilities are facing strained operating conditions to meet the expectation. Therefore, the adhere to the present load scenario is a complex circumstance. Further, the utilities have to maximize the annual profits of the distribution systems by enhancing the energy efficiencies with the quality of power to customers. A lot of algorithms have been used to maximize the benefit of proper accommodation of the energy resources in distribution networks. Each algorithm has a unique application and process to optimize a particular type of objective. Therefore, each algorithm finds out the global solution in specific boundaries. This chapter describes a theoretical background and application of the meta-heuristic methods to the allocation of the renewable energy systems in the distribution network. M. Kumawat (B) · V. Shrivastava Department of Electrical and Electronics Engineering, National Institute of Technology Delhi, Narela, Delhi 110040, India e-mail: [email protected] N. Gupta Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, JLN Marg, Jaipur 302017, India N. Jain Department of Electrical Engineering, CTAE, MPUAT, Udaipur 313001, India G. Sharma Department of Electrical Power Engineering, Durban University of Technology, Durban 4001, South Africa © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_12

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Keywords Firefly method, Jaya algorithm · Harmony search · Metaheuristics algorithms · Renewable energy systems · Teaching-learning based optimization

Nomenclature Di f f er ence D, Dim dm E bτ , E aτ F = { }, f ( ) firefly (i) HMCR Ilimit i iter, itr JY JY JYbest JYwor st K max Kχ k loc locαR E S , locαSCs learner i Mean MaxIt m n lv , n b nn Np Nd Popi .Sz k , Popi .Stk Pop. Sz , Pop. St Popnewik , Popoldik Popr PAR P PD PR E S Ploss PGrid

Difference value between teacher’s score and mean value Dimensions Current number of dimension Energy Losses of the System with and without RES Objective Function of energy loss Population for FM The Value of Harmony Memory Considering Rate Current limitation value Current population Current Iteration number New computed value of candidate Previous computed value of candidate Best candidate and worst candidate Total number of iteration permitted Total number of RES Current design variable Location of the candidate Site of each RESs and SCs at αth iteration Population value for ith learner Mean value of all learner’s score Maximum Iteration size Number of shunt capacitor Total number of load level and branch Count of nodes index Total size of population Number of design variables kth population for RES size and location All population for size and site New and old population data of ith population and kth design variable Randomly selected population The Value of Pitch Adjusting Rate Resistivity of earth (-meter) Load demand value for Active power of the system (kW) Active power after integrate the Renewable Energy System (kW) Total real power loss Total active power supplied by grid substation

Applications of Meta-heuristics in Renewable Energy Systems

P max , P max QD Q SCs Q min , Q max Q Grid R Rαβ r1 , r2 Sαβ Sline St , Sz max Sline tτ TF T eacher T eacher.Sz T eacher.St V Vm Vmin , Vmax ∇Vαβ X x Z α β τ ρ

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Minimum and maximum active power injection by RES Load demand value for Reactive power of the system (kVAr) Reactive power after integrate shunt capacitors (kVAr) Minimum and maximum active power injection by RES Reactive power injuction by grid Resistance of the line () Resistance of line between αth and βth node Random numbers Power flow injection between node α and β Total power flow in the line (MVA) Total number of RES site and size Maximum power flow limitation of the branch (MVA) The period of time for each load level Teaching factor The best learner The best size for RES The best site for RES Node Voltage of the linear load (V) Magnitude of voltage profile (pu) Permissible limit of bus voltage The Voltage drop vector between α and β buses Resistance of the linear load () Function variable Impedance of branch for linear load () Present node number Present branch number Present value of load level Penalty factor

1 Introduction The living standard of human life is globally increasing by the use of electrical energy, and it makes ease to lifemanship. The ever increasing energy demand and scarcity of electric power will significantly impact the future electrical system towards economic evolution. It is approximated that the generation of power in the upcoming decade will require the double capacity from current production [1]. Therefore, the difference between demand and supply might be filled by non-renewable and renewable energy resources. However, most of the International and National policies are restricted pollutants from conventional resources. Therefore, the regulatory commission has done the amendment in the electricity act to increase the percentage contribution in

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power generation by Renewable Energy Systems (RES) in the distribution network [2]. The amendment of the electricity act has been directed to extra benefit to the utility. The integration of renewable sources in the conventional passive network has switched the characteristics of the distribution system into an active network. Thus, the accommodations of the RES act an essential character in the future reconfiguration of the distribution service [3]. Moreover, the accommodation of the RES should be adopted with precision; otherwise, the alteration of the distribution system may introduce the threaten to lose the healthy circumstance [4]. Therefore, the allocation of the RES has attracted the attention of the optimization approaches for efficient usage of electrical power. Various analytical algorithms, artificial intelligence search algorithms, and meta-heuristic optimization techniques can be applied to optimize the global solution. The conventional algorithms take more computational time and less robust to solve the nonlinear optimization problem with the integer variables. Therefore, these algorithms are not suitable for multiple RES planning. The meta-heuristic-based approaches can handle both unconstrained and constrained problems for multivariable function with each equality and inequality constraint [5]. Moreover, the metaheuristic algorithms are generated groovier exploration and diversity in the multidimensional population(s) besides the single. Further, the faster convergence has been also achieved by the momentum effect of the particles. Although meta-heuristic methods have a greater advantage, some parameters are compulsory to tune for the achievement of the optimum solution [6]. This prime condition of some algorithms is introduced the complication in the initial process. However, tuning of the parameter has not clogged for the Jaya algorithm and Teaching–Learning-Based Optimization. These two methods require the only number of iterations and population size [7–10]. Initially, the classification of various distributed generation technologies is demonstrated in this chapter. These technologies have a unique application that is based on fuel injection. Several algorithm-specific optimization algorithms are described in previous chapters. Therefore, the chapter describes a theoretical background and application of the Firefly Method (FM), Teaching Learning Based Optimization (TLBO), Harmony Search (HS), and Jaya algorithm to allocate the RES in the radial distribution system. These meta-heuristic based approaches are applied on 69 and 83-bus radial distribution networks to explore the application of algorithms in the RES. The simulation results have explored the effectiveness of the meta-heuristic algorithm in terms to increase the percentage reduction rate of energy losses with renewable while preserving the profile of the node voltage. The salient feature of the chapter is given below: 1. The application of meta-heuristic is explained by using of Firefly method, Harmony search, Teaching learning based optimization, and Jaya algorithm. The pseudo-code of each method is discussed, which can be helpful to understand the basic process of the algorithm. 2. The optimal accommodation of the RES has been expressed the rigidness of meta-heuristic algorithms.

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2 Renewable Energy Resources The distribution systems of the traditional framework are transformed into an active distribution network after the interconnection of the Renewable Energy System (RES). In the electricity market paradigm, mostly RES technologies are matured; however, some technologies are still under the developing stage [6, 11]. These technologies are photovoltaic, wind energy, small hydropower generation, geothermal, and solar thermal, which are demonstrated in Fig. 1. All these energy resources are explained in detail under the following section:

2.1 Photovoltaic In this technology, solar panels convert solar energy into electrical energy. The cell of the solar panel is made of two types of material which are poly-silicon and monocrystalline silicon. The parallel and series connection of the cell is arranged according to the rating of current and voltage. However, the efficiency of the system is relatively low as compared to other sources and it is lying between 10 to 24 percentages [12]. In the present scenario, lots of research work has been primarily focusing on the cell material. Further, this system used the power converter to supply the power to the grid. However, the uses of inverters produced harmonics into the distribution system. Therefore, investigation is required on multi-level inverter to reduce the percentage of total harmonics distortion.

Fig. 1 Current restructured power system

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2.2 Wind Energy The wind turbine converts wind energy into electrical energy. The wind range of 4–25 m/s is suitable otherwise the connection is cut off from the turbine. Further, power generation from park station of the wind turbine has been increased 20 kW to 4 MW in the recent decade [13]. Moreover, these technologies have suited that place where availability of wind speed is constant for the long duration. Therefore, off-shore type of power generation is most prominent where the large rating of the wind turbine in a large number can be connected to a high voltage electrical system. However, one wind turbine is attached to the grid at 10–20 kV voltages level of the distribution system. Although, the power quality problems are introduced in the system with direct interconnection to the grid [14].

2.3 Biomass Biomass will be a fast-growing renewable energy technology among distributed energy resources in the near future. Since, the crops, plant and waste of animals are used as a fuel in biomass plant. Moreover, waste of forestry and agriculture can also be recycled as fuel which is shown in Fig. 2. The world’s energy production is 11% by biomass plant according to the US International Energy Agency. Moreover, developing countries are driving 90% of the total energy production [15]. Further, the characteristic of this technology may help to compensate for the energy demand of the distribution system. This technology can be used in the hybrid vehicle because of fuel clearness as compared to oil.

Cow dung Pressed sugercane

Switchgrass

Corn stovers

Rice husk

Fig. 2 Biomass technology resources

Biomass

Sewage

Household waste

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2.4 Small Hydropower Generation Small capacity of the dam is used to produce the power in the range of 5 kW to 100 MW on the concept of the hydropower plant, which is called a small hydropower plant. Moreover, it is also divided into two parts. First is micro-hydroelectric which operates in a range of 5–100 kW and those plants can produce the power in the range of 500 kW and 10 MW that called mini hydro-power stations [16]. This plant adopted the electromechanical solutions to construct the plant and operations, which reduce the capital cost with assured return on investment.

2.5 Geothermal The heat energy is stored in the earth which can be used as geothermal energy to produce electricity. This technology is used in many countries across the world [17, 18]. The geothermal power plant is environment friendly and the cost of the generating station is less as compared to other stations. However, the accessibility of geothermal hot spots is very rare in the world.

2.6 Solar Thermal This technology converts solar radiation energy into thermal energy. In this technology, water is heated to 1000 °C temperature to generate the steam, which drives the electric turbine generators or for the production of hydrogen by chemical process [12]. The classification according to temperature, this technology is divided into three parts as low-, intermediate-, or peak-temperature collectors. Further, the lowand medium-temperature collectors are employed the flat plates to warm the water for commercial and residential purposes. Moreover, peak-temperature collectors are used the reflectors to concentrate sunlight. Therefore, the last collector technology mostly used to generate electrical power. In Table 1, all RES technology is enumerated with their operating range, merits, and demerits that are useful to choose the technology according to the application of the utility.

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Table 1 Various renewable energy sources and their key features S. No. RESs technologies Operating range

Specialty

1.

Photovoltaic

1 kW–2.1 GW

• Fuel less technology • Uncertain nature • Environment • High capital cost friendly • Less maintenance cost

Drawback

2.

Wind energy

20 kW–4 MW

• Low operating cost • Uncertain nature • Fuel less technology • Noise pollution • Bird hazard

3.

Biomass

100 kW–2.6 GW • Renewable Source • Reduce GHG emission • Stop desertification

• Air pollution • maintenance are more • Soil erosion

4.

Small hydropower generation

5 kW–100 kW

• Eco-friendly • Zero operating cost • Renewable Source

• Affected in flood time • High capital cost • Less efficiency

5.

Geothermal

5 MW–1.5 GW

• Economical • Fuel free • Constant price with time

• Water pollution • Gases spread out into atmosphere • Noise pollution

6.

Solar thermal

25 kW–510 MW

• Fuel Free • Eco-friendly

• High capital cost • Large solar collector

3 Meta-heuristic Algorithms In the optimization of problem-solving methods, heuristic and meta-heuristic methods are developed to create strategies for the optimal solution. The metaheuristic methods can be approached for real problems [8, 9, 10, 19, 20, 21, 22] because it is problem independent techniques, whereas the heuristic methods are problem-dependent techniques that can be used in limited specific problems. A meta-heuristic can be applied to the problem without knowing anything about the problem. Further, meta-heuristic methods are higher-level procedures which are designed to provide a set of guidelines or strategies to develop algorithms within the limited computation capacity. Consequently, the term meta-heuristic is also employed to nullify the problem-specific implementation of a fundamental heuristic algorithm according to the guidelines structured in such a framework [23]. Some meta-heuristics algorithms have been discussed in the previous chapters so new four algorithms have been elaborated in this chapter to explore the application of meta-heuristics algorithms in the RES.

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3.1 Firefly Method (FM) The FM is one of the meta-heuristic algorithms for global optimization, which is stimulated from the flashing behavior of the fireflies. In 2008 [23], Xin-She Yang had proposed this method. Many families of insects live-in environment. One of them is fireflies, who find in the tropical environment and produce a light chemically. A firefly attracts other fireflies by using their flashing behavior. Moreover, they normally use fireflies’ brightness to send signals to the other fireflies. In mathematical optimization, the purpose of the signal system in their lives is fulfilled by a firefly’s flash specialty to attract other fireflies by assuming three main FM terms contains as follows: FM Terms Defined Rules Attraction All fireflies in the population are unisexual. Therefore, anyone of fireflies can be attractive to all the other fellows Distance

The brightness of a firefly reflects its attractiveness that is proportional to intensity. Among any randomly selected two fireflies, the firefly that has low brightness will be noticed and liked by the second firefly which has more brightness. Hence the distances between the fireflies would be increased according to the decrement of their intensity in brightness

Motion

The name of this term defines itself. The motion means ‘movement of fireflies’. The present firefly is compared with others. If it has more brightness than others then it can be moved randomly. Further, the feature ‘brightness’ of fireflies should be targeted

Fireflies behave like twinkling their colored wings to attracting to each other. The communication between the fireflies is made by attracting partners. They use the protective technique to flashing as male fireflies to female or female to male. Whenever the distance between the fireflies increases or extended then the communication between them breaks up or blurred. Because their lighting will be absorbed by the air between them and becomes the weakest to further weakest. In [24], the FM is updated with the extra features appended for the allocation of the RESs with fulfill various conditions as decreases the power losses both active and reactive. Further, it improves their voltage profile applying in several different load models.

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M. Kumawat et al. The pseudo-code for FM isBegin Declare the objective function of the problem and define it as: F= { } Assign the initial value of the population for all the fireflies. Determine the intensity of the brightness in the best or strongest firefly. Set the predefined value for the absorption light by the air which is a coefficient. Set iter : 1 While (iter is less than user-defined maximum iteration allowed) For i=1 to all generated fireflies //pick up only one firefly For j=1 to all randomly generated firefly // pick up the comparative firefly If (firefly (i) contains a better solution than firefly (j)) Then Step out to the firefly (i) to j within all dimension defined End if Distance increase between them and the brightness lost Evaluate new solutions for new steps Update the value of brightness intensity End for End for Arrange the all fireflies as maximum brightness hold Find the Best from presently solved function. End while Display the solution to the user screen. End

3.2 Harmony Search Algorithm The prime concept of harmony search (HS) method has been firstly introduced by Z. W. Geem in 2001 [25]. The HS method is also known as a ‘Mimicking Algorithm’, which is a society inspired algorithm like the group of sounds from different sides considered by the music of harmony. This is one of the meta-heuristic methods which is based on the statement: “Musician plays a note for harmony”. Here, ‘musician’ refers to decision variables, ‘plays’ means generates, ‘note’ used for value, and ‘harmony’ describes searching the best global optimum. The HS method is applied to detect better harmony by searching various combinations of pitches using aesthetic standards. These standards use the simulating the instruments’ pitches and estimate the values for all parameters following three rules: HM Terms

Defined Rules

Plays anyone pitches

Choose any random value from the HS memory

Play the adjacent pitch of the selected pitch

Select an adjacent figure from the memory used in the HS method

Play a random pitch from the permitted range

In the course of successive trials concludes that find a random value from the permitted value range

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This algorithm is effectively directed through so many parameters like PAR (Pitch Adjusting Rate), size of harmony, HMCR (Harmony Memory Considering Rate), maximum change amount in pitch adjustments, and amount between two neighboring values [26]. Harmony Search pseudo-code: Begin Introduce objective function Generates initial harmonies in the real number Set the parameters of HS As: HM = the initial value for HS Memory HMCR= the calculated rate value for HS memory and PAR= the rate value for adjustment in pitches MaxIt= maximum iteration, size of HM Evaluate objective function initially Select randomly generated solution and assign as HM Detect the worst solution For i=1 to MaxIt While stop condition = False For j=1 to number of decision parameter If Random_Harmony Q min

(14)

where, PRES and QSCs value should follow the standard of interconnection. Moreover, the size of the capacitor is assumed to discrete and integer in the chapter. 5. Network Compensation Limit Total injection power through RES and SCs must be less than the demand of the network. nn  α=2 nn 

PR E S,α ≤ PD Q SCs,α ≤ Q D

(15)

α=2

The candidate site (loc) of each the RES and SCs should not repeat in every iteration which is defined as RES α ∈ n n , α = 1 locαR E S = locα+1 SCs locαSCs = locα+1 α ∈ n n , α = 1

(16)

In this chapter, some meta-heuristic methods have been applied to optimize the capacity, site and number of the RES in the described formulation to minimize the energy losses for three load levels with satisfying all constraints of the power system.

4.3 Implementation of Meta-heuristic Algorithm The meta-heuristic method maintains all the attributes of the desired distribution networks. Some of them are the voltage profile of bus, constraints definition, the balance value for power, and the capacity of power flow within the predefined range for the applied system. Whenever the placement of the RESs having an optimal size at the best location in the system is done then the performance of the renewable resources is frequently evaluated. The attributes of performance are the reduction rate of losses and enhancement percentages of the voltage profile. The specific procedure of solving the objective function of optimum RESs allocation using any of meta-heuristic algorithms is elaborated in the following steps: 1. Assign the initial value to the algorithm-specific variables and declare the value for all parameters. The objective function for the problem’s definition have: Decision Parameters, Number of design variables Maximum size of populations allowed N p = 10

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Iterations (Total number of generations) K max = 300 Constraints and rules for termination. Every algorithm has its own constraints and rules that should be followed for the optimal solution. 2.

The objective function used in this chapter as defined in Eq. (17) will be minimized by this algorithm. Maximi ze f (X ) =

n lv 

E bτ

−

τ =1

3.

4.

 E aτ

(17)

τ =1

where the objective function ‘f (X)’ finds the annual energy losses after allocating the renewable energy system. Randomly generate values for all populations as the different RES size and RES site: Popik . It is necessary to satisfying every decision variable’s constraints. It is expressed in the equation as: Popi = R E Ss(Sz , St ) ∀i ∈ Np

(18)

Popi .Sz k = {R E Ss si ze :  → k} ∀k ∈ Nd , ∀i ∈ N p

(19)

Popi .Stk = {R E Ss location :  → k} ∀k ∈ Nd , ∀i ∈ N p

(20)

According to the objective function, decision variables are two: RES size and RES site. For both decision variables, the population are generated, which can be expressed as: RES.Sz Decision Variable ⎛ ⎞ a1,1 a1,2 . . . a1,Nd Pop.Sz = ⎝ a2,1 a2,2 . . . a2,Nd ⎠ a N p ,1 a3,2 . . . a N p ,Nd

5.

nlv 

RES.St Decision Variable ⎛ ⎞ a1,1 a1,2 . . . a1,Nd Pop.St = ⎝ a2,1 a2,2 . . . a2,Nd ⎠ a N p ,1 a3,2 . . . a N p ,Nd (21)

Execute the load-flow function with parameter as populations Popi . and computes the energy losses. The load flow (any load-flow like Backward Forward, Gauss-Siedel, Newton-Raphson, etc. methods) is applied to identify the attributes of the real bus system. FResulti = f (X )

(22)

St.to Vm , Sline , Ilimit

(23)

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6.

Implement any of the meta-heuristic algorithms like FM, HS, TLBO, and Jaya algorithms, etc., which is suitable for the defined problem. According to the selected method, the population data will be updated using the algorithm’s equation or rule. The parameters are frequently updated during the process, based on the optimal solution/best solution for the objective function. 7. Further, the load-flow() is executed with parameters as the new accepted population. Afterward, examine that the newly generated values give a better solution then it will be accepted, else previously value remains intact. 8. While the new results are optimal than the previously taken then the updated population for both decision variables will be accepted. This process is implemented according to the chosen algorithm. 9. Further, the constraint handling mechanism can be used to examine the predefined range of parameters and replicas. Assure the modified accommodation of RESs has not any replicas. If these constraints are not fulfilled then new values will be generated randomly. 10. The algorithm will be terminating if ‘K max ’ is reached and display the solution as the optimal result. Else, repeat the steps from the 4th step and execute the overall procedure again until stopping predefined criterion is not fulfilled. The process of optimization algorithms for RES is illustrated to understand the behavior of algorithms via a flowchart in Fig. 3.

4.4 Results and Discussions In this subdivision, meta-heuristics algorithms have been applied on two test systems, one is the modified standard 69-bus [29], and the second is a realistic distribution network of 83-bus that is operated by Taiwan Power Company [30]. The alterations in the realistic network are made to prove the feasibility of RES in the radial networks. Moreover, the daily load profile of the distribution network is categorized into three levels of load as Low (L), Medium (M), and High (H). The medium load level is constant demand that is multiplying of 1 and, low and high is 0.5 and 1.6 of the medium system load; further, 2000, 5260, and 1500 h are the duration of the respective load level in a year. In the radial distribution system, the backward/forward distribution load flow approach gives the perfect analyzed result. Therefore, it is used to obtain the basic argument of the both test system. Each load level results of every system are compared with the results of each algorithm. 1. Standard 69-Bus Test System 100 MVA and 12.66 kV are base power and voltage in the standard 69-bus test network. The location and size of RES with system performance of each metaheuristic algorithm are demonstrated in Table 2. Each meta-heuristic algorithm is applied for 10 population (size/site) and run for 100 iterations. Further, the best solution of each method found the different best

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Start

Renewable Energy System Data

Input the system Data

Initialize the Population Np, Control Parameters, Algorithm specific Variables Generate the initial pop as RESs size and site Evaluate the Objective Function for all population

Implement the Meta-Heuristic Algorithm

FM

TLBO

Jaya

HM

Meta- HeurisƟc Algorithms

Reject

No

Evaluate f( ) , If solution is better

If desired scenario achieved

Yes End Fig. 3 Flowchart for implementation of the algorithm

Yes

No

Accept

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Table 2 Performance comparison of meta-heuristic algorithms for standard 69-bus test system Algorithms

Load level

Optimal dispatches of RES Power loss (kW)

Node voltage (pu)

Energy loss (MWh)

Energy loss reduction (%)

FM

L

64(291), 61(730), 17(118)/21(200), 64(100), 61(500)

3.20

0.9949

126.84

94.40

M

64(502), 61(1388), 17(297)/21(300), 64(200), 61(1000)

9.43

0.9896

H

64(425), 61(1761), 17(536)/21(300), 64(300), 61(1200)

47.23

0.9685

L

17(291), 64(129), 61(667)/11(200), 62(100), 61(500)

2.16

0.9968

122.06

94.61

M

17(481), 64(221), 61(1510)/11(300), 62(200), 61(1000)

8.68

0.9926

H

17(473), 64(623), 61(1640)/11(300), 62(400), 61(1200)

48.07

0.9712

L

17(280), 61(750), 64(118)/21(200), 64(200), 61(400)

1.790

0.9971

108.47

95.21

M

17(520), 61(1362), 64(398)/21(200), 64(300), 61(1000)

7.497

0.9936

H

17(423), 61(1790), 64(525)/21(400), 64(300), 61(1200)

L

17(280), 61(741), 64(118)/21(200), 64(100), 61(500)

1.735

0.9971

102.79

95.46

M

17(532), 61(1434), 64(279)/21(300), 64(200), 61(1000)

6.731

0.9939

H

17(421), 61(1784), 64(528)/21(300),64(400), 61(1200)

HM

TLBO

JAYA

43.64

42.61

0.9733

0.9729

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size and site of the RES. The Jaya and the TLBO algorithm are determined the same site. Therefore, both algorithms computed the approximate performance of the system. The Jaya algorithm is performed best in each load level as compared to other algorithms. The voltage profile of other algorithms is best as compared to the Jaya method as shown in Fig. 4. However, the Jaya approach has obtained the flat voltage profile as compared to other algorithms. There are minor variations in light and nominal load level. In the peak load profile, voltage goes down at bus 27 but it always performs in permission region. The voltage profile should be constant throughout the duration of the planning. However, it is not possible because the distance acts as a significant character in the radial network. Therefore, accommodation of the RES is a sensitive approach that can be well handled by the meta-heuristic algorithms. 2. Practical 83 Bus Test System A realistic 11.4 kV network of the distribution system has 11 feeders that are operated for peak active power 28.35 MW and reactive power demand 20.70 MVAr. The decision parameters for optimal allocation of each algorithm are obtained the percentage annual reduction of energy losses from 62.72 to 64.21 which is demonstrated in Table 3. However, the percentage of energy reduction is less as compared to the standard test system that is due to the realistic nature of the practical distribution system. The Jaya algorithm has also performed superior as compare to other meta-heuristic algorithms on a standard test system. Moreover, the performance of the TLBO is mostly similar to the Jaya algorithm. Both algorithms are parameter-less algorithm; therefore, they do not waste time to manage the parameters. In each load level, sites of the RES must be similar for each algorithm as the location of RES could not be changed once it fixed. However, the supply of generation might be altered when the demand for power switched to another level. Figure 5 proves that all meta-heuristics algorithms also achieve the optimal accommodation of the RES for a practical distribution system. The irregularity of the voltage profiles in the base case implies the realistic nature of the radial system. In addition, the meta-heuristic methods are also enhanced profile of voltage in the practical radial distribution network that validates the application of algorithms in the RES.

5 Conclusions The accommodation of Renewable Energy Sources (RES) is accomplishing worldwide prominence due to the significant positive impacts on the distribution network. However, the optimal RES allocation in the deregulated electrical system has several challenges for the planner in the modern distribution system. In this chapter, it has been closely observed that the consideration of load level produced the rigidity in the planning; therefore, a robust, accurate and reliable meta-heuristic method is required to solve the network issues. Hence, Firefly Method (FM), Harmony Search (HS), Teaching Learning Based Optimization (TLBO), and Jaya algorithms are selected to

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(i). Low Load Level

(ii). Medium Load Level

(iii). High Load Level Fig. 4 Voltage profile of the standard 69-bus test network

HM

L (DG/SC)

FM

L (DG/SC)

H (DG/SC)

M (DG/SC)

Load level

Algorithms 48.72

Power loss (kW)

58(500), 9(1100), 79(1200), 35(1100), 72(600)

8(1560), 54(1625), 81(1580), 72(1302), 20(1221)

62(1400), 6(3100), 79(4400), 35(4700), 71(3000) 48.88

72(5000), 19 (5000), 81(4287), 522.47 6(4892), 52(4211)

62(900), 6(2100), 79(2700), 35(1700), 71(2800)

72(3500), 19 (3005), 81(2437), 202.56 6(3195), 52(2648)

62(400), 6(1100), 79(1100), 35(1200), 71(700)

72(1625), 19 (1560), 81(1380), 6(1502), 52(1321)

Optimal dispatches of RES

0.9868

0.9588

0.9743

0.9875

Node voltage (pu)

Table 3 Performance comparison of meta-heuristic algorithms for realistic 83 bus test system

1942.92

1946.63

Energy loss (MWh)

62.80

62.72

(continued)

Energy loss reduction (%)

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TLBO

Algorithms

M (DG/SC)

L (DG/SC)

H (DG/SC)

8(3450), 54(3025), 81(2337), 72(3095), 20(2748)

M (DG/SC)

35(1400), 9(2000), 58(700), 79(2100), 72(1700)

8(3062), 20(2982), 54(2511), 81(3021), 72(2531)

35(700), 9(900), 58(600), 79(1400), 72(700)

8(1480), 20(1314), 54(1200), 81(1511), 72(1102)

58(1800), 9(3100), 79(4400), 35(4500), 72(2900)

8(5000), 54(4998), 81(4287), 72(4792), 20(4311)

58(800), 9(2200), 79(2400), 35(1900), 72(2800)

Optimal dispatches of RES

Load level

Table 3 (continued)

194.21

48.03

519.75

202.57

Power loss (kW)

0.9751

0.9872

0.9582

0.9744

Node voltage (pu)

1872.39

Energy loss (MWh)

64.15

(continued)

Energy loss reduction (%)

278 M. Kumawat et al.

JAYA

Algorithms

H (DG/SC)

M (DG/SC)

L (DG/SC)

8(4789), 20(4937), 54(3784), 81(4821), 72(4021)

H (DG/SC)

9(3200), 79(3100), 58(1600), 35(3200), 72(2700)

8(4789), 72(4021), 20(4933), 54(3784), 81(4821)

9(2000), 79(2000), 58(800), 35(1600), 72(1600)

8(3062), 72(2524), 20(2993), 54(2512), 81(3023)

9(900), 79(1300), 58(500), 35(700), 72(700)

8(1480), 72(1106), 20(1310), 54(1200), 81(1511),

35(3200), 9(3100), 58(1600), 79(3300), 72(2600)

Optimal dispatches of RES

Load level

Table 3 (continued)

503.71

193.45

47.97

503.20

Power loss (kW)

0.9602

0.9752

0.9871

0.9603

Node voltage (pu)

1869.02

Energy loss (MWh)

64.21

Energy loss reduction (%)

Applications of Meta-heuristics in Renewable Energy Systems 279

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(i). Low Load Level

(ii). Medium Load Level

(iii). High Load Level Fig. 5 Voltage profile of the practical 83-bus test network

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optimize the power injection of the RESs at particular places in both standard and practical radial distribution networks for three load levels. The performance of the distribution system is measured by two vital parameters as energy loss and voltage profile of the system. The results show that meta-heuristic algorithms drastically reduce the energy losses in each load level of the test systems. The Jaya method has been achieved the best performance as compared to FM, HS, and TLBO in every case study. Moreover, each meta-heuristic algorithm has performed well within the specified boundaries of the constraints in the standard distribution system. Further, the TLBO and Jaya algorithms did not require to be tuned for any parameter of the algorithm that prompted to enforce the optimal RES planning.

References 1. A. Colmenar-Santos, C. Reino-Rio, D. Borge-Diez, E. Collado-Fernández, Distributed generation: a review of factors that can contribute most to achieve a scenario of DG units embedded in the new distribution networks. Renew. Sustain. Energy Rev. 59, 1130–1148 (2016) 2. V. Mohan, J.G. Singh, W. Ongsakul, Sortino ratio based portfolio optimization considering EVs and renewable energy in microgrid power market. IEEE Trans. Sustain. Energy 8(1), 219–229 (2017) 3. M. Kumawat, N. Gupta, N. Jain, R.C. Bansal, Swarm-intelligence-based optimal planning of distributed generators in distribution network for minimizing energy loss. Elect. Power Comp. Sys. 45(6), 589–600 (2017) 4. N.R. Battu, A.R. Abhyankar, N. Senroy, DG planning with amalgamation of operational and reliability considerations. Int. J. Emer. Electr. Power Syst. 16(2), 1–11 (2016) 5. P. Prakash, D.K. Khatod, Optimal sizing and siting techniques for distributed generation in distribution systems: a review. Renew. Sustain. Energy Rev. 57, 111–130 (2016) 6. P. Duc, K. Dervis, Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks (Springer Science Business Media, 2012) 7. R.V. Rao, V.J. Savsani, D.P. Vakharia, Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303–315 (2011) 8. T. Mahto et al., Load frequency control of a solar-diesel based isolated hybrid power system by fractional order control using particle swarm optimization. J. Intell. Fuzzy Syst. 35(5), 5055–5061 (2018). https://doi.org/10.3233/JIFS-169789 9. T. Mahto, et al., Fractional order control and simulation of wind-biomass isolated hybrid power system using particle swarm optimization, in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 698 (2018), pp. 277–287. https://doi.org/10.1007/978-981-13-1819-1_28 10. N.K. Nandan, et al., Solving nonconvex economic thermal power dispatch problem with multiple fuel system and valve point loading effect using fuzzy reinforcement learning. J. Intell. Fuzzy Syst. 35(5), 4921–4931 (2018). https://doi.org/10.3233/jifs-169776 11. N. Jain, S.N. Singh, S.C. Srivastava, Meta-heuristic approach for distributed generation planning in electricity market paradigm, in Proceedings of IEEE International Conference on Power and Energy Society General Meeting, July 2012 12. V. Hengsritawat, T. Tayjasanant, N. Nimpitiwan, Optimal sizing of photovoltaic distributed generators in a distribution system with consideration of solar radiation and harmonic distortion. Int. J. Electr. Power Energy Syst. 39(1), 36–47 (2012) 13. A.A. Tamimi, A. Pahwa, S. Starrett, Effective wind farm sizing method for weak power systems using critical modes of voltage instability. IEEE Trans. Power Syst. 27(3), 1610–1617 (2012)

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14. N. Jain, S. Singh, S.C. Srivastava, PSO based placement of multiple wind DGs and capacitors utilizing probabilistic load flow model. Swarm Evol. Comput. 19, 15–24 (2014) 15. V. Kirubakaran et al., A review on gasification of biomass. Renew. Sustain. Energy Rev. 13, 179–186 (2009) 16. M.F. Akorede, H. Hizam, E. Pouresmaeil, Distributed energy resources and benefits to the environment. Renew. Sustain. Energy Rev. 14(2), 724–734 (2010) 17. A.R. Jordehi, Allocation of distributed generation units in electric power systems: a review. Renew. Sustain. Energy Rev. 56, 893–905 (2016) 18. I.B. Fridleifsson, Geothermal energy for the benefit of the people. Renew. Sustain. Energy Rev. 5, 299–312 (2001) 19. M. Kumawat, N. Gupta, N. Jain, R.C. Bansal, Optimal planning of distributed energy resources in harmonics polluted distribution system. Swarm Evol. Comput. 39, 99–113 (2018) 20. A. Khatri, et al., Optimal design of power transformer using genetic algorithm, in Proceedings of IEEE International Conference on Communication System’s Network Technologies (2012), pp. 830–833. https://doi.org/10.1109/csnt.2012.180 21. H. Malik, et al., PSO-NN-based hybrid model for long-term wind speed prediction: a study on 67 cities of India, in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 319–327. https://doi.org/10.1007/ 978-981-13-1822-1_29 22. S. Smriti et al., Special issue on intelligent tools and techniques for signals, machines and automation. J. Intell. Fuzzy Syst. 35(5), 4895–4899 (2018). https://doi.org/10.3233/JIFS169773 23. M. Kumawat, N. Gupta, N. Jain, R.C. Bansal, Jaya algorithm based optimal allocation of distributed energy resources, in Lecture Notes in Electrical Engineering, vol 607 (2020), pp. 805–814 24. X.S. Yang, Firefly algorithm, stochastic test functions and design optimization. Int. J. Bio-Inspir. Comput. 2(2), 78–84 (2010) 25. M.M. Othman, W. El-Khattam, Y.G. Hegazy, Y.A. Abdelaziz, Optimal placement and sizing of voltage controlled distributed generators in unbalanced distribution networks using supervised firefly algorithm. Int. J. Electr. Power Energy Syst. 82, 105–113 (2016) 26. Z.W. Geem, J.H. Kim, G. Loganathan, A new heuristic optimization algorithm: harmony search. Simulation 60–68 (2001) 27. R. Rao, Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016) 28. K. Nekooei et al., An improved multi-objective harmony search for optimal placement of DGs in distribution systems. IEEE Trans. Smart Grid 4(1), 683–695 (2013) 29. N. Acharya, P. Mahat, N. Mithulananthan, An analytical approach for DG allocation in primary distribution network. Int. J. Elect. Power Energy Syst. 28(10), 669–678 (2006) 30. C.T. Su, C.F. Chang, J.P. Chiou, Distribution network reconfiguration for loss reduction by ant colony search algorithm. Elect. Power Syst. Res. 75(2), 190–199 (2005)

Data-Driven Occupancy Detection Hybrid Model Using Particle Swarm Optimization Based Artificial Neural Network Nuzhat Fatema and Hasmat Malik

Abstract The occupancy level of the room in a building is responsible for consumption of electrical power within the building. The occupancy level in a room depend on several controllable and/or uncontrollable parameters within and/or outside environment of the building. So, for the optimal demand forecasting and planning within the building, occupancy detection play an important role. In this study, the occupancy is determined by using simple measureable parameters of the inside environment of the building such as light (in lux), temperature (in Celsius), relative humidity (in %), CO2 level (in ppm) and humidity ratio (in kg water-vapor/kg-air). The data-driven occupancy detection using particle swarm optimization (PSO) based artificial neural network (ANN) is designed in R language and proposed approach is validated with different seventeen models by using the measured dataset. The occupancy detection for these models are 77.9–98.95% for ANN models and 87.8–99.5% for PSO-ANN models, which shows that PSO based ANN model’s performance is more acceptable in comparison to only ANN models. Keywords R language · PSO · Feedforward neural network · Feature selection · Machine learning · Optimization · Occupancy · Smart building · Detection · Attribute evaluation

Nomenclature ACMV Air-conditioning and mechanical ventilation N. Fatema (B) Intelligent Prognostic Private Limited, Delhi, India e-mail: [email protected]; [email protected] H. Malik Division of ICE, NSIT Delhi, Delhi, India e-mail: [email protected] BEARS, University Town, NUS Campus, Singapore, Singapore © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_13

283

284

ANN CO2 CRAE DE FNN GA GRAE HR HVAC IGAE ORAE PIR ppm PSO RFAE RH SA StdDev SUAE Temp

N. Fatema and H. Malik

Artificial neural network Carbon dioxide Correlation attribute evaluation Differential evolution Feedforward neural network Genetic algorithm Gain ratio attribute evaluation Humidity ratio Heating ventilation and air-conditioning Information gain attribute evaluation One R attribute evaluation Passive infrared Part per million Particle swarm optimization Relief F attribute evaluation Relative humidity Simulated annealing Standard deviation Symmetrical uncertainty attribute evaluation Temperature

1 Introduction The level of the occupancy of the commercial/domestic building is responsible for the consumption of electrical energy within the building’s components and/or subsystem level. So accurate identification/forecasting of occupancy level always leads to optimal planning and precise demand side management. Therefore, occupancy prediction (OP) is the key component in the building, which leads the optimal operation of HVAC/ACMV system, which is main energy consumer within the building. Generally, ~70% of electricity is consumed in form of cooling plus ventilation operation, which is the very hug amount and it depends on occupancy level of the building envelop [1]. The building occupancy information can be collected in form of following [2]: (1) occupancy detection, (2) occupancy counting, (3) occupancy identity, (4) occupancy tracking and (5) occupancy location. Moreover, the building OP can be performed by using several methods such as: (1) OP by vision sensors based different measurement systems, and (2) OP by using other sensors based measurement systems. The vision sensory systems are further classified as: (a) Non-depth cameras based systems, and (b) depth cameras based systems. The other sensory system based OP is further categories as: (a) WiFi, (b) PIR sensors, (c) CO2 sensors, (d) electricity meters, (e) measurement systems based on sensor fusion etc. The all possible OP methods are summarized in Fig. 1.

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Fig. 1 Summary of OP methods

Moreover, the synthetic criterions for OP are classified into broad three categories such as: (1) mode of sensing the signals (single mode and multimode sensing of signals), (2) sensing categories and types as shown in Figs. 1 and 3, occupancy modes (i.e., single occupancy space and multi occupancy space). In this way, a number of study has been done for the OP by using several methods which are summarized in [2–5]. In this chapter, a simple framework has been proposed to predict the occupancy by using simple measurable parameters, which is explained in detail in subsequence sections. In the organization the chapter and proposed research work is as follow: Sect. 1 introduces the introduction about the problems occurs in OP and motivation, Sect. 2 presents the proposed approach framework which is developed in this study in a very simple way, Sect. 3 represents the detail analysis of the recorded dataset and its relevancy w.r.t. the occupancy prediction, Sect. 4 explains the proposed techniques used for OP using ANN and PSO-ANN, Sect. 5 shows the results and discussion of the study and finally conclusion is represented in Sect. 6.

2 Proposed Framework The proposed framework for occupancy detection in a room is shown in Fig. 2, which involves the following activities such as the raw dataset collection, pre-processing the collected dataset, attribute extraction, attribute correlation analysis, attribute selection, model development and occupancy detection. In the proposed framework, firstly, the trend of the recorded attributes is analyzed. Then, the correlation analysis of each attribute are analyzed to find out the importance level of each attribute with respect to (w.r.t.) occupancy or un-occupancy condition of the room. The importance level evaluation has been performed by using six machine learning approaches by

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Fig. 2 Proposed approach for online and off-line occupancy detection

using R-code. These six evaluation methods are: (1) CRAE: correlation attribute evaluation (CorrelationAttributeEval), (2) GRAE: gain ratio attribute evaluation (GainRatioAttributeEval), (3) IGAE: information gain attribute evaluation (InfoGainAttributeEval); (4) ORAE: one R attribute evaluation (OneRAttributeEval), (5) RFAE: relief F attribute evaluation (ReliefFAttributeEval), and (6) SUAE: symmetrical uncertainty attribute evaluation (SymmetricalUncertAttributeEval). Finally, the selected most relevant attributes are utilized in occupancy identification. In this study, artificial neural network (ANN) and optimized ANN by using particle swarm optimization (PSO) technique have been utilized for occupancy detection of the room, in which the attribute selection, ANN, PSO-ANN modelling, training, testing, and iterative identification are involved.

Data-Driven Occupancy Detection Hybrid Model …

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3 Brief Detail of Dataset 3.1 Dataset Collection The dataset is collected in two position of the building office (i.e., occupied and unoccupied room condition). The dataset is collected to identify the room occupancy from humidity (RH in %), temperature (Temp in Celsius), CO2 level (in ppm), Light intensity (in Lux) and humidity ratio (HR in kgwater-vapor/kg-air). HR is evaluated value from temperature and humidity. The room occupancy is recorded in form of occupied or unoccupied condition. The dataset is collected for seventeen days starting from 2nd February to 18th February, which is represented graphically in Fig. 3 for all recorded parameters for one day. The statistical variables of the whole recorded

Fig. 3 Recorded raw data representation for one day

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Table 1 Statistical parameters of recorded whole dataset S. No.

Minimum

Maximum

1

Temp.

19

24.408

Mean

2

RH

16.745

39.5

27.656

4.982

3

Light

0

1697.3

130.757

210.431

4

CO2

412.75

2076.5

690.664

311.204

5

HR

0.003

0.006

0.004

0.001

20.906

StdDev 1.055

data set have been mentioned in Table 1, which includes minimum value, maximum value, mean value and standard deviation of all attributes. The correlation of the recorded raw data with occupancy of the room is represented in Figs. 4 and 5 for all recorded attributes, which is shown in blue and red colored for occupied and unoccupied situation of the room. Approximate 23% of total time period of the room uses has been occupied by the occupant and for remaining ~77% time period, room was unoccupied in the building. The total recorded data samples for this occupied and unoccupied period was 20,560, which were collected by Luis M. Candanedo and Véronique Feldheim, University of Mons, Belgium [5].

3.2 Dataset Correlation Analysis The dataset correlation analysis represents the relevancy of the particular attribute’s importance level for the occupancy detection in a building. Here total five number of attributes have been evaluated for their importance level for occupancy detection. The evaluation has been performed by using six different evaluation methods based on ranker search method in the R language platform [6]. These six evaluation methods are: (1) CRAE: correlation attribute evaluation (CorrelationAttributeEval), (2) GRAE: gain ratio attribute evaluation (GainRatioAttributeEval), (3) IGAE: information gain attribute evaluation (InfoGainAttributeEval); (4) ORAE: one R attribute evaluation (OneRAttributeEval), (5) RFAE: relief F attribute evaluation (ReliefFAttributeEval), and (6) SUAE: symmetrical uncertainty attribute evaluation (SymmetricalUncertAttributeEval). The ranker search method based rank of each attribute has been evaluated using all six methods, which is represented in Fig. 6. The relevancy of each attribute has been presented in percentage value for the easy of reader’s understanding. After analyzing Fig. 6, it is concluded that the order of the relevancy of all attribute (i.e., higher to lower relevancy) is light, Temperature, CO2 , HR and RH for all evaluation method. Hence, temperature and RH have higher and lower relevancy respectively with respect to occupancy identification.

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Fig. 4 Correlation representation of recorded raw data with occupancy of the room

4 Proposed Framework Development Using PSO Based ANN The ANNs with three layers (i.e., input-hidden-output layer) have widely utilized for the classification, prediction, regression, forecasting etc. problems [7–32]. In the ANN, the learning process is an important function for its performance ability at higher level of accuracy. Generally, BP (Back-Propagation) algorithm (PBA) is utilized for ANNs training, but it has some shortcomings (slow processing, trapping in the local minima, bad convergence rate etc.). So, there is a research gap to find out the

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Fig. 5 Correlation analysis of each sample recorded sample w.r.t room occupancy

optimum combination of weights (w) and biases (b) values which can achieve lower side of error value. According to [7–32], BPA is dependent highly on (w), (b) and its parameters (i.e., momentum and learning rate). So, several optimization algorithm (i.e., SA, GA, and DE etc.) have been implemented to overcome these shortcoming of the BPA [7–32], but these approaches tranquility agonize from sluggish convergence rates. Moreover, PSO is the solution for vanquishing these shortcoming of BPA as well as other optimization algorithms [34–38]. The mathematical modelling for PSO is as follow: νit+1 = ωνit + C1 × rand × ( pbesti − χit ) + C2 × rand × (gbest − χit ) χit+1 = χit + νit

(1) (2)

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Fig. 6 Attribute correlation representation for occupancy detection using six different methods

where, νit = velocity, i = particle number, t = iteration number, w = weight, rand = random number between 1 and 0, χit = present position, gbest = best solution, pbesti = best solution for ith particle, ωνit = deliver exploration capability, C1 × rand × ( pbesti − χit ) = dispense private thinking, C2 × rand × (gbest − χit ) = dispense collaboration of particles. Equation 1 is utilized to evaluate the velocity of the each particle and then Eq. 2 is used to evaluate the position of the particle and this process of changing the position of particle will be continue until it is not met optimal criterion. Now, this PSO is utilized to find out the optimal value of (w), and (b) of the ANN, so that error can be minimized. For PSO based ANN designing, following two points necessity to delineate. These two points are fitness function and strategy for encoding. Fitness function modelling (FFM): Step #1: The output value of each hidden node is evaluated as: 1  n  f (S j ) =  1 + exp − i=1 ωi j · χi − λ j

(3)

n ωi j · χi − λ j , n = number of input nodes, h = number of hidden where, S j = i=1 nodes, j = jth node in hidden node, λ j = bias value of each hidden node, ωi j = weight value between input and hidden node, χi = input value. Step #2: The output value of each output node is evaluated as:

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yk =

h 

ωk j · f (S j ) − λk

(4)

i=1

where, ωk j = weight value between hidden and output nodes, k = kth node of output node, λk = bias value of each output node. Step #3: now, learning error (ε) for a fitness function is evaluated as: εk =

m  

Oik − Rik

2

(5)

i=1

ε=

g  εk k=1

g

(6)

where, g = training samples, Rik = required output of model, Oik = targeted output Step #4: Now, fitness value evaluation of the training sample as: f itness(χi ) = ε(χi )

(7)

Strategy for encoding (SFE): After fixing the fitness function for PSO based ANN, it is required to select the SFE (i.e., vector method, matrix method and binary method) for showing the (w), and (b) of the ANN [35, 37, 38]. In the proposed framework, matrix SFE is utilized for training of ANN as shown below (Fig. 7): p(:, :, i) = [ω1 , b1 , ω2 , b2 ]

Fig. 7 Three layered ANN architecture (Structure of ANN: 2-3-1) [33]

(8)

Data-Driven Occupancy Detection Hybrid Model …

⎡ ⎡ ⎤ ⎤ ⎤ w13 w23 w36 λ1 ω1 = ⎣ w14 w24 ⎦, ω2 = ⎣ w46 ⎦, b1 = ⎣ λ2 ⎦, b2 = [λ4 ] w15 w25 w56 λ3

293

⎡

(9)

5 Results and Discussion Total eighteen models have been designed and tested for occupancy detection using ANN (9 models) and PSO-ANN (9 models). The performance accuracy for all models have been listed in Table 2, which shows the correct and incorrect occupancy detection in percentage. The ranges of occupancy detection is varies with variation of the number of input variables and the physical correlation of the variables w.r.t. the occupancy of the room. The occupancy detection for these models are 77.9–98.95% for ANN models and 87.8–99.5% for PSO-ANN models, which shows that PSO based ANN model’s performance is more acceptable as comparison to only ANN models. Although proposed framework needs more optimization of the performance accuracy, which will be covered in the forthcoming research using one step-ahead optimization process of ANN as compared with current solution of PSO-ANN. Moreover, proposed PSO-ANN model using all attributes as an input can be used for future prospective of the occupancy detection. The detailed class-wise analysis for model #9 of ANN and PSO-ANN is given in Tables 3 and 4 respectively for the better understanding of the readers.

6 Conclusion Presented study represents the possibility of the proposed framework for occupancy detection in a room by using simple measureable parameters within the room environment such as Temperature, CO2 , Light, RH and HR. A correlation analysis of each measured parameter has been performed to represent the importance level of the parameter for identification of occupancy. This correlation has been performed by using six different machine learning approaches (i.e., CRAE, GRAE, IGAE, ORAE, RFAE, and SUAE), which shows that light and RH have highest and lowest correlation importance level respectively with the occupancy level in the room. After correlation analysis, eighteen different classification models have been designed, trained and tested using all variables. The occupancy detection by PSO-ANN model #9 has highest performance accuracy of 99.5%.

*

*

*

✓

*

*

*

✓

✓

✓

Model #4

Model #5

Model #6

Model #7

Model #8

Model #9

✓

✓

✓

✓

✓

✓

✓

✓

✓

✓

*

*

*

1.0554

1.050

1.0749

1.0895

1.07

22.1158

*

✓

✓

*

*

15.9922

*

✓

23.1031

*

*

98.9446

98.9494

98.9251

98.9105

98.93

77.8842

84.0078

76.8969

85.107

0.555

0.6188

0.8971

0.8794

0.5979

11.908

4.9

12.2142

4.0188

Incorrect classification

99.4450

99.3812

99.1029

99.1206

99.4021

88.092

95.10

87.7858

95.9812

Correct classification

PSO-ANN based occupancy detection

✓ = used variable, * = unused variables Bold portion indicates that Model#9 has highest detection accuracy in comparision of of other developed model

*

*

*

*

*

*

✓

*

14.893

Model #3

*

Model #2

*

*

*

✓

Model #1

Correct classification

Incorrect classification

HR

ANN based occupancy detection

CO2

RH

Temp.

Light

Input variables

Designed model number

Table 2 Summary of designed ANN, PSOANN model with respect to different input variables

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Data-Driven Occupancy Detection Hybrid Model …

295

Table 3 Detailed accuracy by occupancy-class for ANN Model #9 TP rate

FP rate

Precision

Recall

F-measure

MCC

ROC area

PRC area

Class of occupancy

0.995

0.012

0.961

0.995

0.978

0.971

0.994

0.964

Occupied

0.988

0.005

0.999

0.988

0.993

0.971

0.994

0.998

Unoccupied

0.989

0.007

0.990

0.989

0.990

0.971

0.994

0.990

Weighted Avg.

Table 4 Detailed accuracy by occupancy-class for PSO-ANN Model #9 TP rate

FP rate

Precision

Recall

F-measure

MCC

ROC area

PRC area

Class of occupancy

0.995

0.012

0.960

0.995

0.978

0.971

0.994

0.965

Occupied

0.988

0.005

0.999

0.988

0.993

0.971

0.994

0.998

Unoccupied

0.989

0.006

0.990

0.989

0.990

0.971

0.994

0.991

Weighted Avg.

Acknowledgements Authors are very thankful to Intelligent Prognostic Private Limited, India to provide the all type of technical and non-technical facilities, cooperation, and support in each stage to make this chapter in reality. Authors are also very thankful to Luis M. Candanedo and Véronique Feldheim, University of Mons, Belgium [5] to provide open access dataset at UCI machine learning repository [https://archive.ics.uci.edu/ml/datasets/Occupancy+Detection+].

References 1. N. Fatema, H. Malik, A. Iqbal, Big-data analytics based energy analysis and monitoring for multi-storey hospital buildings: case study, in Soft Computing in Condition Monitoring and Diagnostics of Electrical and Mechanical Systems, Advances in Intelligent Systems and Computing, vol. 1096 (2020), pp. 325–343. https://doi.org/10.1007/978-981-15-1532-3_14 2. K. Sun, Q. Zhao, J. Zou, A review of building occupancy measurement systems. Energy Buildings 216, 109965 (2020). https://doi.org/10.1016/j.enbuild.2020.109965 3. W. Jung, F. Jazizadeh, Human-in-the-loop HVAC operations: a quantitative review on occupancy, comfort, and energy-efficiency dimensions. Appl. Energy 239, 1471–1508 (2019). https://doi.org/10.1016/j.apenergy.2019.01.070 4. Z. Chen, C. Jiang, L. Xie, Building occupancy estimation and detection: a review. Energy Buildings 169, 260–270 (2018). https://doi.org/10.1016/j.enbuild.2018.03.084 5. L.M. Candanedo, V. Feldheim, Accurate occupancy detection of an office room from light, temperature, humidity and CO2 measurements using statistical learning models. Energy Buildings 112, 28–39 (2016). https://doi.org/10.1016/j.enbuild.2015.11.071 6. R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, Austria, 2014). http://www.R-project.org/ 7. H. Malik et al., Soft Computing in Condition Monitoring and Diagnostics of Electrical and Mechanical Systems (Springer Nature, Berlin, 2020), 496 p. https://doi.org/10.1007/978-98115-1532-3. ISBN 978-981-15-1532-3

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8. H. Malik et al., Applications of Artificial Intelligence Techniques in Engineering, vol. 1 (Springer Nature, Berlin, 2018), 643 p. https://doi.org/10.1007/978-981-13-1819-1. ISBN 978-981-13-1819-1 9. H. Malik et al., Applications of Artificial Intelligence Techniques in Engineering, vol. 2 (Springer Nature, Berlin, 2018), 647 p. https://doi.org/10.1007/978-981-13-1822-1. ISBN 978-981-13-1822-1 10. A.K. Yadav et al., ANN- and multiple linear regression-based modelling for experimental investigation of photovoltaic module maximum power production under outdoor condition of mountainous region, in Modern Maximum Power Point Tracking Techniques for Photovoltaic Energy Systems (Springer Nature, Berlin, 2020), pp. 229–245. https://doi.org/10.1007/978-3030-05578-3_8 11. V.K. Reddy et al., Novel application of relief algorithm in cascade ANN model for prognosis of photovoltaic maximum power under sunny outdoor condition of Sikkim India: a case study, in Soft Computing in Condition Monitoring and Diagnostics of Electrical and Mechanical Systems (Springer, Berlin, 2019), pp. 387–405. https://doi.org/10.1007/978-981-15-1532-3_17 12. H. Malik, S. Mishra, Artificial neural network and empirical mode decomposition based imbalance fault diagnosis of wind turbine using TurbSim, FAST and Simulink. IET Renew. Power Gener. 11(6), 889–902 (2017). https://doi.org/10.1049/iet-rpg.2015.0382 13. H. Malik et al., Application of neuro-fuzzy scheme to investigate the winding insulation paper deterioration in oil-immersed power transformer. Electr. Power Energy Syst. 53, 256–271 (2013). https://doi.org/10.1016/j.ijepes.2013.04.023 14. H. Malik, R. Sharma, EMD and ANN based intelligent fault diagnosis model for transmission line. J. Intell. Fuzzy Syst. 32(4), 3043–3050 (2017). https://doi.org/10.3233/JIFS-169247 15. A.K. Yadav et al., Application of rapid miner in ANN based prediction of solar radiation for assessment of solar energy resource potential of 76 sites in northwestern India. Renew. Sustain. Energy Rev. 52, 1093–1106 (2015). https://doi.org/10.1016/j.rser.2015.07.156 16. A.K. Yadav et al., Selection of most relevant input parameters using WEKA for artificial neural network based solar radiation prediction models. Renew. Sustain. Energy Rev. 31, 509–519 (2014). https://doi.org/10.1016/j.rser.2013.12.008 17. Azeem et al., k-NN and ANN based deterministic and probabilistic wind speed forecasting intelligent approach. J. Intell. Fuzzy Syst. 35(5), 5021–5031 (2018). https://doi.org/10.3233/ JIFS-169786 18. A.K. Shah et al., EMD and ANN based intelligent model for bearing fault diagnosis. J. Intell. Fuzzy Syst. 35(5), 5391–5402 (2018). https://doi.org/10.3233/jifs-169821 19. A.K. Yadav, H. Malik, Comparison of different artificial neural network techniques in prediction of solar radiation for power generation using different combinations of meteorological variables, in Proceedings of IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES) (2014), pp. 1–5. https://doi.org/10.1109/pedes.2014.7042063 20. A.K. Yadav et al., ANN based prediction of daily global solar radiation for photovoltaics applications, in Proceedings of IEEE India Annual Conference (INDICON) (2015), pp. 1–5. https://doi.org/10.1109/indicon.2015.7443186 21. R. Sharma et al., Selection of most relevant input parameters using weka for artificial neural network based transmission line fault diagnosis model, in Proceedings of the International Conference on Nanotechnology for Better Living, vol. 3, no. 1 (2016), p. 176. https://doi.org/ 10.3850/978-981-09-7519-7nbl16-rps-176 22. H. Malik, Savita, Application of artificial neural network for long term wind speed prediction, in Proceedings of IEEE CASP-2016, 9–11 June 2016, pp. 217–222. https://doi.org/10.1109/ casp.2016.7746168 23. Azeem et al., Artificial neural network based intelligent model for wind power assessment in India, in Proceedings of IEEE PIICON-2016, 25–27 Nov 2016, pp. 1–6. https://doi.org/10. 1109/poweri.2016.8077305 24. S. Saad, H. Malik, Selection of most relevant input parameters using WEKA for artificial neural network based concrete compressive strength prediction model, in Proceedings of IEEE PIICON-2016, 25–27 Nov 2016, pp. 1–6. https://doi.org/10.1109/poweri.2016.8077368

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25. A. Kukker et al., Forearm movements classification of EMG signals using Hilbert Huang transform and artificial neural network, in Proceedings of IEEE PIICON-2016, 25–27 Nov 2016, pp. 1–6. https://doi.org/10.1109/poweri.2016.8077417 26. A. Azeem et al., Application of Waikato environment for knowledge analysis based artificial neural network models for wind speed forecasting, in Proceedings of IEEE PIICON-2016, 25–27 Nov 2016, pp. 1–6. https://doi.org/10.1109/poweri.2016.8077352 27. H. Malik, S. Garg, Long-term solar irradiance forecast using artificial neural network: application for performance prediction of Indian cities. Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 285–293. https://doi.org/10.1007/978-981-13-1822-1_26 28. H. Malik, T. Sharma, A novel intelligent bifurcation classification model based on artificial neural network (ANN). Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 698 (2018), pp. 53–61. https://doi.org/10.1007/978-981-13-1819-1_6 29. H. Malik et al., Feature extraction using EMD and classifier through artificial neural networks for gearbox fault diagnosis. Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 309–317. https://doi.org/10.1007/978-981-13-1822-1_28 30. A.K. Yadav, H. Malik, Short term wind speed forecasting for power generation in Hamirpur, Himachal Pradesh, India, using artificial neural networks. Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 263–271. https://doi.org/10.1007/978-981-13-1822-1_24 31. H. Malik et al., PSO-NN-based hybrid model for long-term wind speed prediction: a study on 67 cities of India. Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 697 (2018), pp. 319–327. https://doi.org/10.1007/978-981-13-1822-1_29 32. N. Fatema et al., Data driven intelligent model for sales prices prediction and monitoring of a building, in Soft Computing in Condition Monitoring and Diagnostics of Electrical and Mechanical Systems (2019), pp. 407–421. https://doi.org/10.1007/978-981-15-1532-3_18 33. S.A. Mirjalili et al., Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl. Math. Comput. 218, 11125–11137 (2012). https://doi.org/10.1016/j.amc.2012.04.069 34. N.K. Nandan et al., Solving nonconvex economic thermal power dispatch problem with multiple fuel system and valve point loading effect using fuzzy reinforcement learning. Journal of Intelligent & Fuzzy Systems, 35(5), 4921–4931 (2018). https://doi.org/10.3233/jifs-169776 35. S. Smriti et al., Special issue on intelligent tools and techniques for signals, machines and automation. J. Intell. Fuzzy Syst. 35(5), 4895–4899 (2018). https://doi.org/10.3233/JIFS169773 36. A. Khatri et al., Optimal design of power transformer using genetic algorithm, in Proceedings of IEEE International Conference on Communication System’s Network Technologies (2012), pp. 830–833. https://doi.org/10.1109/csnt.2012.180 37. T. Mahto et al., Load frequency control of a solar-diesel based isolated hybrid power system by fractional order control using particle swarm optimization. J. Intell. Fuzzy Syst. 35(5), 5055–5061 (2018). https://doi.org/10.3233/JIFS-169789 38. T. Mahto et al., Fractional order control and simulation of wind-biomass isolated hybrid power system using particle swarm optimization. Book chapter in Applications of Artificial Intelligence Techniques in Engineering, Advances in Intelligent Systems and Computing, vol. 698 (2018), pp. 277–287. https://doi.org/10.1007/978-981-13-1819-1_28

A Maiden Application of Competitive Swarm Optimizer for Solution of Economic Load Dispatch with Parameter Estimation Abhishek Rajan, Abhay Sahu, Debashish Deka, and Tanmoy Malakar

Abstract This work, presents a novel application of newly developed Competitive Swarm Optimizer (CSO) in solving a non-linear, non-convex and constrained Economic Load Dispatch (ELD) problem of power systems. A comparative analysis is performed between Particle Swarm Optimization (PSO) and CSO. CSO is basically inspired by the behavior of well-known PSO algorithm. Similar to PSO, CSO is also swarm based optimization technique and has both cognitive as well as social component. The difference lies in the fact that CSO neither uses local best nor global best in updating the position of their particles, which makes the algorithm memory free. A pair wise competition is performed and only loser particles are updated after getting experience from the winner one. The performance of algorithm is tested on 4 benchmark systems with 5 case studies. Case studies include both small as well as bigger system with various degree of constraints such as; Power balance, Prohibited Operating Zone (POZ), ramp limits, valve point loading etc. Moreover, general and standard statistical tests (t-test) are also performed to investigate the consistency and robust of the proposed algorithm. The performance of CSO is significantly dependent on its social factor (φ) and population size. In view of this, in the present work the performance of CSO with the variation in population size and (φ) are also studied. Parametric study is also performed for all cases to judge the sensitivity of the algorithm. The study reveals that the proper tuning of social factor (φ) and population A. Rajan (B) Electrical and Electronics Engineering Department, NIT Sikkim, Ravangla, India e-mail: [email protected] A. Sahu Oil and Natural Gas Corporation, Mumbai, India e-mail: [email protected] D. Deka Samsung India R&D, Bengaluru, India e-mail: [email protected] T. Malakar Electrical Engineering Department, NIT Silchar, Silchar, Assam, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H. Malik et al. (eds.), Metaheuristic and Evolutionary Computation: Algorithms and Applications, Studies in Computational Intelligence 916, https://doi.org/10.1007/978-981-15-7571-6_14

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size significantly reduce the search space which helps the algorithm to accelerate its convergence. Keywords Competitive swarm optimizer · Particle swarm optimization · Economic load dispatch · Ramp limits

1 Introduction Economic load dispatch (ELD) is basic tool for dispatching power from generating end to load end in a most economical way, simultaneously satisfying all operational and physical constraints [1]. ELD is highly nonlinear constrained optimization problem because of the presence of practical constraints like ramp rate limits, prohibited operating zone (POZ), valve point loadings etc. [1]. Hence, to solve such a constrained optimization problem, an efficient tool was required that should have no restrictions on the nature of the objective function. In view of this, Sinha and Chattopadhyay in 2003 suggested evolutionary programming techniques to solve ELD problems [2]. Similarly in [3] authors have proposed efficient evolutionary strategies for solving ELD problems in 2005. Since then several more methods have been tried by the researchers to improve the solution of ELD problem. Methods such as: Taguchi method (TM) [4], genetic algorithm (GA) [5], pattern search (PS) [6], firefly algorithm (FA) [7], simulated annealing (SA) [8] etc. have been implemented by the researchers to solve the ELD problem. In [9–19] some more algorithms like Charge system algorithm (CSA), Differential evolution (DE), Tabu search (TS), Biogeography based optimization (BBO), Seeker optimization algorithm (SOA) etc. have been tried to judge their performance in solving the constrained ELD problem. Basic drawbacks with above said optimization techniques are, their higher tendency of trapping into local optima and sometimes slow convergence [20–23]. To solve these aforesaid problems, researchers have tried to hybridize the algorithm with many suitable techniques in order to allow more intense exploration and exploitation. Some hybrid algorithms are reported in [24–37], which are applied to solve the economic load dispatch problem. In [25] authors have introduced wavelet mutation in PSO. In [27] original GA is merged with bounded crossover and wavelet mutation strategies. In [33] Panigrahi and Pandi incorporate local search technique (Nelder-Mead optimization) in bacterial foraging algorithm to improve its exploitation property. Bhattacharya and Chattopadhyay in [37] has proposed hybrid version of DE and BBO, and successfully applied to solve the problems of ELD. Results are also compared with the original algorithm to claim the improvement in the solution obtained from hybrid algorithm. Researchers have also tried to solve multi-objective ELD problem either by converting different objective function into one function or by converting the algorithm into multi-objective optimization algorithm [38–56]. Fuel cost and environmental emissions are the two fundamental objective functions considered

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in solving multi-objective ELD. Other than compromised solution, extreme solutions are also declared to represent the performance of algorithms in solving single objective functions. Particle Swarm Optimization (PSO) [57–61], is most probably, the first swarm based optimization techniques developed by Kennedy and Eberhart in the year 1995. PSO is inspired by the swarm behaviors of animals such as flocking of birds. PSO is utilized in solving various engineering optimization problems, however; some researchers have also reported its drawback of frequently trapping in local optima, especially in a high dimensional problem with multiple local optimal points [62– 65]. In order to improve the balance between exploration and exploitation, number of variant of PSO like h-PSO [17], PSO-SQP [26], OLPSO [59], TVAC-PSO [60] etc. have been proposed. Chang and Yaochu proposed a new algorithm called Competitive Swarm Optimizer (CSO) most recently and reported their work in [66]. CSO is also inspired by PSO and as like PSO, CSO have both cognitive as well as social components. The main conceptual difference lies in the updation process of the particles. Unlike PSO, CSO neither uses global best nor local best particles for updating the swarm. CSO perform pair wise competition and only losers are updated after learning from winner particles while winners are passed directly to the next generation [66]. Since memory is not required to memorize the global and local best values, speed of the algorithm is fast. Authors of CSO have also performed the parametric analysis of its tunable parameter ϕ, and discussed its correlation with swarm size with proper mathematical proof. The above versatile qualities of CSO inspired the present authors to investigate its overall performance in solving a constrained electrical engineering optimization problem. To realize the efficiency and robustness of any new algorithm, it is required to solve highly non liner, non convex optimization problem. Further, the tunable parameter need to adjust properly so that algorithm can perform better. In view of this, the present work deals with the solution of ELD problems on 4 systems. It is utilized to solve ELD problems to understand how the algorithm tackles nonlinearity and non-convexity like valve point loading effect, ramp limits and POZ’s with fuel cost. It will help in investigating the quality, computational efficiency and consistency of CSO in solving complex objective functions. Parametric studies are also performed on case studies and suitable value of the tunable parameter i.e. ϕ is suggested after performing the rigorous tuning of the parameter. Performance of the algorithm under different swarm size and ϕ are also taken into observation. Section 2 of the chapter describes mathematical formulation of ELD problems with practical constraints and its valid reason of occurrence. Sections 3 and 4 deal with CSO algorithm and its implementation in ELD problem respectively. Results are discussed in Sect. 5 whereas parametric studies are carried out in Sect. 6. Conclusions are drawn in Sect. 7.

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2 Problem Formulation 2.1 Objective Function 2.1.1

Quadratic Fuel Cost Minimization

The fuel cost function of the generator is the simplest form of cost equation and is dependent on the real power output, therefore; it is a function of active power outputs from the generating units. As explained in the above section, ELD aims to optimize the fuel cost simultaneously satisfying all the equality and inequality constraints (explained in section B) in its best possible way. Mathematically the total fuel cost function of the generator can be represented as: Minimi ze F Cost =

Ng  (αk Pk2 + βk Pk + γk )

(1)

k=1

where for the kth generating unit αk , βk , γk represents the fuel cost coefficient of the quadratic function and N g being the representative for the total number of generating units.

2.1.2

Quadratic Fuel Cost Minimization with Valve Point Loading Effect

In practical operation, the generator is provided with multi steam valves, these valves are used for controlling the flow of steam over the turbine. The control operation is accomplished by gradual closing and opening of the multi steam valves. The above control operation and the wire drawing effects are also non-linear in nature. These two effects cohesively and individually capable and responsible for initiation of sudden or spontaneous increase in the generator losses resulting in non-linear power output of the generating units. The non-linear variation in the power output is usually represented by a rippled curve along with the basic quadratic cost curve thereby making the overall cost curve highly non-linear, increasing the number of local optimum. The above practical behavior of the generating units must be considered for the calculation of total fuel cost. Hence the original cost function is modified into a linear summation quadratic and sinusoidal functions of generator real power output (2). Figure 1 shows fuel cost with valve point loading effect. Mathematically the modified total fuel cost function of the generator can be represented as: Minimi ze F

Cost

Ng  = (αk Pk2 + βk Pk + γk ) + |ek × sin(h k × (Pkmin − Pk )| (2) k=1

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Fig. 1 Fuel cost with valve point loading effect-a, b, c, d [15] With Valve point

Generation Cost ($/hr)

Without Valve point

d c b a

Output Power (MW)

where ek and h k are the constants representing valve point loading of the kth generating unit. Where ek and h k are the constants representing valve point loading of the kth generating unit.

2.2 Constraints 2.2.1

Equality Constraints

Real Power Balance Equation In a practical AC power system, the alternating electrical energy cannot be stored and at any instant. The total generation by the generating units must balance the total load on power system along with the total transmission loss PL . This dynamic nature of the AC power systems gives rise to the real power balance constraint. The constraint can be mathematically formulated as: Ng 

PK = PD + PL

(3)

K =1

where PD and PL represents the total load demand and the total real power loss respectively. Pk is the power output of the kth generating unit. N g is the total number of generating unit. For the calculation of line losses conventional B loss coefficient matrices are used. The mathematical representation of total real power loss as a function of real power output is given in Eq. (4).

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PL =

Ng Ng  

Pk Bkl Pl +

k=1 l=1

Ng 

B0k Pk + B00

(4)

k=1

where B00 the constant of the loss coefficient is, B0k is the kth element of loss coefficient vector and Bkl is the klth element of the loss coefficient matrix.

Calculation of Slack Generator Output To satisfy the real power balance constraint, one of the generating units among all available units is made dependent. Thus, the real power output of this unit cannot be considered as a control variable. Out of the total say N number of generating units usually the unit having highest range of real power output is selected as the slack generator. The role of slack generator is to provide the power loss which occurs in the transmission line while satisfying the its real power output limit constraint. To realize the slack generator calculations for first (N − 1) generators real power loading is assumed to be specified. The real power loading the Nth generating unit is calculated as: PN = PD + PL −

−1) (N 

Pi

(5)

i=1

The total transmission loss is also dependent on the power output of all generating units including slack or dependent generator, so the PL can be calculated as [31]: PL =

N −1 N −1  

Pi Pi j P j + 2PN

i=1 i=1

+

N −1 

 N −1 

 B N i Pi

+ B N N PN2

i=1

B Oi Pi + B O N PN + B O O

(6)

i=1

By proper expansion and rearrangement of (5) a more simplified and understandable expression (7) can be obtained for further analysis. ⎛ B N N PN2 + ⎝2 ⎛ + ⎝ PD

N −1

⎞ B N i Pi + B O N − 1⎠ PN

i=1 N −1 N −1 i=1 j=1

Pi Pi j P j +

N −1 i=1

B Oi Pi

N −1

⎞ Pi + B O O ⎠ = 0

(7)

i=1

The real power loading of the Nth dependent generating unit can be calculated by solving (7). Above equation can be written in a very simple quadratic equation form (8) [31].

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U PN2 + V PN + W = 0

(8)

U = BN N

(9)

where,

 V = 2 ⎛ W = ⎝ PD +

N −1 

 B N i Pi + B O N − 1

(10)

i=1 N −1 N −1  

N −1 

Pi Pi j P j +

i=1 j=1

B Oi Pi −

i=1

PN =

−V ±

N −1 

⎞ Pi + B O O ⎠

(11)

i=1

√ 2

V 2 − 4U W 2U

(12)

where, V 2 − 4U W ≥ 0.

(13)

To satisfy the real power balance constraint and slack generator real power output limit constraint only positive roots of (12) are chosen as power loading or power output of the Nth generating unit.

Constraints Handling of Equality Constraint Equality constraints are one of the toughest constraints to handle. It is also found that rate of feasible solution in the search space of a constraints optimization problem becomes low if there are more equality constraints required to satisfy [67]. Hence in this work the above mentioned equality constraint is converted into inequality constraints by making the Nth generator output as dependent variable. Researchers have proposed many methods to handle inequality constraints like, Penalty Factor method (PF), Feasibility Rules (FR), Stochastic Ranking (SR), ε-constrained etc. [67]. In The present work most popular constraint handling technique called PF method is applied to treat the inequality constraints. If the real power output limit constraint of the slack or dependent generating unit is not satisfied then violation from its nearest bond value is calculated a suitable penalty is imposed on the fitness. In this way the solutions having higher violation are gradually discarded from the solution set. The penalty factor can be chosen based on the value of fitness and by trial and error method. Selection of penalty factor is completely dependent on the experience. The objective function after imposing the constraints of slack generator power output (dependent variable) can be re written as:

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Minimi ze F Cost =

Ng 

2 (αk Pk2 + βk Pk + γk ) + λ PN PN − PNlimit

(14)

k=1

where λ PN is the penalty is factor and PN − PNlimit is the violation. The value of PNlimit can be defined as: ⎧ min PN i f PN < PNmin ⎪ ⎪ ⎨ max PN i f PN > PNmax = ⎪ else ⎪ ⎩ PN

PNlimit

(15)

PNmin , PNmax and PN are the minimum, maximum and actual active power generation of slack generator (dependent variable)

2.2.2

Inequality Constraints

Generation Real Power Output Limits The boilers of the thermal generating units are designed to operate in a specified range of temperature for safe operation. For this a particular generator must operate in a specified or restricted range of power output. The range depends on boiler thermal constraint. Hence, a lower and upper bound of real power output is fixed for concerned generating unit. The above constraint for the kth generating unit can be formulated as: Pkmin ≤ Pk ≤ Pkmax

(16)

where Pkmin and Pkmax are respectively the lower and upper real power generation limits of the kth generating unit.

Generator Prohibited Operating Zone The multi steam valves of the generating units are continuously regulated depending on the load frequency control mechanism. Due to this control process, input of the turbine shaft experiences change in the flow of the steam which causes vibration in the shaft. These vibrations may occur with a frequency close to the normal operating frequency. Such scenario with vibrational frequencies in close vicinity of power frequency is capable enough to drive the generating unit into sub-synchronous resonance. To avoid such catastrophic phenomenon the generator real power output is restricted or rather bounded in certain zones. The zones where sub-synchronous resonance are most likely to occur are referred as prohibited operating zones (as shown

A Maiden Application of Competitive Swarm Optimizer … Fig. 2 Prohibited operating zones

307

Total Fuel Cost ($/hr0

Prohibated Operating Zone (POZ)

Power Output

in the Fig. 2). This constraint can be mathematically formulated as: z Pkmin ≤ Pk ≤ Pk,1

(17)

z u Pk,l−1 ≤ Pk ≤ Pk,l

(18)

u Pk,P Z k ≤ Pk ≤ Pkmax for k = 1, 2, 3, . . . , NG

(19)

Generator Ramp Rate Limit In a practical power system the loads are not constant and are varying during hours and periods of a day. The variation in load demand can be met by continuously varying the steam input to the shaft of the generator. These variations does not results in the instantaneous change in generator real power output due to the massive mechanical inertia of the generating units. Hence, in order to realize the actual operation of the generating unit, a limit is fixed on the power output units known as ramp rate limit. The up ramp rate limit and the down ramp rate limit determine the various intermediate limits of power output within its extreme range for a particular generating unit. It can be mathematically formulated as: max(Pkmin , Pk0 − D Rk ) ≤ Pk ≤ min(Pkmax , Pk0 + U Rk )

(20)

where Pkz , Pkz−1 , U Rz , D Rz are the present, previous power outputs and ramp-up and ramp-down limits respectively.

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Constraints Handling of Inequality Constraint The inequality constraints presented in Sect. 2.2.2 deals with the active power generation of generators. Since in all the three constrains, range of power output is given and the power generation of generators are considered as continuous variables, these are initialized with uniformly distributed random numbers within their range; e.g., PK = rand[Pkmin , Pkmax ] in this work. In Section “Calculation of Slack Generator Output” it is mention that generator will not generate the power in certain region between maximum and minimum range of the power output as these zone are declared as prohibited operating zone by the manufacturers, hence, in order to handle this constraint, the random initialization of power by Kth generator is restricted within their operating limits. Similar type of logic is applied in Section “Constraints Handling of Equality Constraint” to take care of ramp limits.

3 Competitive Swarm Optimizer The various phenomena occurring in nature like reproduction in flowering plants through pollination, swarm action, frog leaping or ant colony activity etc. have inspired many researchers to develop several nature based optimization techniques. Gaining inspiration from social behavior of flocking of birds, and its group activity while moving together for seeking food, motivated Kennedy and Eberhart to devise an optimization technique called Particle Swarm Optimization (PSO) [57] in the year 1995. In fact it is one of the oldest swarm based optimization technique (After ACO) and gradually it became popular among the researchers. Its conceptual simplicity, high search efficiency and ease in implementation attracts the researchers to a great extent [57]. PSO, being a distinctive population based optimizer, sometimes faces the problem of trapping into local optima, slow speed of convergence and premature convergence. In order to avoid such problems, many researchers have tried to improve the features of PSO and as a result of that, number of its variants are developed. Some of them are ALC-PSO [58], OLPSO [59], PSO-TVAC [60], IDPSO [65] etc. These algorithms are developed with an aim to resolve the problem of premature convergence associated with PSO. In a similar manner, Cheng and Jin developed a novel Competitive Swarm Optimizer (CSO) [66] in the year 2015 to improve the phenomenon of premature convergence occurring in PSO. They were motivated from the fact that because of the global impact of gbest of PSO, pbest as the likeliness to obtain a value similar to or more or less same as gbest and thereby suppressing the diversity of the swarm. In CSO, the particles were updated through a pair wise competition system between particles in each swarm. The outcome of each competition resulted in the updating the loser in accordance to the winner particle’s information whereas the winners are kept intact. The difference between CSO and PSO lies in the following two aspects [66].

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1. There is no gbest and pbest concept in CSO where as these two are the vital factors present in canonical PSO. 2. No memory is required to preserve the current and global best solution in case of CSO. Particle which lose the competition, learn from the winner one in the current swarm only [66]. The algorithm is first initialized randomly with a swarm P(t) consisting of m particles. Where, ‘m’ is the swarm size and ‘t’ being the generation index. In terms of position, each particles are n-dimensional with xi (t) = xi1 (t), xi2 (t), . . . , xin (t) and have an n-dimensional velocity vector vi (t) = vi1 (t), vi2 (t), . . . , vin (t). After each iteration, a random couple out of m/2 couples (taking the swarm size m as an even number) is taken and a competition is made between the particles of each couple. The Particle with better fitness is declared as winner and keeping intact, it is passed to the next generation, P(t + 1), whereas the loser updates its position and velocity from the experience of the winner. After updating, the loser is passed to swarm P(t + 1). Each Particles compete for only once and they are passed to the next generation after their position and velocity gets updated. The position and velocity of the winner and loser in the kth round of competition in generation ‘t’ with X wk (t), X lk (t) and Vwk (t), Vlk (t) respectively, where k = 1, 2,…, m/2 [66]. Accordingly, after the kth competition the loser’s velocity will be updated using the following learning strategy.

Vl,k (t + 1) = R1 (k, t)Vl,k (t) + R2 (k, t) ∗ X w,k (t) − X l,k (t)

+ ϕ R3 (k, t) X k (t) − X l,k (t)

(21)

As a result, the position of the loser can be updated with the new velocity. X l,k (t + 1) = X l,k (t) + Vl,k (t + 1)

(22)

where R1 (k, t), R2 (k, t) and R3 (k, t) are the random number between [0, 1], Xk (t) is the mean position value of the relevant particles, φ is a parameter that controls the influence of X(t). The first part R1 (k, t)Vl,k (t) is similar to the inertia term in the canonical PSO, only the inertia weight ω in PSO is replaced by a random vector R1 (k, t). The second part R2 (k, t)∗ (X w,k (t) − X l,k (t)) is also called cognitive component. The third part φ R3 (k, t) ∗ X (t) − X l,k (t) is termed social component, same as that of PSO but in this component of CSO, gbest of PSO is replaced by the mean position of the current swarm (X (t)). This modification avoids the memory requirement [66]. Since, φ is the only one tunable parameter in the algorithm, controlling the search space while maintaining its exploration and exploitation become easier. Proper tuning of φ can also reduce the search space. The details of the algorithm is clearly explained in [66]. Flow chat of CSO algorithm is given in Fig. 3.

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Fig. 3 Flow chart of CSO algorithm

4 Implementation of CSO in ELD Problem In this section implementation of CSO algorithm is discussed to solve the ELD problem of power system. All equality and inequality constraints mentioned in Sect. 2.2.2 are successfully implemented. The problem of power mismatch is eliminated by separately treating the dependent variable i.e. slack generator power output. The detailed analysis can be seen in Sect. 2.2.2. The process of implementation of CSO in ELD problem is described below. Step 1: Initialization Since CSO algorithm, similar to PSO, is a population based algorithm, it is necessary to initialize the population of swarm and positions of their particles in the search space. Let ‘m’ be the number of particles in the swarm and ‘n’ be the number of dimensions of each particle. In ELD problems of power system, the generator real

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311

power generations are the decision variables which forms the individual particle of the swarm and real power output of all generators represents position of each particles of the swarm in n dimensional space. The complete population of the swarm can be represented in the following matrix form. ⎤ P1,1 · · · P1,n ⎥ ⎢ = ⎣ ... . . . ... ⎦ Pm,1 · · · Pm,n ⎡

Pi, j

where, i = 1, 2, 3,…, m and j = 1, 2, 3, …, n. Pi, j represents the complete swarm. P1,1 , . . . , P1,n represents the first vector of Pi, j . P1,1 (Real power output of one generator) is the position of first particle of Pi, j . Each particle is one of the possible solutions of economic load dispatch problem. For the initialization purpose, the number of particles i.e. m and the number of dimension of each particle (generating units) i.e. ‘n’ are chosen. Transmission line coefficient (B-coefficient) and maximumminimum limits of all generating units are specified. Maximum number of cycles is also set to define the stopping criterion of the algorithm. Each particle of Pi, j is initialized randomly within the specified operating limit of the real power output of the generators. Equations (16) and (20) are used for the initialization of output power of generators without ramp and with ramp limits respectively. The ith vector of swarm P can be initialized by utilizing following formula:

Pi, j=1...n = Pi,Lj + rand × Pi,Uj − ViLj

(23)

where Pi,Lj and Pi,Lj are lower and upper bound of the jth position of the ith particle of the swarm Pi, j . “rand” is the uniform random number between [0, 1]. Step 2: Evaluation of fitness Since this chapter deals with the optimization of fuel cost of the generating units simultaneously satisfying the all equality and inequality constraints mentioned in Sect. 2.2.2, fitness of the particular swarm represents the fuel cost for required generations. Before calculating the fitness, losses in the transmission line must be calculated using loss coefficient formula mentioned in Eq. (4). The treatment of slack bus is performed according to the details given in Sect. 2.2.1.2. Each particles of the complete swarm population P must satisfy the Eq. (3). If there are ‘n’ number of generators in complete set of ith particle which is also the dimension of the problem. The particular vector, Pi can be represented as:   Pi = Pi,1 , Pi,2 , Pi,3 , . . . , Pi,n

(24)

where, i = 1, 2, 3, …, m; Pi,1 and Pi,n represents the first and nth generating unit of ith particle of the swarm respectively.

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Step 3: Competition between particles After calculation of fitness, all ‘m’ number of particles of swarm ‘P’ are randomly divided into m/2 number of pairs. Competition is made between each pair of particles. The particle with better fitness (less fuel cost) is considered as winner and passed directly for the next generation, (P(t + 1)) of the swarm (‘t’ is present generation and ‘t + 1’ is the next generation), while the looser learn from winner and update its velocity and then position in the specified search space. The process of competition can be implemented in the following ways: Randomly choose two particles Pir 1 (t), Pir 2 (t) from P.

where, Pir 1 (t), Pir 2 (t) are randomly selected two probable solutions of ELD from swarm P. Pw (t) is winner solution as its fitness i.e. fuel cost is better in comparison to Pl (t) and hence, Pl (t) is named as loser. Step 4: Learning and updation of looser particles: The looser gets learning from winner particles and they try to mobilize their positions towards the elite particles. This is done by using Eqs. (21) and (22). After their updation in positions, the violation in position (maximum and minimum limit of jth generating unit) are checked. If the violation in any particular position of the particle is observed from their bound values, that position is sealed with its corresponding limiting value. In terms of ELD problem, these updated loser particles are known as new modified generation values of generators (Pi, j new). This can be done in following ways:

where, Pi, j min and Pi, j max represents the minimum and maximum generation capacity of jth generator in ith particle. Pi, j (t + 1) indicates the generation of jth generator of ith particles in the new swarm P(t + 1).

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Step 5: Formation of new swarm: All m/2 updated looser particles are now moved to P(t + 1) to form the complete set of swarm which already consists of m/2 number of winner particles. With the movement of m/2 updated looser particles in P(t + 1) swarm, the population of P(t + 1) swarm become equal to the initial population (P(t)) of swarm. Step 6: Stopping criterion: This is the last step of tth iteration. In this step, algorithm compares the present cycle number with the predefined maximum cycle number. If present cycle is less than the maximum cycle, then algorithm again moves to step 2 else it terminates.

5 Simulation Results and Analysis The proposed approach is successfully implemented in solving ELD problem of power system. In the present chapter authors have solved 5 case studies on different systems incorporating several operational and physical constraints mentioned in Sect. 2.2.2. In all the cases fuel costs of generating units are minimized simultaneously satisfying its physical and operational constraints. Results obtained are compared with several reported results from different literatures. Algorithm is tested on 6-generator system (two Cases), 20-generator systems, 40 generator systems and 110-generator system to examine the consistency, reliability and robustness of proposed approach. For 6 generator system, two cases are considered and results are compared with GA [22], PSO [21], and several other reported method methods. For 20, 40 and 110 generator system, results are compared with the established algorithms like GA [22], PSO [21], SA [9], TS [9], BBO Bhattacharya et al., BF [33], FA [7] and other methods. Parametric studies are also performed to evaluate the performance of CSO. Source of loss-coefficient data are mentioned in appendix. Codes for the proposed algorithm is written in MATLAB-14 platform with 2 GB RAM, i3 processor. Different case studies, their corresponding test system information’s and the simulation results are discussed below:

5.1 Different Case Studies and System Information’s 5.1.1

Case 1: Fuel Cost Optimization with Losses, Valve Point Loading and Prohibited Zone

For this case, IEEE 30 bus system having 6-generators are considered. These generators are the decision variable. Hence for this case there are 6 control variables. The System has load demand of 283.4 MW. The system data including the range of POZ is taken from [20]. The optimized solution with complete control settings obtained

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from CSO and PSO is mentioned in Table 1 and the corresponding convergence plots are shown in Fig. 4. The solution obtained by CSO is compared with various other reported algorithms also in Table 1 and few more comparisons are drawn in Table 2.

5.1.2

Case 2: Fuel Cost Optimization with Ramp Limits and Prohibited Zone

The present case also deals with 6 decision variables i.e. 6-generator systems like Case 1. Ramp limit constraints are added to realize the performance of CSO more practically. The concept of ramp limit is explained in Sect. 2.2.2. The system data is taken from [9]. The load demand is 1263 MW. Apart from PSO, the results obtained from CSO are compared with several other reported algorithms in Table 3. Some additional comparisons are also shown in Table 4. The convergence plot correspond to the best result obtained with CSO and PSO are shown in Fig. 5.

5.1.3

Case 3: Fuel Cost Optimization with Loss

A 20-Generator system (20 decision variables) is considered in this case for the optimization purpose. The system load demand is 2500 MW and the data is taken from [24]. The result obtained with CSO is compared with different optimizer like PSO, BBO [15], HM [19] and LI [24]. The control variable settings are given in Table 5 and convergence plots of both PSO and CSO are represented in Fig. 6.

5.1.4

Case 4: Fuel Cost Optimization Without Losses and with Valve Point Effect

In this case, system with higher dimension (40 generator system) is taken to check the performance of CSO. To make the system more complex, valve point loading as a non-linearity is added. Losses are neglected for this case for the comparison point of view. System data is taken from [35]. Total system demand considered is 10,500 MW. The comparative results between PSO and CSO are presented in Table 6. Comparison from other reported algorithms for the same system are shown in Tables 6 and 7 as well. The convergence curve correspond to the best solution with CSO and PSO are plotted shown in Fig. 7.

5.1.5

Case 5: Fuel Cost Optimization Without Losses, 110-Generators

The performance of the algorithm is also tested on highly complex system which carries 110 generators. Loss calculation is neglected for this case. System data is taken from [35]. The system is having load demand of 15,000 MW. The result obtained from proposed algorithm is compared with several other methods in Table 8. However,

150.724

133.981

182.47

199.633

199.599

197.864

199.601

GA [22]

GA-APO [22]

NSOA [22]

MSG-HP [21]

FPSOGSA [23]

PSO

CSO

20

50.3374

20

20

48.3525

37.215

60.870

P2

23.8409

15

23.989

23.7624

19.855

37.7677

30.896

P3

Bold signifies the best results obtained by proposed algorihm

P1

Power (MW)

Table 1 The best power output for Case-1 (PD = 283.4 MW) P5

10 18.1385

19.1485

18.2154

17.1018

13.6677

18.7929

19.488

10

18.8493

18.8493

17.137

28.3492

14.213

P4

P6

13.6611

12

13.8506

15.6922

12.3487

38.0525

15.915

Net power

294.39

295.202

294.5045

294.5829

293.83

294.16

292.10

Cost ($/h)

924.893

925.758

925.413

925.640

984.93

1101.49

996.03

Loss (MW)

10.9901

11.8022

11.1044

11.183

10.4395

10.7563

8.706

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Fig. 4 Convergence plot for Case-1

Table 2 More comparisons of power output for Case-1 Method

DE [11]

PSO [12]

ABC [13]

EP [13]

IEP [13]

Cost($/h)

963.00

925.7

928.4

955.508

953.57

Method

TS [13]

ITS [13]

SADE-ALM [13]

TS-SA [13]

CSO

Cost($/h)

956.498

969.1

944.031

959.56

924.89

Bold signifies the best results obtained by proposed algorihm

Table 3 The best power output for Case-2 (PD = 1263 MW) Power (MW)

P1

P2

P3

P4

P5

P6

Loss (MW)

Cost ($/h)

HHS [23]

449.909

172.73

262.9

136.03

166.96

86.87

12.48

15,442.8

SA [9]

478.125

163.02

261.7

125.76

153.706

93.79

13.131

15,461.1

TS [9]

459.075

185.06

264.20

138.12

154.471

74.99

12.942

15,454.8

MTS [18]

448.12

172.80

262.59

136.96

138.684

87.33

13.020

15,450.0

BBO [15]

447.3

173.23

263.31

138.0

165.41

87.0

12.46

15,443.0

PSO

447.497

173.32

263.4

139.05

1165.476

87.12

12.958

15,450

CSO

447.058

173.24

263.80

138.99

165.66

86.66

12.422

15,442.7

Bold signifies the best results obtained by proposed algorihm

the best control settings obtained with CSO and PSO are shown in Table 9. Their corresponding convergence plots are shown in Fig. 8.

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Table 4 More comparisons of power output for Case-2 Methods

New MPSO [15]

SOH_PSO [15]

PSO_LRS [15]

NPSO [15]

NPSOLRS [15]

HAS [16]

Cost($/h)

15,447.0

15,446.0

15,450

15,450

15,450

15,449

Methods

TSA [16]

SAPSO [17]

APSO [17]

CPSO1 [23]

CPSO2 [23] HIS [23]

Cost($/h)

15,451.6

15,455

15,449.99

15,447.0

15,446.0

Methods

BFO [18]

SGA [18]

DE [18]

CSS [39]

CSO

Cost($/h)

15,443.8

15,447.0

15,449.766

15,446.0

15,442.63

15,447.9

Bold signifies the best results obtained by proposed algorihm 4

1.558

x 10

CSO PSO

Total Fuel Cost ($/hr)

1.556 1.554 1.552 1.55 1.548 1.546 1.544

0

20

40

60

80

100 120 Iterations

140

160

180

200

Fig. 5 Convergence plot for Case-2

5.2 Comparative Study and Its Analysis 5.2.1

Qualitative Analysis

The algorithm parameters like population size and φ, controls the optimization process of the algorithm. A parametric study has been carried out in Sect. 6 which shows the variation of optimal fuel cost with different values of φ and population size. 50 trial runs are taken for each case study. The minimum cost obtained by CSO for all the 5 cases are 924.8937 $/h, 15,442.73$/h, 62,454.31,191$/h, 121,421.3667 $/h and 197,988.1803 $/h, whereas, for the same case studies the optimum cost obtained by PSO are 925.758, 5450, 62,455.5, 122,994.1, and 197,988.180 $/h respectively. Tables 1, 3, 5, 6, and 9 report the best cost and optimal control settings of both CSO and PSO. From the above presented costs of different case study we can conclude that CSO performs better with respect to PSO. In all the five cases, except for Case 4, the fuel cost obtained by CSO is found to be less than other methods. However, the minimum fuel cost with CSO for Case 4 is found to be higher than those reported

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Table 5 The best power output for Case-3 (PD = 2500 MW) Power (MW)

BBO [15]

HM [19]

LI [24]

PSO

CSO

P1

513.0892

512.7804

512.7805

512.02647

510.8201646

P2

173.3533

169.1035

169.1033

171.56076

166.5330687

P3

126.9231

126.8897

126.8898

124.20183

125.7334791

P4

103.3292

102.8656

102.8657

93.300736

100.7071383

P5

113.7741

113.6836

113.6386

114.97085

113.9111766

P6

73.06694

73.5709

73.571

71.554345

73.38880727

P7

114.9843

115.2876

115.2872

113.71725

114.5664678

P8

116.4238

116.3994

116.3994

118.36579

116.2072013

P9

100.6948

100.4063

100.4062

102.2828

100.5679584

P10

99.99979

106.0267

106.0267

103.5961

109.1443611

P11

148.977

150.2395

150.2394

156.17275

151.1602585

P12

294.0207

292.7647

292.7648

293.48643

291.448511

P13

119.5754

119.1155

119.1154

122.40456

119.0610146

P14

30.54786

30.8342

30.8144

40.577239

37.90417843

P15

116.4546

115.8056

115.8057

113.74743

115.3371114

P16

36.22787

36.2545

36.2545

36.597024

36.31556905

P17

66.58943

66.859

66.89

62.214654

66.55516637

P18

88.54701

87.972

87.972

85.529402

87.41460599

P19

100.9802

100.8033

100.8033

102.47829

101.0186295

P20

54.2725

54.305

54.305

54.54001

54.2663293

Total power

2591.8311

2591.967

2591.9329

2593.325

2592.061197

Cost ($/h)

62456.7792

62456.6341

62456.6391

62455.5

62454.31191

Power mismatch (MW)

0

0.00021

−0.000187

0.00167

−1.04E−12

Loss (MW)

92.1011

91.9669

91.967

93.32333

92.06119713

Bold signifies the best results obtained by proposed algorihm 4

7.4

x 10

7.2

4

6.247 Total Fuel Cost($/hr)

CSO PSO

x 10

7 6.246

6.8 6.6

6.245 280 285 290 295

6.4 6.2 0

50

Fig. 6 Convergence plot for Case-3

100

150 200 Iteration number

250

300

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Table 6 The best power output for Case-4 (PD = 10, 500 MW) Power (MW)

BBO [15]

SOH-PSO [32]

PC_PSO [32]

NPSO [28]

PSO

CSO

P1

110.0465

110.8

113.98

113.9891

111.37885

113.79903

P2

111.5915

110.8

114.0

113.6334

113.48532

113.81137

P3

97.60

97.4

97.26

97.550

110.51186

98.719229

P4

179.905

179.73

179.51

180.0059

182.36409

179.86251

P5

88.30

87.8

89.38

97.00

89.002888

96.936037

P6

139.9992

140

105.2

140.00

140

140

P7

259.6313

259.6

259.55

300.00

298.21916

266.02799

P8

284.7316

284.6

286.9

300.00

286.73696

290.21665

P9

284.7801

284.6

284.7

284.5797

291.49465

288.62077

P10

130.2484

130

206.24

130.0517

130

130.13795

P11

168.8461

94

166.52

243.7131

95.317224

94.007245

P12

168.8239

94

94.00

169.0104

99.975249

94.011434

P13

214.7038

304.52

214.56

125.000

209.61324

215.25552

P14

304.5894

304.52

392.76

393.9662

398.02627

394.38589

P15

394.761

394.28

306.24

304.7586

286.44074

304.67406

P16

394.2409

398.28

394.88

304.5120

405.4247

394.28816

P17

489.2919

489.28

489.26

489.6024

494.73641

491.06724

P18

489.4188

489.28

489.82

489.6087

487.75272

489.37885

P19

511.2997

511.28

510.62

511.7903

522.01526

512.33481

P20

511.3073

511.27

511.68

511.2624

517.90305

512.00496

P21

523.417

523.28

523.52

523.3274

518.99485

523.51529

P22

523.2795

523.28

523.26

523.2169

529.05926

523.6869

P23

523.3795

523.28

523.98

523.4707

534.71695

523.80806

P24

523.3225

523.28

523.21

523.0661

548.12439

524.82521

P25

523.3661

523.28

523.54

523.3987

523.32243

523.27285

P26

523.4362

523.28

523.10

523.2897

532.30388

523.35059

P27

10.05316

10

10.00

10.0208

10

10.060826

P28

10.01135

10

10.00

10.0927

10.169263

10.093668

P29

10.00302

10

10.00

10.0621

11.697599

10.014031

P30

88.47754

97

89.05

88.9456

95.448942

96.920168

P31

189.9981

190

190.00

189.9951

170.96697

189.95474

P32

189.9881

190

190.00

190.00

179.05448

189.951

P33

189.9663

190

190.00

190.00

186.91018

189.96896

P34

164.8054

185.2

200.00

165.9825

177.86912

199.98874

P35

165.1267

164.8

164.78

172.4153

200

199.90519 (continued)

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Table 6 (continued) Power (MW)

BBO [15]

SOH-PSO [32]

PC_PSO [32]

NPSO [28]

PSO

CSO

P36

165.7695

200

172.89

191.2987

190.45884

199.9634

P37

109.9059

110

110.00

109.9893

104.82235

109.98084

P38

109.9971

110

110.00

109.9521

104.23392

110

P39

109.9695

110

94.24

109.8733

87.421127

109.99586

P40

511.2794

511.28

511.36

511.5671

514.0268

511.20401

Total power (MW)

10499.67

10504

10499.99

10500

10500

10500

Total fuel cost ($/h)

121426.953

121,501.14

121,767.89

121,704.7391

122,994.1

121,421.3667

Bold signifies the best results obtained by proposed algorihm Table 7 More comparisons of power output for Case-4 Methods

Best fuel cost ($/h)

Methods

Best fuel cost ($/h)

NPSO LRS [15]

121,664.431

HPSOM [25]

122,112.4

CDE [15]

121,741.979

PSO-SQP [26]

122,094.67

SPSO [15]

122,049.66

Improved GA [27]

121,915.93

EP_SQP [15]

122,324

HPSOWM [25]

121,915.3

HSS [23]

121,415.59

IGAMU [5]

121,819.25

HGPSO [25]

124,797.13

HDE [29]

121,813.26

SPSO [25]

124,350.4

DEC(2)-SQP(1) [30]

121,741.97

PSO [26]

123,930.45

PSO [31]

121,735.47

CEP [2]

123,488.29

APSO(1) [31]

121,704.73

HGAPSO [25]

122,780

ST-HDE [29]

121,698.51

IFEP [2]

122,679.71

NPSO-LRS [28]

121,644.43

MFEP [2]

122,647.57

APSO(2) [31]

121,633.52

IFEP [2]

122,624.35

SOPHO [32]

121,501.14

TM [4]

122,477.78

BF [33]

121,423.63

EP-SQP [26]

122,323.97

GA-PS-SQP [34]

121,458.00

MPSO [27]

122,252.26

PS [6]

121,415.14

ESO [3]

122,122.16

FA [7]

121,415.05

CSO Bold signifies the best results obtained by proposed algorihm

121,421.3667

A Maiden Application of Competitive Swarm Optimizer …

321

5

Total Fuel Cost($/hr)

1.45

x 10

CSO PSO

1.4 1.35 1.3 1.25 1.2

0

50

100

200 150 Iteration number

250

300

Fig. 7 Convergence plot for Case-4

Table 8 Comparisons of power output with CSO for Case-5 Methods

ORCCRO [36]

SAB [8]

SAF[8]

SA [34]

BBO [37]

DE-BBO [37]

Cost($/h) 198,016.32 206,912.90 207,380.5164 198,352.6413 198,241.166 198,231.06 CSO

197,988.180

Bold signifies the best results obtained by proposed algorihm

in Ref. [6, 7]. In this chapter, the result of Case-1 is compared with 15 different methods, Case-2 with 22, Case 3 with 4, Case-4 with 39 and Case 5 with 7 different methods. These comparisons reflect the competency of proposed algorithm among several reported literature. 1. Computational Efficiency Figures 4 and 5 show the convergence plot for two different cases of the 6-generator system. A careful review of Fig. 4 reveals that the solution obtained from both PSO and CSO converges before 100th iteration but the rate of convergence is faster in case of CSO (add function evaluation). A similar observation of Fig. 5 reveals that CSO converges around 50th iteration whereas, PSO take more than 200 iteration to converge for Case 2. For same case and under same environment when BBO [15] is utilized to solve the problem and it take around 75 iteration to converge. Further, it is observed that the convergence of CSO is achieved at 65th iteration for Case 3, 200th iteration for Case 4, 210th iteration for Case 5 and these are shown in Figs. 6, 7 and 8 respectively. For same case studies PSO takes more number of iteration to converge. Since in both the algorithms, particular solution vector is used only for one time to evaluate the objective function, the number of function evaluation is less in case of CSO as it takes less number of iteration to converge for almost all the case studies. From this comparison, it can be noted that the overall convergence pf CSO is faster than that of PSO. Moreover, the power balance constraint (3) is successfully obeyed

CSO

2.40073469

2.40003197

2.4

2.40006655

2.40315153

4.00032021

4.00044324

4.00058703

4.00105868

65.3139226

62.0768168

35.2110504

56.1899226

25.0026151

25

25.0046779

154.999545

154.991082

154.989349

155

68.9012365

Power (MW)

P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

P20

P21

69.08264

151.9543

154.8596

153.0542

152.8509

25.18447

25

25.82534

55.53762

38.97323

74.49859

67.95182

4.005403

4

4

4.231932

2.685222

3.068884

2.737149

2.870959

2.781392

PSO

P59

P58

P57

P56

P55

P54

P53

P52

P51

P50

P49

P48

P47

P46

P45

P44

P43

P42

P41

P40

P39

Power (MW)

Table 9 The best power output for Case-5 (PD = 15000 MW)

35.05711274

35

25.28971393

25.22243913

12.00288272

12

12.00001165

12

8.407885171

8.400624293

8.401628387

5.402144793

5.4

615.3259225

659.9980394

559.9999033

439.9932081

219.9918054

157.2669477

119.9814278

99.9609703

CSO

8.493534

5.660307

5.747935

648.3668

659.1504

560

439.6734

220

150.7146

99.89684

95.83204

68.96741

39.60538

399.4971

357.3089

249.4786

67.96668

16.85574

10

97.57302

197.8212

PSO

P97

P96

P95

P94

P93

P92

P91

P90

P89

P88

P87

P86

P85

P84

P83

P82

P81

P80

P79

P78

P77

Power (MW)

3.60159299

471.177800

599.997984

499.999074

439.996698

96.5750183

58.7455143

90.0093397

80.9928305

23.2920739

14.3058257

439.970754

324.643489

199.914729

20.1860774

12.0907395

10.006047

98.7389374

177.483030

295.655587

160

CSO

(continued)

19.5831

435.4703

306.9351

178.6619

35.97499

19.40319

10.14162

103.1974

179.6167

254.0721

193.7955

49.48314

86.72593

215.7613

123.2381

399.6877

397.7135

354.0712

70.54292

70.27866

70.59804

PSO

322 A. Rajan et al.

68.900639

68.9012918

349.999521

399.999828

399.995903

499.945013

499.984282

199.963532

100

10.0001810

19.9831564

79.6774741

249.994809

360

399.9902111

39.96079805

69.97188751

P22

P23

P24

P25

P26

P27

P28

P29

P30

P31

P32

P33

P34

P35

P36

P37

P38

67.95182

4.005403

4

4

4.231932

2.685222

3.068884

2.737149

2.870959

2.781392

495.1268

498.2693

399.4566

399.0748

349.6879

68.96545

69.36773

PSO

Power (MW)

P76

P75

P74

P73

P72

P71

P70

P69

P68

P67

P66

P65

P64

P63

P62

P61

P60

Bold signifies the best results obtained by proposed algorihm

CSO

Power (MW)

Table 9 (continued)

49.99370805

89.98631395

192.553554

107.5682357

399.9977474

399.999238

359.9758187

70.00317104

70.00144983

70.0032493

185

184.9853611

184.9856646

184.9836796

45.00796659

45.00223502

45.01536864

CSO

174.15

175.523

182.2331

176.8291

45

45.62826

45.96783

39.30037

38.37633

26.31228

36.92601

12.30361

12.11103

12.14571

12

9.328258

8.4

PSO

Power mismatch (MW)

Cost ($/h)

Total power

P110

P109

P108

P107

P106

P105

P104

P103

P102

P101

P100

P99

P98

Power (MW)

0

197988.180

15000 (MW)

20.0014901

40.0013067

30.0003230

50.0009765

40.0008297

40.0000180

20.0047089

20.0014664

10.0051893

10.06963

4.40357907

4.40564884

3.60111335

CSO

0

198310.4

15000(MW)

4.855584

4.558639

3.727217

3.982409

487.6517

596.5566

498.7918

439.403

88.16604

62.58101

93.84453

63.53641

33.17576

PSO

A Maiden Application of Competitive Swarm Optimizer … 323

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2.4

x 10

CSO PSO

Total Fuel Cost($/hr)

2.3 5

1.985

2.2 2.1

1.98 360 380 400

2 1.9 0

x 10

50

100

150

200

250

300

350

400

Iteration number

Fig. 8 Convergence plot for Case-5

by CSO in all case studies and almost appears to be zero or very close to zero. These observations indicate the superiority of CSO over PSO other reported methods as well. 2. Statistical Analysis As stated in the above section, 50 trial runs are taken for each case study to confirm the best near global optimum solutions. Since randomization is the inherent property of these approaches, the optimum results for every trial run may be different. Thus, it becomes essential to perform the experiment number of times before claiming the solution to be optimum. Average cost and standard deviations for Cases 1, 2, 3, 4 and 5 are shown in Table 10. It is observed from Table 10 that for Case 1, the average cost ($ 924.90) is found to be very close to the best cost ($ 924.8937). Similarly, for Cases 2 and 3, not only the best costs, but even the average costs obtained by CSO are much better than BBO and other methods reported in [15]. For 40-generating units (Case-4), though CSO fails to achieve the best cost (reported in [6, 7, 23]) but; its average cost is found much better than that reported by BBO and other methods [15]. Simulation of 110 units (Case 5) also provides convincing results. The best cost Table 10 Statistical analysis (50 trial runs) Case-1 Case-2 Case-3 Case-4 Case-5

CSO PSO CSO PSO CSO PSO CSO PSO CSO PSO

Best cost ($/h) 924.8937 925.758 15442.73 15442.75 62454.311 62455.5 121421.366 122994.1 197988.180 198310.4

Mean cost ($/h) 925.01506 925.90384 15442.741 15442.98 62454.56 62456.01 121421.38 122994.4873 197988.4402 198310.674

Bold signifies the best results obtained by proposed algorihm

Worst cost ($/h) 925.32 926.21 15442.75 15443.25 62455.01 62457.15 121421.9 122995.2 197989.01 198311.01

Std. dev. 0.14035 0.16243 0.0087 0.0132 0.0125 0.0313 0.151844 0.44104 0.313573805 0.259022808

Success rate 38/50 35/50 41/50 36/50 41/50 29/50 36/50 32/50 43/50 28/50

A Maiden Application of Competitive Swarm Optimizer …

325

($ 197,988.1803) reported by CSO is found better than that reported recently by DEBBO ($ 198,231.06) and other methods [37]. The success rates out of 50 trials are also reported in Table 10. High success rates and corresponding less standard deviation indicates its ability to reach the global optimal solution consistently. Less deviation of the best results from its mean value also informs about its high robustness and ability to solve constrained ELD problems of much higher dimensions. The convincing results of CSO in solving ELD problems, provide some motivation for applying CSO theory in solving other power system problems in future.

6 Parametric Study of CSO Similar to other swarm based optimization techniques, CSO has also been developed in such a manner so that it could maintain the balance between exploration and exploitation. Exploration process is required at the beginning of the algorithm to search the global optimal solution and its location in the entire search space. Exploitation hunts for the improvement of the solution in the particular location in search space. Therefore, managing these processes in a complete cycle of algorithm need lot of mathematical exercise. Authors of CSO have introduced a controlling parameter called phi (ϕ) which controls the influence of mean position value X(t), and the variation in the population size [66]. In algorithmic term, this factor is known as social factor. As indicated in [66], for better solution, ϕ should be varied between −1 and 1. In order to investigate the effect of variation of ϕ on optimum solution of ELD problem, parametric sensitivity study is carried out for each case discussed in the previous section. For this purpose, ϕ is varied from −1 to 1 for different swarm size ‘m’. 50 independent trial runs are taken for every value of ϕ and ‘m’ to declare the optimum solution. Figures 9, 10, 11, and 12 show the variations in the best cost obtained at different swarm size and ϕ for Case-2, 3, 4, and 5 respectively. From Figs. 9, 10, 11, and 12 it can be seen that when the value of ϕ is zero and the swarm size is minimum, the optimized value of cost increases; whereas, for the same swarm size with ϕ ranging between −0.6 and −0.4, the best cost is around its minimum value. For more clarification, results of parametric studies of Cases 2–5 are also presented in Tables 11, 12, 13 and 14 respectively. The best values are indicated with bold letters. The observation from figures and tables indicate that the optimal results are obtained with ϕ values between −0.6 and −0.4. For example, it can be seen from Table 12 that the optimum cost obtained for Case 3 is $ 62,454.312 when ϕ is −0.4. Further, it is observed that the algorithm also proceeds for optimum point even when ϕ is zero. But, at this juncture, the algorithm demand for larger population size for the optimum solution as is evident from Tables 12, 13 and 14. For example, at ϕ = 0, the optimum cost obtained for Case 3, 4 and 5 are $ 62,454.801, $ 123,554 and $ 207,877.53 at swarm size of 300, 300 and 270 respectively. Case 2, being a smaller system of just 6 generating units, not much variation is recorded with the change in swarm size and ϕ which is evident from Table 11.

326

A. Rajan et al.

1.5444

x 10

4

Parametric plot for case-2 30

-------CSO

Population Sizes.

60

1.5444 Total Fuel Cost ( $/hr).

90 120

1.5444

150 1.5443

180 210

1.5443

240 270

1.5443

300

1.5443 1.5443 -1

-0.8

-0.6

-0.4

-0.2 0 0.2 0.4 Variable Parameter - PHI.

0.6

0.8

1

0.6

0.8

1

Fig. 9 Parametric plot for Case-2

6.252

x 10

4

Parametric study for case-3 Population Sizes.

30

6.251

60 90

Total Fuel Cost ( $/hr).

6.25

120 150

6.249

180 210

6.248

240 270

6.247

300

6.246 6.245 -1

-0.8

-0.6

-0.4

-0.2 0 0.2 Variable Parameter - PHI.

0.4

Fig. 10 Parametric plot for Case-3

After tuning and setting the proper value of ϕ (−0.6 to −0.4), optimum solution is obtained even with lesser number of swarm size; resulting the reduction of the search space. The best combination of ϕ and swarm size for obtaining optimal solution for all the cases is shown in appendix. From the graphical as well as tabular representation, it can be concluded that for the optimum solution, the best value of ϕ lies between −0.6 and −0.4. This observation is in close agreement with the original literature of

A Maiden Application of Competitive Swarm Optimizer … 5

1.34

327

Parametric study for case-4

x 10

30

Population Sizes.

60

1.32

90 120

Total Fuel Cost ( $/hr).

1.3

150 180

1.28

210 240

1.26

270 300

1.24 1.22 1.2 -1

-0.8

-0.6

-0.4

-0.2 0 0.2 Variable Parameter - PHI.

0.4

0.6

0.8

1

0.4

0.6

0.8

1

Fig. 11 Parametric plot for Case-4

2.25

x 10

5

Parametric study for case-5 30

Population Sizes.

60

2.2

Total Fuel Cost ( $/hr).

90 120

2.15

150 180

2.1

210 240

2.05

270 300

2

1.95 -1

-0.8

-0.6

-0.4

-0.2 0 0.2 Variable Parameter - PHI.

Fig. 12 Parametric plot for Case-5

CSO.The optimal settings of the parameters of proposed algorithm for all the cases are given in Appendix (Table 16).

62 −24083.59806

50

0

96

−29.275909

6.0539E−50

1.66088144

1.2108E−49

1.98498431

Hypothesized mean difference

df

t stat

P(T