Benchmarks and Hybrid Algorithms in Optimization and Applications (Springer Tracts in Nature-Inspired Computing) 9819939690, 9789819939695

Table of contents :
Preface
Contents
1 Nature-Inspired Algorithms in Optimization: Introduction, Hybridization, and Insights
1 Introduction
2 Optimization and Algorithms
2.1 Components of Optimization
2.2 Gradients and Optimization
3 Nature-Inspired Algorithms
3.1 Recent Nature-Inspired Algorithms
3.2 Other Nature-inspired Algorithms
4 Hybridization
4.1 Hybridization Schemes
4.2 Issues and Warnings
5 Insights and Recommendations
References
2 Ten New Benchmarks for Optimization
1 Introduction
2 Role of Benchmarks
3 New Benchmark Functions
3.1 Noisy Functions
3.2 Non-differentiable Functions
3.3 Functions with Isolated Domains
4 Benchmarks with Multiple Optimal Solutions
4.1 Function on a Hyperboloid
4.2 Non-smooth Multi-layered Functions
5 Parameter Estimation as Benchmarks
6 Integrals as Benchmarks
7 Benchmarks of Infinite Dimensions
7.1 Shortest Path Problem
7.2 Shape Optimization
8 Conclusions
References
3 Review of Parameter Tuning Methods for Nature-Inspired Algorithms
1 Introduction
2 Parameter Tuning
2.1 Schematic Representation of Parameter Tuning
2.2 Different Types of Optimality
2.3 Approaches to Parameter Tuning
3 Review of Parameter Tuning Methods
3.1 Generic Methods for Parameter Tuning
3.2 Online and Offline Tunings
3.3 Self-Parametrization and Fuzzy Methods
3.4 Machine Learning-Based Methods
4 Discussions and Recommendations
References
4 QOPTLib: A Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems
1 Introduction
2 Description of the Problems
2.1 Traveling Salesman Problem
2.2 Vehicle Routing Problem
2.3 Bin Packing Problem
2.4 Maximum Cut Problem
3 Introducing the Generated QOPTLib Benchmarks
4 Preliminary Experimentation
5 Conclusions and Further Work
References
5 Benchmarking for Discrete Cuckoo Search: Three Case Studies
1 Introduction
2 COPs Statements
2.1 Studied COPs
2.2 Formal Definitions
3 DCS Common Resolution
3.1 General Algorithm
3.2 Main Functions
4 Studied Case Resolutions
4.1 Solutions
4.2 Moves
5 Experimental Tests
5.1 Parameters
5.2 Instances
5.3 Statistic Tests
6 Conclusion
References
6 Metaheuristics for Feature Selection: A Comprehensive Comparison Using Opytimizer
1 Introduction
2 Literature Review
3 Hands-on Opytimizer: A Python Implementation for Metaheuristic Optimization
4 Case Study: Feature Selection
4.1 Methodology
4.2 Experiments
5 Conclusions
References
7 AL4SLEO: An Active Learning Solution for the Semantic Labelling of Earth Observation Satellite Images—Part 1
1 Introduction
2 State of the Art
3 Data Set Description
4 Active Learning
5 Semantic Labelling
6 Conclusions
References
8 AL4SLEO: An Active Learning Solution for the Semantic Labelling of Earth Observation Satellite Images—Part 2
1 Typical Examples
1.1 Semantic Multi-level Labelling
1.2 Semantic Multi-sensor Labelling
1.3 Semantic Multi-temporal Labelling
1.4 Conclusions
References
9 Deep Learning-Based Efficient Customer Segmentation for Online Retail Businesses
1 Introduction
2 Literature Review
3 Clustering Algorithms
3.1 K-Means Algorithm
3.2 K-Means++ algorithm
3.3 Evaluation Metrics
4 Dimensionality Reduction Algorithms
4.1 Principal Component Analysis (PCA)
4.2 AutoEncoders
5 Libraries
6 Proposed Approach
7 Conclusion
References
10 Optimization of Water Use in the Washing Process of Industrial Orange Juice Extractors for a Circular Economy Approach
1 Introduction
2 Methodology
2.1 Objective Function of this Research
3 Results
4 Discussion of Results
5 Conclusions
6 Future Research
References
11 Optimizing ROVs in Metaverse for Marine Oil Pipeline Maintenance Using Gorilla Troops Optimizer Algorithm
1 Introduction
2 Metaverse Environment Where the Project Is Implemented
3 Implementation of Gorillas Nature-Inspired Metaheuristics
4 GTO Algorithm with ROV System Datasets
5 Conclusions and Future Work
References
12 Parameter Identification of the Combined Battery Model Using Embedded PSO-GA
1 Introduction
2 Combined Battery Model
3 Evolutionary Method
3.1 Genetic Algorithm (GA)
3.2 Particle Swarm Optimization (PSO)
4 Embedded PSO-GA
5 Parameter Identification System
6 Results and Discussion
7 Conclusion
References
13 IoT Applied to Slowing the Effects on Pets Trapped in a Wildfire After a CONAGUA Alert Using an Intelligent Voice-Recognition Assistant
1 Introduction
2 Purpose
3 Theoretical Framework
3.1 IoT Definition
3.2 Wildfires
3.3 Principal Causes
3.4 Consequences and Conditions that Influence the Form and Speed at Which Fire Spreads
3.5 Related Research
4 How Are We Going to Retard the Fire
5 Methodology
5.1 Research Contribution
5.2 Novel Approach
6 System Assembly and Functionality
7 Components Needed to Assemble Our Intelligent Proposal
8 Results
8.1 Discussion of Results
9 Conclusion and Future Research
References

Citation preview

Springer Tracts in Nature-Inspired Computing

Xin-She Yang   Editor

Benchmarks and Hybrid Algorithms in Optimization and Applications

Springer Tracts in Nature-Inspired Computing Series Editors Xin-She Yang, School of Science and Technology, Middlesex University, London, UK Nilanjan Dey, Department of Information Technology, Techno India College of Technology, Kolkata, India Simon Fong, Faculty of Science and Technology, University of Macau, Macau, Macao

The book series is aimed at providing an exchange platform for researchers to summarize the latest research and developments related to nature-inspired computing in the most general sense. It includes analysis of nature-inspired algorithms and techniques, inspiration from natural and biological systems, computational mechanisms and models that imitate them in various fields, and the applications to solve real-world problems in different disciplines. The book series addresses the most recent innovations and developments in nature-inspired computation, algorithms, models and methods, implementation, tools, architectures, frameworks, structures, applications associated with bio-inspired methodologies and other relevant areas. The book series covers the topics and fields of Nature-Inspired Computing, Bio-inspired Methods, Swarm Intelligence, Computational Intelligence, Evolutionary Computation, Nature-Inspired Algorithms, Neural Computing, Data Mining, Artificial Intelligence, Machine Learning, Theoretical Foundations and Analysis, and Multi-Agent Systems. In addition, case studies, implementation of methods and algorithms as well as applications in a diverse range of areas such as Bioinformatics, Big Data, Computer Science, Signal and Image Processing, Computer Vision, Biomedical and Health Science, Business Planning, Vehicle Routing and others are also an important part of this book series. The series publishes monographs, edited volumes and selected proceedings.

Xin-She Yang Editor

Benchmarks and Hybrid Algorithms in Optimization and Applications

Editor Xin-She Yang Department of Design Engineering and Mathematics Middlesex University London, UK

ISSN 2524-552X ISSN 2524-5538 (electronic) Springer Tracts in Nature-Inspired Computing ISBN 978-981-99-3969-5 ISBN 978-981-99-3970-1 (eBook) https://doi.org/10.1007/978-981-99-3970-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 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

Benchmarking is an important part of validating new algorithms and techniques in optimization and applications. To test the performance of an algorithm and its variants, we must use it to solve various benchmark problems. There are many different benchmarks in the literature, though most of these benchmarks are smooth functions or modified forms of existing benchmark functions. Mathematically speaking, these functions are usually multimodal with multiple modes and possibly multiple optimal solutions. However, these functions are idealized benchmarks and they have almost nothing to do with problems in real-world applications. Ideally, test benchmarks for validating new algorithms and techniques should be diverse, with problems derived from different types of applications, such as linear programming, integer linear programming, engineering designs, aerospace engineering applications, machine learning problems and even business applications as well as industrial applications. However, this kind of multidisciplinary benchmarking is very difficult in practice because researchers tend to work in one main area of research or applications. In addition, the implementation of benchmarks and interpretations of results all require specialized knowledge and programming, which again makes it difficult to have multidisciplinary benchmarks. Furthermore, simple smooth function benchmarks usually have known optimality or solutions that can be verified mathematically or theoretically, whereas realistic benchmark problems do not have simple solutions. In fact, optimality is usually not known for most of realistic benchmarks. Thus, it is understandable that the types of benchmarks for optimization are quite limited. Furthermore, benchmarking itself is a time-consuming process because the evaluations of the objective functions are usually time-consuming, especially for applications in engineering, biology, machine learning and big data science. An important development in optimization is the recent progress in nature-inspired computing. Many optimization algorithms and techniques nowadays are natureinspired, swarm intelligence-based algorithms. These algorithms are flexible, sufficiently efficient and yet simple enough to implement. However, the testing of such algorithms has been mainly using smooth functions, which can only show one side of the performance of such algorithms. To truly validate such algorithms, they need

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to be able to solve real-world problems. There are some studies using realistic benchmarks, such as pressure vessel design, compression spring design, parameter estimation, inverse problems, beam designs and other structural design problems. However, these problems tend to be small scale with a few design variables up to a few dozen variables. Therefore, one of the tasks in this book is to summarize some of the latest case studies and applications, which can be used as benchmarks for future research. In addition, we also provide ten new benchmarks with more diverse properties, such as non-differentiability, noise, parameter estimation and benchmarks of infinite dimensions. Another important development in nature-inspired computing is hybrid algorithms. Recent studies seem to indicate that hybridization can provide a good way for algorithm design and applications. The intention of hybridization is to draw the good features of different algorithms to form a new hybrid or a variant so that it may be more efficient than each individual algorithm. Some studies show that good hybridization can be achieved, though it is not clear how. Algorithm components and structure are important, but it is difficult to see what structure and components should be selected to make a hybrid effective. Therefore, another aim of this book is to summarize the main ideas of hybridization, and then show how hybrid algorithms may be used for different applications. Topics covered in this book are diverse, including the review of hybrid algorithms, new benchmarks, parameter tuning, quantum computing, parameter identification, feature selection and deep learning. Applications are also very diverse, ranging from travelling sales problems, scheduling and vehicle routing to semantic labelling of satellite images, and from online retailing, oil pipeline maintenance optimization and Internet of Things to the optimization of water usage. Therefore, this book can act as a useful reference for graduates, researchers and lecturers in nature-inspired computing, computer science, engineering, machine learning, artificial intelligence, water engineering and environmental science as well as industrial case studies. London, UK May 2023

Xin-She Yang

Contents

1

Nature-Inspired Algorithms in Optimization: Introduction, Hybridization, and Insights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xin-She Yang

1

2

Ten New Benchmarks for Optimization . . . . . . . . . . . . . . . . . . . . . . . . . Xin-She Yang

3

Review of Parameter Tuning Methods for Nature-Inspired Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geethu Joy, Christian Huyck, and Xin-She Yang

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QOPTLib: A Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems . . . . . . . . . . . . . . . . . . . . . . . Eneko Osaba and Esther Villar-Rodriguez

49

Benchmarking for Discrete Cuckoo Search: Three Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aziz Ouaarab

65

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5

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Metaheuristics for Feature Selection: A Comprehensive Comparison Using Opytimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Douglas Rodrigues, Leandro Aparecido Passos, Luiz Fernando Merli de Oliveira Sementille, Mateus Roder, Gustavo Henrique de Rosa, and João Paulo Papa

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AL4SLEO: An Active Learning Solution for the Semantic Labelling of Earth Observation Satellite Images—Part 1 . . . . . . . . . . 105 Corneliu Octavian Dumitru, Gottfried Schwarz, and Mihai Datcu

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AL4SLEO: An Active Learning Solution for the Semantic Labelling of Earth Observation Satellite Images—Part 2 . . . . . . . . . . 119 Corneliu Octavian Dumitru, Gottfried Schwarz, and Mihai Datcu

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Contents

Deep Learning-Based Efficient Customer Segmentation for Online Retail Businesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Jayesh Soni, Nagarajan Prabakar, and Himanshu Upadhyay

10 Optimization of Water Use in the Washing Process of Industrial Orange Juice Extractors for a Circular Economy Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Amaury Nabor-Lagunes, Alberto Ochoa-Zezzatti, and Luis Sandoval 11 Optimizing ROVs in Metaverse for Marine Oil Pipeline Maintenance Using Gorilla Troops Optimizer Algorithm . . . . . . . . . . 191 Irving Azuara, Roberto Contreras-Masse, Alberto Ochoa-Zezzatti, and Lucia Sada-Elizondo 12 Parameter Identification of the Combined Battery Model Using Embedded PSO-GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Elmahdi Fadlaoui and Noureddine Masaif 13 IoT Applied to Slowing the Effects on Pets Trapped in a Wildfire After a CONAGUA Alert Using an Intelligent Voice-Recognition Assistant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Rubén Moreno, Fernanda Romero, Alberto Ochoa-Zezzatti, Luis Vidal, and Elías Carrum

Chapter 1

Nature-Inspired Algorithms in Optimization: Introduction, Hybridization, and Insights Xin-She Yang

1 Introduction Nature-inspired algorithms and their various hybrid variants have become popular in recent years for solving optimization problems, due to their flexibility and stable performance. In many applications related to science and engineering, problems can often be formulated as optimization problems with design objectives, subject to various constraints. A typical optimization problem consists of one objective, subject to various inequality and inequality constraints. The objectives can be the main goal to be optimized, such as the minimization of cost, energy consumption, travel distance, travel time, CO2 emission, wastage, and environmental impact, or the maximization of efficiency, accuracy, and performance as well as sustainability. Almost all design problems have design constraints or requirements. Constraints can be design requirements, such as physical dimensions, capacity, budget, design codes/regulation, time, and other quantities such as stress and strain requirements. They are often written as mathematical inequalities or equalities. Due to the nonlinear nature of such optimization problems, sophisticated optimization algorithms and techniques are required to solve them. In the current literature, there are many optimization techniques and algorithms for solving optimization problems. In the last few decades, gradient-free nature-inspired algorithms have received a lot of attention with significant developments. One class of such nature-inspired algorithms is based on swarm intelligence [1–4]. The literature of nature-inspired algorithms and swarm intelligence is expanding rapidly; here, we will introduce some of the most recent and widely used nature-inspired optimization algorithms.

X.-S. Yang (B) School of Science and Technology, Middlesex University London, The Burroughs, London NW4 4BT, United Kingdom e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_1

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2 Optimization and Algorithms Before we introduce some nature-inspired algorithms in detail, let us discuss briefly the four key components of optimization and their related issues.

2.1 Components of Optimization Once an optimization problem has been formulated properly with the right objective and the correct constraints, the next step will be to find the optimal solutions using an efficient algorithm or optimization technique. In general, to solve an optimization problem involves four main components: The choice of algorithm, handling the constraints, evaluation of the objective function, and making sense of the solutions (Fig. 1). • Choice of algorithms: To solve any optimization problem, an efficient algorithm, or a sufficiently good algorithm, should be selected. In many cases, the choice may not be easy, because either there are many different algorithms to choose from or there may not be any efficient algorithms at all. In many cases, the choice of the algorithm may depend on the type of problem, the expertise of the user, the availability of the computational resource, the time constraint, the quality of the desired solutions, and other factors.

Fig. 1 Important components of optimization

1 Nature-Inspired Algorithms in Optimization …

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• Handling the constraints: Even if an efficient algorithm is used for solving an optimization problem, the handling of constraints is an important part of problem solving. Otherwise, the solutions obtained may not satisfy all the constraints, leading to infeasible solutions. There are many constraint-handling techniques, such as the penalty method, dynamic penalty, evolutionary method, epsilon-constraint method, and others. A good choice of proper constraint-handling techniques will help to ensure the solution quality. • Evaluation of the objective: Depending on the type of optimization problems, the evaluation of the objective functions can be a very time-consuming part. For function optimization, such evaluations are straightforward. However, for many design problems such as protein folding and aerodynamic design problems, each evaluation of such objective values can take hours or even days due to the extensive use of external simulators or software packages. In any good optimization procedure, the number of objective evaluations should be minimized so as to save time and cost. • Make sense of the solutions: Once a feasible set of solutions are obtained, users or designers have to make sense of the solutions by checking if all constraints are satisfied, understanding what these solutions may imply, figuring out the stability and robustness of the solutions, and then deciding which solution(s) to use for the design and further refinement. For single-objective optimization problems, this may not cause any issues in selecting an optimal solution. However, for multiobjective optimization problems, multiple options from the Pareto front will be available, the choice may require some higher-level criteria or decision-makers to make the final choice, by considering other factors that may not be implemented in the optimization problems. Due to the complexity of real-world optimization problems, it is usually challenging to obtain satisfactory results, while maintaining all the relevant interacting components to be suitable for solving the optimization problem under consideration. For the rest of this chapter, we will focus on algorithms.

2.2 Gradients and Optimization Traditional optimization techniques, such as Newton-Raphson-based methods, use first-order derivatives or gradients to guide the search. From a mathematical perspective, if the objective is sufficiently smooth, the optimal solutions should occur at critical points where f  (x) = 0 or at the boundaries. In this case, gradients provide the key information needed for finding the locations of the possible optima. Even for smooth objectives without any constraints, it can become complicated when f (x) is highly nonlinear with multiple optima. One well-known example is to find the maximum value of f (x) = sinc(x) = sin(x)/x in the real domain. If we can naively use

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f  (x) =

 sin(x)  x

=

x cos(x) − sin(x) = 0, x2

(1)

we have an infinite number of solutions for x = 0. There is no simple formula for these solutions; thus, a numerical method has to be used to calculate these solutions. Even with all the efforts to find these solutions (it may not be easy in practice), we have to be careful because the true global maximum f max = 1 occurs at x∗ = 0. This highlights the potential difficulty for nonlinear, multimodal problems with multiple optima. Obviously, the requirement for smoothness may not be satisfied at all. For example, if we try to find the optimal solution by using f  (x) = 0 for f (x) = |x| exp[− sin(x 2 )],

(2)

we will not be able to use this condition because f (x) is not differentiable at x = 0, but the global minimum f min = 0 indeed occurs at x∗ = 0. This also highlights an issue that optimization techniques that require the calculation of derivatives will not work for non-smooth objective functions. High-dimensional problems can become more challenging. For example, the nonlinear function [2] f (x) =

n  

n n        sin2 (xi ) − exp − xi2 · exp − sin2 |xi | ,

i=1

i=1

(3)

i=1

where −10 ≤ xi ≤ 10 (for i = 1, 2, ..., n), has the global minimum f min = −1 at x ∗ = (0, 0, ..., 0), but this function is not differentiable at the optimal point x ∗ . Therefore, in order to solve different types of optimization problems, we have to have a variety of optimization techniques so that they can use gradient information when appropriate and do not use it when it is not well defined or not easily calculated. In addition, constraints, especially nonlinear constraints, tend to make the search domain irregular and even potentially with isolated regions. This will make such problems more challenging to solve. To complicate things further, we may have several objective functions instead of just one function for some design problems, and multiple Pareto-optimal solutions are sought. This will in turn make it more challenging to solve.

3 Nature-Inspired Algorithms A diverse range of nature-inspired algorithms and their applications can be found in the recent literature [2, 5–7]. Now we will briefly introduce some of the most recent nature-inspired algorithms.

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3.1 Recent Nature-Inspired Algorithms Our intention here is not to list all the algorithms, which is not possible. Instead, we would like to use a few algorithms as examples to highlight the main components and mechanisms that can be used to carry out effective optimization in the solution or search space.

3.1.1

Particle Swarm Optimization

Particle swarm optimization (PSO), developed by Kennedy and Eberhart in 1995, intends to simulate the swarming characteristics of birds and fish [1]. For the simplicity of discussions, we now use the following notations: x i and v i denote the position (solution) and velocity, respectively, of a particle or agent i, for a population of n particles, thus we have i = 1, 2, ..., n. Both the position of a particle i and its velocity are iteratively updated by v it+1 = v it + α 1 [g ∗ − x it ] + β 2 [x i∗ − x it ],

(4)

x it+1 = x it + v it+1 ,

(5)

where  1 and  2 are two uniformly distributed random numbers in [0,1]. The parameters α and β are usually in the range of [0,2]. Here, g ∗ is the best solution found so far by all the particles in the population, often considered as some sort of center of the swarm (not the actual geometrical center). In addition, each individual particle has its own individual best solution x i∗ during its iteration history. There are thousands of articles about PSO with a diverse range of applications [1, 8]. However, there are some drawbacks because PSO can often have so-called premature convergence when the population loses diversity and thus gets stuck locally. Various improvements and modifications have been developed in recent years with more than two dozen different variants. Their performance varies with different degrees of improvements. One simple and yet quite efficient variant is the accelerated particle swarm optimization (APSO), developed by Xin-She Yang in 2008 [9]. APSO does not use velocity, but only uses the position or solution vector, which is updated in a single step (6) x it+1 = (1 − β)x it + β g ∗ + α t , where α is a scaling factor that controls the randomness. The typical values for this accelerated PSO are α ≈ 0.1 ∼ 0.4 and β ≈ 0.1 ∼ 0.7. Here,  t is a vector of random numbers, drawn from a normal distribution. In order to reduce the randomness as the iterations continue, a further modification and improvement to the accelerated PSO is to use a monotonically decreasing function such as

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α = α0 γ t , (0 < γ < 1),

(7)

where t is a pseudo-time or iteration counter. The initial value of α0 = 1 can be used for most cases.

3.1.2

Bat Algorithm

Based on the echolocation characteristics of microbats, the bat algorithm (BA), developed by Xin-She Yang in 2010, uses some frequency-tuning f and variations of pulse emission rate r and loudness A [10, 11] to update the position vectors in the search space. For bat i with position x i and velocity v i , the updates are carried out by f i = f min + ( f max − f min )β,

(8)

v it = v it−1 + (x it−1 − x ∗ ) f i ,

(9)

x it = x it−1 + v it ,

(10)

where β ∈ [0, 1] is a random vector drawn from a uniform distribution so that the frequency can vary from f min to f max . In the above equations, x ∗ is the best solution found so far by all the virtual bats up to the current iteration t. In the BA, the effective control of exploration and exploitation is achieved by varying loudness A(t) from a high value to a lower value and simultaneously varying the emission rate r from a lower value to a higher value. Mathematically speaking, the variations take the form of Ait+1 = α Ait , rit+1 = ri0 (1 − e−γ t ), 0 < α < 1, γ > 0.

(11)

Numerical simulation shows that BA can have a faster convergence rate in comparison with PSO. Various studies have extended the BA to solve multi-objective optimization with various variants versions and applications [11–16]. A recent study also proved its global convergence [17].

3.1.3

Firefly Algorithm

The firefly algorithm (BA) was developed by Xin-She Yang developed in 2008 [9, 18], inspired by the light-flashing behavior of tropical fireflies. FA uses the position vector x i for firefly i and its brightness to associate with the fitness or landscape of the objective. The solution or position is then updated iteratively by x it+1 = x it + β0 e−γ ri j (x tj − x it ) + α  it , 2

(12)

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where β0 is the attractiveness parameter, and α is a scaling factor controlling the step sizes. Parameter γ can be considered as a tunable parameter to control the visibility of the fireflies (and thus search modes). Here, ri j represents the distance between firefly i at x i and firefly j at x j . During each iteration, a pair comparison is carried out for evaluating the relative fitness among all fireflies. Briefly speaking, all the main steps of FA can be outlined as the pseudocode in Algorithm 1.

Algorithm 1: Firefly algorithm. 1 2 3 4 5 6 7 8 9 10 11 12

Initialize all the parameters α, β, γ , and population size n; Determine the light intensity/fitness at x i by f (x i ); while t < MaxGeneration do for All fireflies (i = 1 : n) do for All other fireflies ( j = 1 : n) with i = j (inner loop) do if Firefly j is better/brighter than i then Move firefly i towards j using Eq.(12); Evaluate each new solution; Accept the new solution if better; Rank and update the best solution found; Update iteration counter t ← t + 1; Reduce α (randomness strength) by a factor 0 < δ < 1;

The role of α is subtle, controlling the strength of the randomness or perturbation term in the FA. In principle, randomness should be gradually reduced so as to speed up the overall convergence. For example, we can use α = α0 δ t ,

(13)

where α0 is the initial value and 0 < δ < 1 is a reduction factor. Parametric studies show that δ = 0.9 to 0.99 can be used in most cases. By analyzing the characteristics of different algorithms, we can highlight some significant differences between FA and PSO. Mathematically speaking, FA is a nonlinear system, whereas PSO is a linear system. Numerical experiments have shown that FA has an ability of multi-swarming, but PSO cannot. In addition, PSO uses velocities and thus has some drawbacks. In contrast, FA does not use any velocities. Most importantly, nonlinearity in FA enriches the search behavior and thus makes it more effective in dealing with multimodal optimization problems [2, 5, 19–21]. A simple MATLAB code of the standard firefly algorithm can be found at the Mathworks website.1

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http://www.mathworks.co.uk/matlabcentral/fileexchange/29693-firefly-algorithm.

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3.1.4

X.-S. Yang

Cuckoo Search

Cuckoo search (CS) algorithm is another nature-inspired optimization algorithm. CS was developed by Xin-She Yang and Suash Deb in 2009 [5, 22, 23], inspired by the brood parasitism of some cuckoo species and interactions between cuckoo-host species. The position vectors in the CS are updated iteratively in two different ways: local search and global search with a switch probability pa . The local search is carried out by (14) x it+1 = x it + αs ⊗ H ( pa − ε) ⊗ (x tj − x tk ), where s is the step size, and x tj and x tk are two different solutions that are randomly selected by random permutation. Here, the Heaviside function H (u) is controlled by the switch probability pa and a random number , drawn from a uniform distribution. The global search is carried out via Lévy flights by x it+1 = x it + αL(s, λ),

(15)

where the step size s is drawn from a Lévy distribution that can be approximated by a power-law distribution with a long tail L(s, λ) ∼

λΓ (λ) sin(π λ/2) 1 , (s  0). π s 1+λ

(16)

Here α > 0 is the step size scaling factor. Various studies have shown that CS can be very efficient in finding global optimality in many applications [2, 23].

3.1.5

Flower Pollination Algorithm

Though the flower pollination algorithm (FPA), developed by Xin-She Yang and his collaborators, is not a swarm intelligence-based algorithm, it is a populationbased, nature-inspired algorithm. FPA was developed, inspired by the pollination characteristics of flowering plants [2, 24], mimicking the characteristics of biotic and abiotic pollination as well as co-evolutionary flower constancy. The update of the solution vectors is realized by both local and global pollination characteristics search. They are x it+1 = x it + γ L(λ)(g ∗ − x it ),

(17)

x it+1 = x it + U (x tj − x tk ),

(18)

where g ∗ is the best solution vector found so far. Here, γ is a scaling parameter, L(λ) is a vector of random numbers, drawn from a Lévy distribution governed by the

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exponent λ, in the same form given in (16). In addition, U is a uniformly distributed random number. FPA has been applied to solve many optimization problems such as multi-objective optimization, photovoltaic parameter estimation, economic and emission dispatch, and EEG-based identification [24–29]. A demo MATLAB code of the basic flower pollination algorithm can be downloaded from the Mathworks website.2

3.2 Other Nature-inspired Algorithms In recent years, many other algorithms have appeared. An incomplete survey suggests that more than 200 nature-inspired algorithms and variants have been published in the recent literature [2, 21, 26, 29, 30]. Obviously, it is not possible to list all the variants and algorithms. For simplicity and for the purpose of diversity, we now list a selection of swarm intelligence (SI)-based algorithms and other metaheuristic algorithms. Examples of other swarm intelligence-based algorithms are as follows: • • • • • • • • • • • • •

Ant colony optimization [31] Artificial bee colony [32, 33] Bees algorithm [34, 35] Dolphin echolocation [36] Eagle strategy [37] Egyptian vulture [38] Emperor penguins colony [39] Fish swarm/school [40] Great salmon run [41] Harris hawks optimization [42] Killer whale algorithm [43] Krill herd algorithm [44] Monkey search [45]

Nature-inspired algorithms have also been developed by drawing inspiration from non-swarm behavior, physics, chemistry, and other biological systems. Examples of such algorithms are as follows: • • • • • • • • 2

Bacterial foraging algorithm [46] Big bang-big crunch [47] Biogeography-based optimization [48] Black hole algorithm [49] Charged system search [50]) Ecology-inspired evolutionary algorithm [51] Gravitational search [52] Water cycle algorithm [53] http://www.mathworks.co.uk/matlabcentral/fileexchange/45112.

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It is worth pointing out that some of these algorithms may perform well and provide very competitive results, but other algorithms are not so efficient. The current literature and various studies seem to indicate that their performance and results are quite mixed.

4 Hybridization There are many hybrid algorithms and variants in the current literature. A systematical analysis requires some substantial effort and time to go through all the algorithms and understand their components. However, it is not our intention to do such a complete analysis. Our emphasis here is to outline some of the hybridization schemes that may be relevant to most existing hybrid algorithms and their variants. Loosely speaking, to create a new hybrid algorithm, researchers tend to draw the good or efficient components from different algorithms. Imagine that there are two algorithms (A and B) that are reasonably effective, if you want to design a new hybrid algorithm, you may use some components from Algorithm A and some components from Algorithm B to form a new algorithm. However, you have to decide how to put them together nicely, which requires a good structure. In addition, you may also want to use other components such as initialization and randomization from other algorithms and techniques. We can represent this schematically in Fig. 2. Obviously, there are different ways to analyze and classify the hybrid algorithms. One of such studies is to look at their purpose and different stages of hybridization by

Fig. 2 Steps to create a new hybrid algorithm

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Ting et al. [54]. Based on this study, we can now extend it further and schematically summarize hybrid algorithms into four broad schemes.

4.1 Hybridization Schemes It is not an easy task to summarize all the relevant steps and the actual process for creating a new hybrid algorithm. However, it is possible to give some indications of the potential components and their link structure. For simplicity and ease of discussion, we now use three different algorithms, namely Algorithm A, Algorithm B, and Algorithm C and others.

4.1.1

Sequential Hybrid

One simple way of designing hybrid algorithms is to use a sequential structure (see Fig. 3). For a given population of n solutions, Algorithm A is run first, then the results are fed into Algorithm B. If needed, another algorithm (say, Algorithm C) is used further. In practice, both algorithms will be executed iteratively and the final results are processed together. One additional variation is that the population of n solutions can be split into two or more groups so that each subpopulation is updated by each algorithm. From the numerical simulation and various studies, it seems that this simple structure may be quite popular, but it may not be the best way for hybridization because the solutions are not fully mixed, thus limiting the overall effectiveness of the hybrid algorithm.

4.1.2

Parallel Hybrid

Another simple structure for hybridization is to put two or more algorithms in parallel (see Fig. 4). There is often a switch condition, often using a random number, to decide which algorithm to run during each iteration. Another equally popular way is to split the population into subpopulations and then feed each subpopulation into each algorithm for further iterations. Then, the overall population can be assembled together so as to sort out the best solutions.

Fig. 3 Sequential structure of hybridization

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Fig. 4 Parallel structure of hybridization

Similar to the sequential structure, this structure is also simple and quite popular. However, the solutions may not be fully mixed, thus limiting the diversity of the solutions and consequentially the overall effectiveness of the hybrid.

4.1.3

Full Hybrid

In addition to the above simple structures, a more effective way for hybridization is to fully hybridize all the components. In this case, different components from different algorithms are assembled together in the ways like chromosomes as multiple-site crossover. All the components work closely in the whole population, which can often lead to a more effective form of hybridization. However, the details of each hybridized algorithm may have its own structure, and there is no universal way to achieve a good hybrid. Care should be taken, because there is no guarantee for any success in the hybridization if all the good components are simply being put together. A pile of good materials does not automatically give a beautiful building; a good architect and multiple engineers are needed to finish the building. Similarly, multiple components of different algorithms do not lead to a good hybrid algorithm. Careful design and extensive numerical tests are required to make it a potentially useful algorithm.

4.1.4

Mixed Hybrid

After analyzing various algorithms and their hybrid variants, it seems that many hybrid algorithms have a mixed structure. They can mix the sequential, parallel, and full structures into a single algorithm, or they can use some part or aspect of these structures to build a hybrid algorithm. The overall effectiveness of hybrid algorithms can be quite mixed. Some algorithms have some significant improvements and some can only make it work marginally. Indeed, this is still an open question: How to design a hybrid algorithm effectively? Further research is highly needed in this area.

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4.2 Issues and Warnings Despite the extensive research and various studies concerning hybrid algorithms, there are many serious issues that researchers should be aware of. For example, it seems that some variants appeared to be some random combination of some existing algorithms without any careful thinking, and the performance of some hybrid algorithms may be doubtful. In the previous writing, we warned of the danger of random combinations for hybridization [54]. Now we highlight this serious issue again here. Suppose there are n algorithms, if you randomly choose 2 ≤ k ≤ n algorithms or their components to form (randomly) a so-called new hybrid, then there are Cnk =

n! , k!(n − k)!

(19)

possible combinations. For n = 30 and k = 2, there will be 435 hybrids. For n = 30 and k = 5, there will be 142506 hybrid algorithms. To demonstrate this serious issue further, let us hypothetically imagine that there are three algorithms: Duck chasing algorithm (DCA), Basil leaf algorithm (BLA), and Star gazing algorithm (SGA). One should not randomly form absurd algorithms, such as Star-Duck Algorithm, Basil-Star Algorithm, Basil-Leaf-Duck Algorithm, or Star-Basil-Duck Algorithm. No researchers should ever do it (except, perhaps, for a possible chat-bot mutant). In addition, there are millions of plant species and animal species, researchers should not invent millions of algorithms, called apple algorithm, basil algorithm, cucumber algorithm, aardvark algorithm, dodo algorithm, yak algorithm, or zonkey algorithm. New algorithms should be based on true novelties and true efficiency. Obviously, there are other issues as well. For example, if a hybrid works well, it is not clear how it may work because there is no mathematical or theoretical analysis of how these algorithms work in general. In addition, in performance comparison studies, some researchers used the computational time or running time as a measure for comparing different algorithms or variants, but the actual running time on a computer can depend on many factors, including hardware configurations, software used (as well as any potential background anti-virus software), and the implementation details (such as vector-based approach versus a for loop). In this context, there are no universally accepted good performance metrics at the moment. This is still an open problem.

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5 Insights and Recommendations Based on the current literature and various studies for analyzing different natureinspired algorithms [2, 4], we provide some insights into nature-inspired metaheuristic algorithms. 1. Algorithms can be linear or nonlinear in their solution-update dynamics. For example, PSO is a linear system because its algorithmic equations are linear, but the firefly algorithm is a nonlinear system because Eq. (12) is nonlinear. In general, the characteristics of nonlinear systems tend to be more diverse. For example, the paths traced by individual fireflies can be spare with fractal-like structures, which may explain the search efficiency and good performance of the firefly algorithm. 2. If random walks are used properly, they can improve the search efficiency of an algorithm. For example, Lévy flights with the step sizes being drawn from a Lévy distribution tend to have the characteristics of super-diffusion, which can cover a much larger search region than standard diffusive isotropic random walks with steps being drawn from a Gaussian distribution. Cuckoo search uses Lévy flights, which shows some scale-free properties in the search behavior. A few other later algorithms also used Lévy flights with the intention to improve their performance. 3. Parameter tuning is important for almost all algorithms. Since almost all algorithms have algorithm-dependent parameters, the performance of an algorithm can be influenced by its parameter setting. Thus, the proper tuning of such parameters should be carried out before it can be used to solve optimization problems effectively. However, parameter tuning is itself an optimization problem. Therefore, the tuning of algorithmic parameters can be considered as a hyper-optimization problem because it is the optimization of an optimization algorithm. In fact, how to optimally tune parameter and how to optimally control parameters during iterations are two open problems. 4. Balance of exploration and exploitation is important, though it is very challenging to achieve it in practice. Theoretically, how to achieve this balance is still an open problem. In practice, some techniques have been used to approximate or estimate this balance. For example, the bat algorithm used the variations of loudness and pulse emission rates to control this balance, whereas the genetic algorithm tends to use a 5:1 rule or 80-20 rule for this. Loosely speaking, about 80% of the initial search should be about exploration, and about 20% as exploitation. This can vary according to the iterations in practice. 5. There are many open problems concerning nature-inspired algorithms. For example, there are nonunified theoretical framework for analyzing such algorithms mathematically or statistically so as to gain insights into their stability, convergence, rate of convergence, and robustness. In addition, benchmarking is also an important topic because it is not clear what types of benchmarks are most useful in validating new algorithms. Currently, most benchmarks are smooth functions, which have almost nothing to do with real-world applications.

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For the hybrid algorithms, we would like to make the following recommendations in the future research: Synergy, Structure, and Simplicity. • Synergy: In hybrid algorithms, different components should work together to produce some synergy. Simple use of the best components does not necessarily lead to the best hybrids or results. Obviously, how to achieve a perfect synergy in hybridization is still an open problem. • Structure: Structure does matter. Since a pile of good-quality building materials does not make it a useful building, a loose assemblage of algorithmic components does not create a good hybrid algorithm. The order, role, and strength of each component from different algorithms can be very important. Again, how to achieve this is still an un-resolved issue. • Simplicity: A simple and clear structure is preferred. There are multiple ways of putting together different algorithmic components and, if the overall performance is about the same level, then a simpler structure is preferable, not only because it is simpler to implement but also because it may be easier to understand and analyze. We sincerely hope that this principle of synergy, simplicity, and structure can inspire further research in this area. We also hope that more novel and truly effective hybrid algorithms will appear in the future so that more challenging real-world problems can be solved efficiently.

References 1. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, Piscataway, NJ, USA, IEEE, pp 1942–1948 2. Yang XS (2014) Nature-inspired optimization algorithms. Elsevier Insight, London 3. Yang XS, He XS (2019) Mathematical foundations of nature-inspired algorithms. Springer briefs in optimization. Springer, Cham, Switzerland 4. Yang XS (2020) Nature-inspired optimization algorithms: challenges and open problems. J Comput Sci Article 101104 5. Yang XS (2013) Cuckoo search and firefly algorithm: theory and applications, vol 516. Studies in computational intelligence. Springer, Heidelberg, Germany 6. Yang XS, Papa JP (2016) Bio-inspired computation and applications in image processing. Academic Press, Elesevier, London 7. Yang XS (2018) Optimization techniques and applications with examples. Wiley, Hoboken, NJ, USA 8. Engelbrecht AP (2005) Fundamentals of computational swarm intelligence. Wiley, Hoboken, NJ, USA 9. Yang XS (2008) Nature-inspired metaheurisic algorithms. Luniver Press, Bristol, UK 10. Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Cruz C, González JR, Pelta DA, Terrazas G (eds) Nature inspired cooperative strategies for optimization (NISCO 2010), vol 284. Studies in computational intelligence. Springer, Berlin, Germany, pp 65–74 11. Yang XS (2011) Bat algorithm for multi-objective optimisation. Int J Bio-Inspired Comput 3(5):267–274 12. Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483

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13. Bekas¸s G, Nigdeli M, Yang XS (2018) A novel bat algorithm based optimum tuning of mass dampers for improving the seismic safety of structures. Eng Struct 159(1):89–98 14. Osaba E, Yang XS, Diaz F, Lopez-Garcia P, Carballedo R (2016) An improved discrete bat algorithm for symmetric and asymmetric travelling salesman problems. Eng Appl Artif Intell 48(1):59–71 15. Osaba E, Yang XS, Jr IF, Lopez-Garcia P, Vazquez-Paravila A (2019) A discrete and improved bat algorithm for solving a medical goods distribution problem with pharmacological waste collection. Swarm Evolut Comput 44(1):273–286 16. Jayabarathi T, Raghunathan T, Gandomi AH (2018) The bat algorithm, variants and some practical engineering applications: a review. In: Yang XS (ed) Nature-inspired algorithms and applied optimization, vol 744. Studies in computational intelligence. Springer, Cham, pp 313– 330 17. Chen S, Peng GH, Xing-Shi, Yang XS (2018) Global convergence analysis of the bat algorithm using a markovian framework and dynamic system theory. Expert Syst Appl 114(1):173–182 18. Yang XS (2009) Firefly algorithms for multimodal optimization. In: Watanabe O, Zeugmann T (eds) Proceedings of fifth symposium on stochastic algorithms, foundations and applications, vol 5792. Lecture notes in computer science. Springer, pp 169–178 19. Fister I, Fister I Jr, Brest J, Yang XS (2013) A comprehensive review of firefly algorithms. Swarm Evolut Comput 13(1):34–46 20. Yang XS, Deb S, Zhao YX, Fong S, He X (2018) Swarm intelligence: past, present and future. Soft Comput 22(18):5923–5933 21. Yang XS (2020) Nature-inspired computation and swarm intelligence: algorithms, theory and applications. Academic Press, Elsevier, London 22. Yang XS, Deb S (2009) Cuckoo search via lévy flights. In: Proceedings of world congress on nature & biologically inspired computing (NaBIC 2009). IEEE Publications, USA, pp 210–214 23. Yang XS, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40(6):1616–1624 24. Yang XS (2012) Flower pollination algorithm for global optimization. In: Durand-Lose J, Jonoska N (eds) Unconventional computation and natural computation (UCNC 2012), vol 7445. Springer, Berlin Heidelberg, Germany, pp 240–249 25. Alam DF, Yousri DA, Eteiba MB (2015) Flower pollination algorithm based solar pv parameter estimation. Energy Convers Manag 101(2):410–422 26. Abdel-Basset M, Shawky LA (2019) Flower pollination algorithm: a comprehensive review. Artif Intell Rev 52(4):2533–2557 27. Bekda¸s G, Nigdeli SM, Yang XS (2015) Sizing optimization of truss structures using flower pollination algorithm. Appl Soft Comput 37:322–331 28. Rodrigues D, Silva GFA, Papa JP, Marana AN, Yang XS (2016) Eeg-based person identification through binary flower pollination algorithm. Expert Syst Appl 62(1):81–90 29. Alyasseri ZAA, Khader AT, Al-Betar MA, Awadallah MA, Yang XS (2018) Variants of the flower pollination algorithm: a review. In: Yang XS (ed) Nature-inspired algorithms and applied optimization. Springer, Cham, pp 91–118 30. Das S, Suganthan P (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evolut Comput 15(1):4–31 31. Dorigo M (1992) Optimization, learning, and natural algorithms. PhD Thesis, Politecnico di Milano, Milan, Italy 32. Karaboga D (2005) An idea based on honeybee swarm for numerical optimization, techinical report. Technical report, Eriyes University, Turkey 33. Karaboga D, Basturk B (2008) On the performance of artificial bee colony (abc) algorithm. Appl Soft Comput 8(1):687–697 34. Pham D, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi M (2005) The bees algorithm, technical note. Technical report, Cardiff University, Manufacturing Engineering Center, Cardiff 35. Yang XS (2005) Engineering optimization via nature-inspired virtual bee algorithms. In: Proceedings of IWINAC2005, vol 3562. Lecture notes in computer science. Springer, Berlin, pp 317–323

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36. Kaveh A, Farhoudi N (2013) A new optimization method: dolphin echolocation. Adv Eng Softw 59(1):53–70 37. Yang X, Deb S (2010) Eagle strategy using lévy walk and firefly algorithms for stochastic optimization. In: Cruz C, González J, Pelta D, Terrazas G (eds) Nature inspired cooperative strategies for optimization (NISCO 2010), vol 284. Studies in computational intelligence. Springer, Berlin, pp 101–111 38. Sur C, Sharma S, Shukla A (2013) Egyptian vulture optimization algorithm–a new nature inspired meta-heuristics for knapsack problem. In: The 9th international conference on computing and information technology (IC2IT2013). Springer, Berlin, pp 227–237 39. Harifi S, Khalilian M, Mohammadzadeh J, Ebrahimnejad S (2019) Emperor penguins colony: a new metaheuristic algorithm for optimization. Evolut Intell 12(2):211–226 40. Li X, Shao Z, Qian J (2002) Optimizing method based on autonomous animals: fish-swarm algorithm. Xitong Gongcheng Lilun yu Shijian/Syst Eng Theory Pract 22(11):32–39 41. Mozaffari A, Fathi A, Behzadipour S (2012) The great salmon run: a novel bio-inspired algorithm for artificial system design and optimisation. Int J Bio-Inspired Comput 4(5):286–301 42. Heidari AA, Mirjalili S, Faris H, Alijarah I, Mafarja M, Chen HL (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872 43. Biyanto TR, Matradji Irawan S, Febrianto HY, Afdanny N, Rahman AH, Gunawan KS, Pratama JAD, Bethiana TN (2017) Killer whale algorithm: an algorithm inspired by the life of killer whale. Proc Comput Sci 124:151–157 44. Gandomi A, Alavi A (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845 45. Mucherino A, Seref OO (2007) Monkey search: a novel metaheuristic search for global optimization. Data Min Syst Anal Optim Biomed 953(1):162–173 46. Passino K (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst 22(3):52–67 47. Erol O, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37(2):106–111 48. Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713 49. Hatamlou A (2012) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222(1):175–184 50. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mechanica 213(3–4):267–289 51. Parpinelli R, Lopes L (2011) An eco-inspired evolutionary algorithm applied to numerical optimization. In: The third world congress on nature and biologically inspired computing (NaBIC 2011). IEEE Press, pp 466–471 52. Rashedi E, Nezamabadi-Pour HH, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248 53. Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm-a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110–111(1):151–166 54. Ting TO, Yang XS, Shi C, Huang K (2015) Hybrid metaheuristic algorithms: past, present and future. In: Yang XS (ed) Recent advances in swarm intelligence and evolutionary computation, vol 585. Springer, pp 71–84

Chapter 2

Ten New Benchmarks for Optimization Xin-She Yang

1 Introduction The literature on nature-inspired algorithms and swarm intelligence is expanding rapidly, and most nature-inspired optimization algorithms are swarm intelligencebased algorithms [1–4]. New algorithms for optimization appear regularly in the current literature, and hundreds of papers are being published every year, about new algorithms and their variants as well as their applications. Obviously, new algorithms have to be tested and validated using various known problems with known optimality locations. Simple benchmark functions are often the first set of problems that new algorithms or variants attempt to solve. However, most existing benchmarks are function benchmarks that are usually smooth with known optimality at a single location for a given function benchmark. In addition, the search domains of these functions in terms of their independent variables are usually regular, often expressed in terms of simple bounds and limits. Even though some function benchmarks have constraints, these constraints tend to be sufficiently simple, which do not change the shape of the search domains significantly. The tests using such smooth benchmarks with regular search domains may give some insights into the performance of the algorithms under consideration. However, the usefulness of such benchmarks may be quite limited because these functions have almost nothing to do with realistic optimization problems from realworld applications. Ideally, we should have a diverse set of test benchmarks and case studies derived from real applications so that researchers can use them for testing algorithms, especially new algorithms. However, such test benchmarks are largely not available X.-S. Yang (B) School of Science and Technology, Middlesex University London, The Burroughs, London NW4 4BT, United Kingdom e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_2

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because case studies tend to be very specialized in a specific subject area. Even though we may have such case studies as benchmarks, specialized knowledge in a subject area is needed to solve the problem properly and interpret the results correctly. If we can somehow extract the essential part of the optimization problems and try to make them almost independent of special subjects, we can make the relevant problems as generic benchmarks. In the rest of the chapter, we will first briefly discuss the role of benchmarking and the different types of benchmarks. Then, we will introduce ten new benchmarks with additional properties, such as noise, discontinuity, non-differentiability, multilayered discrete values and optimal paths from the calculus of variations.

2 Role of Benchmarks There are many benchmark functions that are smooth functions with known optimal solutions and optimal objective values [5–7]. Such benchmarks enable researchers to test new algorithms so as to gain a better understanding of the convergence behavior, stability and performance of the algorithm under consideration (Fig. 1). Benchmarks can be very diverse. To validate any new optimization algorithm, a variety of test benchmarks should be used to see how the algorithm under consideration may perform for different types of problems. In general, benchmarks can be divided into five categories.

Fig. 1 Different types of benchmarks

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• Smooth Functions: There are more than 200 smooth functions as benchmarks in the current literature [6–10]. Whether the problems are constrained or often unconstrained, their objective landscapes tend to be smooth. In addition, in some rare cases, such test functions can also be multi-objective optimization [11]. • Composite Functions: Though many simple test functions such as the Ackley function exist, composite functions have been designed to make it harder for algorithms to find the optimal solutions because the locations of the optimality of these functions are shifted and twisted. • Implicit Solvers: In many applications, the exact form of the objective can be difficult to express explicitly. For example, many engineering design problems are required to use finite element analysis (FEM) packages and computational fluid dynamics (CFD) packages to evaluate the design performance. In this case, the actual evaluation of the design objectives is carried out by calling external solvers for given inputs (design variables and parameters) and then extracting the output (some objective or performance metrics). • Special Benchmarks: Sometimes, specialized benchmarks are used to test certain types of optimization techniques. Benchmarks can be very specialized. For example, in protein folding and molecular biological applications, the test cases are often very specialized with the given structure of data and objectives. • Real-World Problems: For new optimization algorithms to be truly useful, they should be able to solve real-world problems. Therefore, extensive tests should be carried out using real-world problems as benchmarks. This category of benchmarks can be extremely diverse to cover almost all areas of applications. Since there are many different types of benchmarks, an important question is naturally: What benchmarks should be used for validating new algorithms? For most of the studies in the current literature, the benchmarking process seems to use a finite set (typically about a dozen to two or three dozens of functions for testing algorithms, even though these functions are selected to have some diverse properties, such as mode shapes, optimality locations, separability of different dimensions and even with some constraints. Though these functions themselves can be quite complicated with multiple modes, they are idealized functions, which may have nothing to do with problems arising from real-world applications. Thus, whatever conclusions may be drawn from testing functions, they may not be of much use in practice. After all, most real-world problems can be even more complex with highly nonlinear constraints and irregular search domains. Therefore, it can be expected that algorithms that work for test functions may not work well in practical applications.

3 New Benchmark Functions Even though the usefulness of simple benchmarking is quite limited, it is still an important part of the algorithm evaluation process. In addition to the existing test functions, we now introduce even more complex functions as new benchmarks.

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These new benchmarks highlight the challenges in algorithm testing and may inspire more research to test new algorithms from a wider perspective, including introducing noise, non-unique optimal solutions and even solutions in an infinite-dimensional functional space.

3.1 Noisy Functions Almost all existing benchmark problems are deterministic in the sense that the function forms and their solutions have no randomness. Now let us add some noise to a smooth function, which may make it more challenging for algorithms to find its optimality. One way for adding noise without affecting the location of its optimality is to multiply a random variable drawn from a uniform distribution. For example, we can have a noisy function D  n xn2 , (1) f (x) = n=1

as the extension to a standard sphere function. Here, all n are drawn from a uniform distribution in [0,1]. We can design an even more complicated function f 1 (x) =

D 

D    xn2n − exp − n xn2n ,

n=1

(2)

n=1

with − 100 ≤ xn ≤ 100,

(3)

where D ≥ 1 is the dimensionality of the function. Again, all n are drawn from a uniform distribution in [0, 1]. Its optimality f min = −1 occurs at x = (0, 0, . . . , 0).

3.2 Non-differentiable Functions The simplest function with a kink is probably f (x) = |x|, which has a global minimum f min = 0 at x∗ = 0. However, this function does not have a well-defined derivative at x = 0. In the D-dimensional space, we can extend it to f (x) =

D  n=1

|xn |,

(4)

2 Ten New Benchmarks for Optimization

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and its global minimum f min = 0 is located at x = (0, 0, . . . , 0). Obviously, we can design more functions with multiple kinks, such as  f 2 (x) =

D 





D      |xn − nπ | exp −  sin(|xn − nπ |) ,

n=1

n=1

(5)

with − Dπ ≤ xn ≤ +Dπ.

(6)

Its optimality f min = 0 occurs at x = (π, 2π, . . . , nπ ).

3.3 Functions with Isolated Domains In most benchmark problems, their search domains are typically regular in the form xn ∈ [a, b], ranging in an interval from xn = a to xn = b. This is usually true for unconstrained optimization problems with simple bounds or limits. For constrained optimization problems, depending on the actual constraints, feasible search domains can have very irregular shapes or even isolated, fragmental regions. For example, we can design a function with two isolated domains f 3 (x) = x12 +

D 

|xn3 |,

(7)

n=2

subject to |x1 − 2a| +

D 

|xn | ≤ a,

(8)

n=2

and

D  (xn − 5a)2 ≤ a 2 , a ≥ 1.

(9)

n=1

The minimum f min = a 2 occurs at x = (a, 0, 0, . . . , 0). More generally, we can have a function with multiple isolated domains with four peaks as its optimal solutions [4] f 4 (x) =

N  i=−N

in the domains of

N

 

|i| + | j| exp −a(x − i)2 − a(y − j)2 , j=−N

(10)

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|x − i| + |y − j| ≤

1 , for − N ≤ i, j ≤ N , a

(11)

where i, j are integers with N = 100 and a = 10. This function has 4(N + 1)2 local peaks, but it has four highest peaks at four corners. However, its domain is formed by many isolated regions, or 4(N + 1)2 = 40401 regions when N = 100.

4 Benchmarks with Multiple Optimal Solutions Almost all benchmark functions have their optimal objective values at a finite number of isolated points. For example, f (x, y) = x 2 + y 2 has only a single optimal solution at the point (0, 0) with f min = 0. To make things more complicated, we can design functions with infinitely many solutions with equal objective values. For example, the function g(x, y) = x 2 + y 2 − 2x y = (x − y)2 has the global minimum f min = 0 on the line y = x. Many researchers use the closeness to the optimal solution such as the point (0,0) to measure the success of the algorithms used in the simulation; this may become the main issue if the optimal solutions are no longer isolated points. We can expect that such types of functions can also make it more challenging for some algorithms to find their optimality.

4.1 Function on a Hyperboloid We can easily extend a standard sphere function to a sphere function with a hyperboloid (of revolution) constraint f 5 (x) =

D 

xn2 ,

(12)

n=1

subject to D−1 2  xn x D2 ≥ + 1, a, b ≥ 1. a2 b2 n=1

(13)

It has a minimum f min = a 2 on a (D − 1)-dimensional hyper-sphere D−1 

xn2 = a 2 ,

n=1

which corresponds to infinitely many solutions.

(14)

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In the case of 3D, we have f (x) = x 2 + y 2 + z 2 ,

(15)

subject to y2 z2 x2 + − ≥ 1, a2 a2 b2 with f min = a 2 on x 2 + y 2 = 1.

4.2 Non-smooth Multi-layered Functions Though the above functions are more complicated, their objective values are still continuous in most cases. There is no jump or discontinuity in their landscapes. In addition to making the search domains for independent decision variables irregular and/or to make the objectives with kinks, we can also design functions with discontinuous objective landscapes. For example, we can make the objective values of a sphere function take only integer values, which can lead to a non-smooth multi-layered function D   (16) xn2 , f (x) = n=1

where x is a floor function, which rounds x to the nearest integer smaller than x. That is, k = x 0 is an integer. Theoretically we know that 

∞ 0

sin(kx) π d x = − tan−1 β, βx xe 2

(26)

which does not depend on k. The maximum value of this integral occurs at β = 0 for any positive integer k. In the case of β = 0.5 and k = 3, the variation of the integrand is shown in Fig. 5. Now let us use the maximization of this integral as a benchmark, which requires to evaluate the integral with an infinite limit. If without any prior knowledge of its true value of this integral, the effective evaluation of the objective function requires some sophisticated numerical integration. This requires careful implementation.

7 Benchmarks of Infinite Dimensions All the function benchmarks in the literature have reasonably a well-defined solution set as the possible optimal solution. Even in the high-dimensional space, such optimal solutions are just points or a region in the D-dimensional search space because the solutions are represented as a solution vector x.

2 Ten New Benchmarks for Optimization

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y

x

Fig. 5 Variation of f (x) = sin(kx)/(x exp(βx)) with k = 3 and β = 0.25

In some applications in science and engineering, the optimal solutions may not be represented by vectors. For example, in the calculus of variations [12], optimal solutions are curves and surfaces that cannot be represented by simple vectors. For this branch of mathematics, we have rigorous theory using the Euler-Lagrange equation to solve such types of problems. Now let us reformulate such problems and try to solve them using optimization algorithms without using the Euler-Lagrange equation. Since almost all optimization algorithms have been designed to represent solutions in terms of vectors, this kind of problem from the calculus of variations can be a major issue for standard optimization algorithms. In aerodynamics and shape optimization, shapes are represented by some parametric curves so as to simplify the representations. Even so, shape optimization can be quite challenging to implement. To provide benchmarks for optimization algorithms from this perspective, let us use two examples to design benchmarks with solutions as paths or curves. Even though the actual space (x, y) is two-dimensional, the representation of solutions may require many points (or infinitely many points) to form a smooth curve. In fact, we need a functional space to represent the potential curves properly. In this case, we can refer to this type of problem as benchmarks in infinite dimensions.

7.1 Shortest Path Problem In the two-dimensional space (x, y), there is a path or curve y(x) that minimizes the integral  1

dy 2 min Q = 1+ d x. (27) dx 0

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From the plane geometry or calculus of variations [12], we know that the solution is a straight line y = x from the origin (0,0) to point (1,1). The challenge for this benchmark as an optimization problem is that the solution is not a single point but a segment of a curve (or a straight line in this case). In order to find this solution (corresponding to infinitely many points), some parametrization of an unknown curve is needed. Therefore, any standard algorithms for solving singleobjective optimization problems have to be modified so that solution paths can be represented effectively. Mathematically, the objective functional can be rewritten as 

1

f 9 (y(x)) =

minimize

 1+

0

dy 2 dx

d x,

(28)

subject to x ≥ 0 and y(x) ≥ 0.

7.2 Shape Optimization The shape of a hanging rope under gravity takes the form that the potential energy is minimized, subject to a fixed length L. The shape of a loose rope hinged between two fixed points (−a, 0) and (a, 0) can be obtained by minimizing the potential energy  minimize E p = ρg

a −a

 y 1 + y 2 d x,

(29)

where ρ is the density of the rope and g is the acceleration due to gravity. Here, we use the notation y = dy/d x for a given smooth function y(x). Without loss of generality, we can use ρg = 1, and thus we have  minimize

f 10 (y(x)) =

a −a

 y 1 + y 2 d x.

(30)

This minimization problem is subject to an equality  L=

a −a



1 + y 2 d x,

(31)

with L > 2a. The solution can be obtained by solving the Euler-Lagrange equation, which corresponds to the shape or curve (see Fig. 6) y(x) = cosh(x) − cosh(a),

(32)

2 Ten New Benchmarks for Optimization

(−a, 0)

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(+a, 0)

Fig. 6 Shape of a hanging rope with a fixed length

with a length

 L=

a −a



1 + y 2 d x = ea − e−a = 2 sinh(a).

(33)

In case of a = 1, we have L = e − e−1 ≈ 2.3504. The challenge of this benchmark is not only to represent the solutions properly but also to deal with the equality constraint correctly. In addition, the algorithm to be used must also be modified to accommodate such additional requirements.

8 Conclusions There are many benchmarks for testing optimization algorithms; however, the benchmarks in the current literature tend to be smooth functions or problems with a finite number of optimal solutions. In addition, the search domains of existing benchmarks are usually regular with simple bounds or limits. To extend benchmarks to be more relevant to realistic problems, we have introduced ten new benchmarks by adding some noise, isolating the search domains and even making problems non-smooth with singularity and discontinuities. These new benchmarks can be used to validate new algorithms and existing algorithms to see if they can cope with problems with non-smoothness and singularity well. We hope that this will inspire more research into benchmark problems and how to test new algorithms properly.

References 1. Yang XS (2014) Nature-inspired optimization algorithms. Elsevier Insight, London 2. Yang XS, He XS (2019) Mathematical foundations of nature-inspired algorithms. Springer Briefs in Optimization. Springer, Cham, Switzerland 3. Yang XS (2018) Optimization techniques and applications with examples. Wiley, Hoboken, NJ, USA

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4. Yang XS (2020) Nature-inspired optimization algorithms: challenges and open problems. J Comput Sci, Article 101104 5. Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84 6. Jamil M, Yang XS (2013) A literature survey of benchmark functions for global optimisation problems. Int J Math Modell Numer Optim 4(2):150–194 7. Suganthan P, Hansen N, Liang J, Deb K, Chen Y, Auger A, Tiwar S (2005) Problem definitions and evaluation criteria for cec 2005, special session on real-parameter optimization, technical report. Technical report, Nanyang Technological University (NTU), Singapore 8. Mazhar AA (2020) Benchmark functions (web site). Technical report, Victoria University of Wellington, New Zealand 9. Hedar A (2011) Global optimization test problems (web site). Technical report, University of Kyoto, Japan 10. Kumar A, Wu G, Ali MZ, Mallipeddi R, Suganthan PN, Das S (2020) A test-suite of non-convex constrained optimization problems for the real-world and some baseline results. Swarm Evolut Comput 56(Article 100693) 11. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: emperical results. Evolut Comput 8(2):173–195 12. Yang XS (2017) Engineering mathematics with examples and applications. Academic Press, London

Chapter 3

Review of Parameter Tuning Methods for Nature-Inspired Algorithms Geethu Joy, Christian Huyck, and Xin-She Yang

1 Introduction Algorithms usually have algorithm-dependent parameters and the performance of an algorithm may largely depend on the setting of its parameter values. Therefore, parameter tuning becomes an important part of algorithm implementations and applications in practice [1–5]. Many design problems in engineering and industrial applications are optimization problems. To find the optimal solutions, or even sub-optimal solutions, to such optimization problems requires optimization techniques and algorithms. Nature-inspired algorithms are a class of recent optimization algorithms that are becoming popular and widely used in solving optimization problems. Like many other algorithms, each nature-inspired optimization algorithm usually has a few parameters that need to be properly tuned. Ideally, we should have a good tool to tune the parameters for a given algorithm so that it can maximize the performance of the algorithm under consideration. However, such tools do not exist. Therefore, tuning parameters can be a challenging problem, especially for tuning optimization algorithms. In essence, parameter tuning of an optimization algorithm is a hyper-optimization problem because it is the optimization of an optimization algorithm [6–11]. Even if a good tuning tool may exist so that we can tune an algorithm such that it performs well for a given problem, this tuned algorithm may not perform well for other problems, especially new problems or a different type of problems with G. Joy · C. Huyck · X.-S. Yang (B) School of Science and Technology, Middlesex University London, The Burroughs, London NW4 4BT, UK e-mail: [email protected] G. Joy Also Computer Engineering and Informatics, Middlesex University Dubai, Dubai Knowledge Park, P.O. Box 500697, Dubai, United Arab Emirates © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_3

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unknown optimality. The reason is that the parameter-tuning process tends to use a given optimization problem (or a small set of optimization problems) to tune an algorithm, and consequently the tuned parameters may be problem-specific. If this is the case, algorithms have to be tuned again for every new problem, at least for every new type of problem. Therefore, parameter tuning can be a very time-consuming task. Since parameter tuning can be computationally extensive, one naive way for solving optimization problems is probably to choose algorithms without any parameters (i.e., the so-called parameter-free or parameterless algorithms). However, such algorithms are rare in the context of optimization. In fact, many so-called parameter-free optimization algorithms in the literature are not entirely parameter-free, and they still have some parameters, such as the population size of a swarm intelligencebased algorithm. In many cases, researchers tend to mean that the number of key parameters is significantly reduced so that the algorithms require little or almost no tuning, even though users have to set the values of some hyper-parameters, such as the population size. But there is a serious issue with parameter-free algorithms because they are less flexible and less efficient. For algorithms to be efficient in solving a class of optimization problems, the parameters in an algorithm should be fine-tuned so that the algorithm becomes effective for solving the specific class of problems under consideration. For an algorithm that is completely free from any parameters, if it does not work well for a given problem, there is no way that we can make it more efficient. In the end, we have to choose other algorithms to deal with unsatisfactory solutions and try to find better solutions. In addition to the above issues concerning parameter tuning, there is another problem, called parameter control. For parameter tuning, once an algorithm is properly tuned, the parameter values are then fixed when running the algorithm for solving problems. However, some studies suggested that it could be advantageous to vary the parameter values during the execution or iterations of an algorithm. Rather than fixing the values of algorithm-dependent parameters, their values can be further tuned by varying or controlling how these may vary during the iteration. This type of problem is called parameter control. At present, it is not clear how to tune parameters effectively and how to control parameters properly for any given algorithm and a given set of problems. In fact, both are still open problems in this area. Therefore, the purpose of this chapter is to provide a timely summary of problems related to parameter tuning and parameter control. Some of the most recent studies concerning parameter tuning will be reviewed and discussed.

2 Parameter Tuning To help our discussions about parameter tuning, let us use A to represent an algorithm under consideration. The parameters in A is a vector p = ( p1 , p2 , ..., pm ) of m parameters. For a given problem Q, its optimal solution is denoted by x∗ , which can

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be obtained by algorithm A starting with a random initial solution (or any educated guess) x0 . Any solution at iteration k is represented by a vector x k = (x1 , x2 , ..., xd ) in the d-dimensional space. The iterative solution process of obtaining the optimal solution to problem Q can be represented by (1) x k+1 = A(x k , p, Q). In the limit of k → ∞, we have x k+1 → x∗ as the optimal solution or the best solution that the algorithm can find.

2.1 Schematic Representation of Parameter Tuning Since the parameter vector p can take different values. Initially, we may have p = p0 , but p0 can be obtained by random initialization or an educated guess. Suppose we have a performance measure for algorithm A, which can be denoted by μ. For example, μ can be considered as the success rate or 1/T , where T is the time needed to find the optimal solution to Q. With such notations, parameter tuning can be represented as an optimization problem to find p so that max μ = F(A, p, Q), (2) where F() is a known function to be defined by the user. However, this requires an iterative process (3) p∗ = lim arg p F(A, p j , Q). j→∞

In practice, we cannot afford a large number of iterations for parameter tuning. Thus, we typically set a computational budget B for parameter tuning, and B can be considered as the maximum number of tuning iterations. Here, p∗ is the vector of tuned parameter values.

2.2 Different Types of Optimality Using the above notations, for a given problem Q and a selected algorithm A, there are two types of optimality: the optimal solution x∗ and the optimal setting p∗ . Therefore, parameter tuning involves two optimization problems at the same time. One optimality does not lead to the other optimality. Traditionally, most researchers focus on the first optimality of x∗ so that they can obtain the optimal solution, or sub-optimal solutions, to their optimization problems. This is fine for small-scale problems or the optimization process is not too time-consuming. For complex, large-scale problems, tuning of parameters becomes

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essential to save computational costs. A well-tuned algorithm may reduce the computational time significantly, though the tuning of algorithm-dependent parameters is an art at the moment, rather than a systematic methodology.

2.3 Approaches to Parameter Tuning Based on the two different types of optimality, there are different ways for approaching parameter tuning [7]. For parameter tuning and control in general, there are always three components: an algorithm, a tuning tool, and a problem (see Fig. 1). Obviously, the first key component is the algorithm to be tuned. To tune the algorithm, we have to use a tuning tool (i.e., a tuner), and apply the algorithm to a problem or a problem instance so as to evaluate the performance of the algorithm being tuned for solving the problem. Therefore, it can be expected that the tuned results in terms of parameter settings can be both algorithm-specific and problemspecific. In addition to parameter tuning, the variations of parameters during iterations can be also advantageous, and such variations are often called parameter control [2, 12]. Though our emphasis here is mainly on parameter tuning, we will also consider parameter control when appropriate.

Fig. 1 Three components of parameter tuning

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Hyper-optimization

Since parameter tuning is the optimization of an optimization algorithm, we can refer it to as hyper-optimization [6]. Some researchers also called it meta-optimization in a slightly different context [13]. In terms of achieving optimal tuning, we can have two different structures: sequential and parallel. The sequential structure means that we tune the algorithm A first for the given problem Q so as to find the optimal setting of parameters p∗ . Whether it is achievable or not is a separate issue. For the moment, suppose that it is possible to find p∗ in this way. Then, we apply the optimal p∗ for algorithm A to solve Q, and then we obtain x∗ as the optimal solution. Again, whether this is achievable or not is another issue. This structure can be schematically represented in Fig. 2. Another way for parameter tuning is to use a parallel structure or a loop structure to carry out tuning and problem-solving iteratively. This can be represented as steps in Fig. 3. If the parameter values can be changed again inside the step of solving the optimization problem, it becomes a problem of parameter control.

Fig. 2 Sequential structure of parameter tuning. This is also called offline tuning Fig. 3 Loop structure of parameter tuning. This is sometimes called online tuning

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Multi-objective Approach

It is difficult to justify which structure is better. In fact, existing studies do not provide any evidence of whether these structures can work effectively. Another way of looking at this parameter-tuning problem is to carry out both optimization processes simultaneously, which can essentially lead to a bi-objective optimization problem min Q = f (x)

and

max μ.

(4)

From this multi-objective perspective, we know from the theory of multi-objective optimization that there is no simple single optimality. Instead, we should have multiple, equally good solutions, which will form the Pareto front. In this sense, we can only find Pareto-optimal settings. This means that there is no unique parameter setting in general. If the problem Q changes to a different problem, the tuned parameters should also change so as to maximize both objectives. 2.3.3

Self-Tuning Approach

Another possibility is to combine the tuning process with the optimization problem to be solved. This leads to the self-tuning framework, developed by Yang et al. [6]. The main idea is to extend the solution vector x = (x1 , x2 , ..., xd ) to include p = ( p1 , p2 , ..., pm ) so as to form a vector of d + m dimensions u = (x, p) = (x1 , x2 , ..., xd , p1 , p2 , ..., pm ),

(5)

we then use u to solve both problems to find the optimal x∗ and p∗ . In this case, we need to combine the bi-objective functions to form a composite objective function min g = α f (x) − βμ,

(6)

to be minimized. Here, α > 0 and β > 0 are two weights. There are other possibilities or approaches for parameter tuning. For example, we can consider parameter tuning as a self-organized system [14]. So, in the rest of the chapter, we will review some of the recent studies.

3 Review of Parameter Tuning Methods 3.1 Generic Methods for Parameter Tuning The classifications of parameter tuning methods can be difficult, depending on the perspective of the classification [7, 15, 16]. For example, Huang et al. [16] used the action of generation of parameters to divide into simple, iterative, or

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high-level generation-evaluation schemes. However, this categorization does not provide enough details about the mechanisms of parameter tuning. Here, we will loosely divide parameter tuning methods into eight different categories: 1. Manual or brute-force method. A naive way to tune the parameters of a given algorithm is to try every possible combination. In general, this is not possible and the most time-consuming method. However, if there is only one parameter, we can subdivide the parameter into smaller discrete intervals, then we can potentially try every possible combination of intervals. This allows us to find the best parameter intervals and enable further fine-tuning if needed. The advantage of this method is that it will ensure to explore every possible interval. However, the major disadvantage is the high computational cost. Thus, this method is only suitable for tuning a single parameter in a discrete range. 2. Tuning by systematic scanning. A slightly improved version of brute-force tuning is systematical scanning. Suppose a parameter p varies in the range of [a, b], we can split this interval into multiple (not necessarily equal) subintervals, and carry out the scanning systematically. For example, if p varies in [0,10], we can try p = 0.0, 0.1, 0.2, ..., 9.8, 9.9, and 1.0. Suppose that we find that the best possible range of values is (for example) 2.5, then we can fine-tune it from 2.4 to 2.6 by using p = 2.40, 2.41, 2.42, ..., 2.59, and 2.60. This process continues until a predefined stop criterion is met. 3. Empirical tuning as parametric studies. In practice, most researchers would use some sort of empirical tuning. Empirical tuning of parameters starts with either an educated guess or a known value from an existing study, then perturbs the parameter values around a larger range so as to fine-tune the parameter or test the robustness as well as the sensitivity of the parameter under consideration. For multiple parameters, we can apply the same procedure to do such parametric studies. The advantage of this method is that it is usually quick to obtain useful parameter values, but it is difficult to provide any useful insights. 4. Monte Carlo based method. The Monte Carlo-based method is a statistical sampling method with relatively solid theoretical basis and the error analysis to ensure that such parameter tuning can work well in practice. However, due to the slow convergence of Monte Carlo-based methods, a large number of samples (typically thousands) or parameter settings need to be evaluated, which is still time-consuming. But compared with manual or brute-force tuning, this is a major improvement and can work well in practice. A possible further improvement is to use the so-called quasi-Monte Carlo method with low-discrepancy sequences, which may reduce some of the computational efforts, though we have not seen any significant work in this area yet. 5. Tuning by design of experiments. As parameter tuning tends to be time-consuming, design of experiments will be useful for tuning parameters with a fixed computational budget. For example, for multiple parameter tuning with a fixed number of possible tuning experiments, methods via design of experiments such as the Latin hypercube and factorial techniques can provide a good

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approach, though there is no guarantee that a good set of parameter settings can be achieved. Obviously, if the tuning budget increases, better parameter settings are more likely to be achievable. 6. Machine learning-based methods. Strictly speaking, machine learning-based algorithms or methods are usually more sophisticated than metaheuristic algorithms. Using machine learning-based methods seems to be a bit over the top and makes things more difficult to understand. However, some studies have shown that they can work well for tuning parameters. But this requires good data and more computational efforts. Therefore, this should not be a first choice as a method for tuning algorithm-dependent parameters. 7. Adaptive and automation methods. In recent years, adaptive parameter tuning becomes more popular due to its ease of implementation. Self-adaptive methods seem to be more effective in tuning parameters online. However, the design of adaptive rules can be another unresolved challenging problem. In addition, automation methods tend to make adaptive tuning more effective and easier to implement. Again, the design of such automation itself is a difficult task. As an example, the self-tuning framework can be considered as a kind of automation method [6]. 8. Other methods. There are other methods that we may not be able to put into the above categories. For example, parameter tuning by sequential optimization is an interesting method [17], which may not fit into any of the above categories. In addition, hybrid approaches to parameter tuning [18], and multi-objective approach to parameter tuning can be considered as alternative methods, which can be equally effective [19]. However, their computational efforts may vary significantly. Also, there is an emerging literature about parameter tuning, which requires a more systematical review in the near future. Though the above categorization includes almost all known parameter tuning methods for offline tuning, online tuning may be relevant to some of these categories. More specially, adaptive and self-adaptive tuning, Monte Carlo-based tuning, machine learning-based tuning, and other methods are relevant to online tuning.

3.2 Online and Offline Tunings Though the theoretical understanding of parameter tuning and parameter control may be quite limited, the numerical experiments on parameter settings are relatively extensive. Here, in the rest of this chapter, we will focus on the review of some of these studies. Loosely speaking, the fine-tuning of parameters can sometimes increase the efficiency of algorithms if the tuning can help to reach a better balance of exploration and exploitation, thus providing a better trade-off and a potentially higher rate of convergence. In general, parameter settings can influence both the quality of the solutions and the balance between local and global exploration. For example, it has

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been demonstrated using different variants of PSO that the best parameter values or algorithm configurations can be time dependent [20]. In addition, performance can be enhanced if exploitation and exploration can be more balanced [21]. According to [22], parametrization is described as finding the best settings of parameters for a given optimization technique by solving a problem instance so as to improve the known performance index. Thus, the process of tuning or setting parameters of a metaheuristic algorithm is also referred to as algorithm configuration in the literature [23]. The term offline parameter tuning or parametrization refers to the setting of parameters prior to the execution of the metaheuristic algorithm used for solving a set of problems. In contrast, online parameter tuning or parametrization means that the parameters can be updated while the metaheuristic algorithm is being executed [24]. Typically, offline tuning methods are carried out in the early stage, usually as part of the pre-processing phase. The values of the parameters are set by observing the parameter values used in similar experiments or setups. Sometimes, additional insights from statistical analysis of the algorithm’s performance on similar problems, while deciding the parameter values during offline tuning, can ensure a decent performance of the algorithm [25]. In this sense, offline parametrization can, in general, be divided into four categories: manual parameterization, parameterization by analogy, parameterization by design of experiments (DOE), and search-based parameter tuning. Offline parameter tuning methods can usually require significant computational efforts to get some sensible statistical measures, and such methods include the sequential model-based optimization [26], ParamILS [27], F-Race [28], and DOE [29]. On the other hand, online parameter control methods usually require the minimal user intervention and the absence of preliminary experimentation. However, there is no guarantee that computational efforts may be less. Typically, parameter control (online tuning) is not part of pre-processing, and in essence is an ad hoc process. The values of parameters may be adjusted in each iteration or after a fixed number of iterations, according to the feedback or outputs obtained from the previous runs. In this sense, online parameter setting methods are more specific and may potentially provide a better performance for the algorithm in terms of its efficiency and effectiveness. Since such tuning is problem-specific, the method in this case can be implemented as part of the solver [30]. However, the disadvantages are overspecialization of this kind of parametrization method to the given algorithm and a given type of problems. In addition, the introduction of new parameters as part of the tuning process itself may expand the parameter domain significantly. In general, the performance of a parameter setting method is evaluated based on the speed of the parameterized algorithm in converging to the solution for a problem set or instances and the quality of the solution or a combination of both [31]. Some authors suggested that online parametrization method could use an approximate gradient search with line search to search for parameter values in the parameter domain [32]. The efficiency of this method was demonstrated using differential evolution with two test suites. This approach was further enhanced by a grid-based search [33]. The search starts with some arbitrary values for the parameters. The

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neighboring values of the initial arbitrary values are then selected using grid search and the algorithm’s performance for the newly selected parameter values is estimated using short runs. The current set of parameter values is then used for several iterations before a new set of values is selected using a grid search method. Then, their influence on the algorithm’s performance is evaluated using more runs. For online tuning methods, an eTuner was developed by [34]. They claimed that their eTuner method can overcome the limitations of some naive brute-force strategies. Though it is no surprise that evolutionary algorithms are used to tune the parameters of a metaheuristic algorithm [13], the evolutionary algorithms themselves are also needed to be tuned. Imagine a case that the evolutionary algorithms are well tuned, then these tuned algorithms can be used to tune metaheuristic algorithms. Although it is still a very computationally intensive process, certain automation reduces the workload involved and the efficiency of this method is demonstrated using facility location problem [13]. Some researchers referred to the process of using a metaheuristic algorithm to tune the parameters of a metaheuristic algorithm as meta-optimization, whereas other researchers called it hyper-optimization. It is worth pointing out that terminologies in this area are not consistent yet and there are no agreed sets of common terminologies. However, we are trying to use a consistent set of terminologies in this chapter.

3.3 Self-Parametrization and Fuzzy Methods A self-parametrization method was developed by the authors of [35], which used a metaheuristic with the parameter space and the solution space. However, it is worth pointing out that this self-parametrization method is not a self-tuning method. A prototype of self-parametrization was then used to analyze the performance of the proposed parametrization framework. For the tested scheduling problem and the traveling salesman problem, they showed that their method was statistically significant better than some manual-parameter-tuning methods. A method using fuzzy inference was suggested in [36] to tune the gray wolf optimizer. A tuning method that combines both the fuzzy C-means clustering [37] and Latin Hypercube sampling [38] was proposed in [31]. The authors suggested the early elimination of parameter configurations to reduce computation cost and tuning time. Each tuning algorithm has its own advantages and disadvantages. An evaluation method based on Monte Carlo simulation was proposed in [39] to explore the influence of parameters on the performance of metaheuristic algorithms. In addition, some of the major pitfalls in algorithm configuration and the best practices to avoid or overcome these pitfalls have been discussed in [40].

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3.4 Machine Learning-Based Methods Some researchers used reinforcement learning for tuning parameters. Though a different approach and from a different perspective, it can involve more computational efforts. In general, parameter tuning methods involving the use of reinforcement learning have the following drawbacks [11]: computationally intensive, final results can be highly dependent on the hyper-parameters in learning, and a very limited number of benchmark functions. In the current literature, other machine learning algorithms were also used to tune the parameters of metaheuristic algorithms [41, 42]. In [41], a random forest was used to tune the parameters of bee colony optimization. The improvement in efficiency of the tuned version was demonstrated some instances of the Traveling Salesman Problem. In [42], the authors used a set of machine learning techniques to tune the parameters of PSO. In addition, a meta-learning approach was developed for tuning parameters [43], which seemed to be effective. Randomization techniques can also be very effective for hyper-parameter optimization [44] if hyper-parameter optimization can be considered as a kind of parameter tuning. Similarly, hyper-parameters can be tuned using deep neural networks [45], whereas a statistical learning-based approach was developed for parameter fine-tuning of metaheuristics [46]. There may be other tuning methods that we have not covered in this chapter, as the literature is evolving in this area. In the rest of this chapter, we will discuss some of the key issues in parameter tuning and will make some recommendations for future research.

4 Discussions and Recommendations Based on the brief review in this chapter, it seems that there have been a lot of efforts in investigating parameter tuning methods, either offline or online. However, it still lacks some true insights about how these parameter tuning methods may work. Equally, in most cases, these methods may not work well as expected, and there are no insights or indicators to explain the possible reasons. Most importantly, there are some serious questions and open problems related to parameter tuning and parameter control. Based on our observations and analysis, there are three main issues concerning parameter tuning: non-universality, high computational efforts, and lack of insights into how the algorithms may behave in terms of convergence. • Non-universality: Almost all the parameter tuning methods require three components: an algorithm, a problem or problem instance, and a tuning tool/rule. Therefore, the settings of parameters that have been properly tuned (if they are achievable) are both problem-specific and algorithm-specific. Thus, we cannot expect the tuned parameter settings that work for an algorithm for a set of prob-

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lems can be equally effective for a different set of problems. In fact, there is no universality in parameter tuning, and further tuning seems to be needed for new problems. • High computational efforts: The main barrier to parameter tuning and parameter control is the high computational cost needed for tuning parameters properly. Multiple runs of the algorithm to be tuned with multiple parameter combinations are needed. Thus, it is highly needed to develop new tuning methods so as to minimize or at least reduce the overall computational efforts significantly. • Lack of insights: Though a good spectrum of diverse tuning methods exists in the current literature, almost all these methods are heuristic methods to a certain degree. Even the tuning methods may work quite well, it lacks insights into how they work and under what conditions. An even more important problem is that if the parameters are best tuned, what do they imply in practice? Alternatively, how good parameter settings may influence the convergence of the algorithm and consequently its convergence is still an open problem. With the above issues and open problems, we would like to make some recommendations for future research concerning parameter tuning in the following three areas: theory, link to convergence analysis, and universal tuning. • Theoretical analysis. It is highly needed to carry out some mathematical or theoretical analysis of how parameter tuning works. Ideally, the possible ranges of parameters can be derived or estimated by analyzing the algorithm itself. • Relationship to algorithm convergence. It can be expected that properly tuned algorithms should have better convergence. However, it is not clear how the parameter settings can directly affect the convergence rate of the algorithm under consideration. Therefore, it is desirable to explore the possibility of establishing some theoretical link between parameter settings and convergence rates. This is still an open problem and more research is highly needed. • Universal tuning. As we have seen earlier, parameter tuning methods seem to produce results that are both algorithm-specific and problem-specific, which limits the usefulness of the tuned algorithms. Ideally, the tuning should be a black-box type without the knowledge of the algorithm and problems, and the tuning can be more general and the results can be potentially universal. However, it is not clear if such methods are possible and how to design such methods. Future research should explore more in this area so as to develop more generic tuning tools. In addition to the two types of optimality we briefly explained earlier, there is a third optimality that concerns the optimal rate of convergence. When we say the parameters are best tuned, it all depends on the performance metric used. If the metric is to minimize the number of iterations or increase in the accuracy of the algorithm for solving a given set of problems, this is not exactly the same as the best rate of convergence. Thus, there are some subtle differences in what we mean “best settings”. In the current literature, different researchers seem to use the best settings to mean different things, according to different rules/metrics. This issue needs to be

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resolved and a set of useful rules should be agreed upon before we can truly make an insightful understanding of parameter tuning and control. As we have seen in this chapter, there are many issues and open problems concerning parameter tuning and parameter control. We sincerely hope that this brief review can inspire more research in this area in the near future.

References 1. Eiben A, Smit S (2011) Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evol Comput 1(03 2011):19–31 2. Yang XS, He XS (2019) Mathematical foundations of nature-inspired algorithms. Springer briefs in optimization. Springer, Cham, Switzerland 3. Yang XS (2020) Nature-inspired optimization algorithms: challenges and open problems. J Comput Sci 46:101104 4. Talbi EG (2009) Metaheuristics: from design to implementation. Wiley 5. Hussain K, Salleh MNM, Cheng S, Shi Y (2019) Metaheuristic research: a comprehensive survey. Artif Intell Rev 52:2191–2233 6. Yang XS, Deb S, Loomes M, Karamanoglu M (2013) A framework for self-tuning optimization algorithm. Neural Comput Appl 23(7–8):2051–2057 7. Yang XS (2020) Nature-Inspired optimization algorithms, 2nd edn. Academic Press, London 8. Joshi SK, Bansal JC (2020) Parameter tuning for meta-heuristics. Knowl-Based Syst 189:105094 9. Lacerda M, Pessoa L, Lima Neto F, Ludermir T, Kuchen H (2021) A systematic literature review on general parameter control for evolutionary and swarm-based algorithms. Swarm Evol Comput 60(2 2021):Article 100777 10. Rathore K (2018) Parameter tuning in firefly algorithm. Int J Adv Res Ideas Innov Technol 4:106–112 11. Lacerda M, Lima Neto F, Ludermir T, Kuchen H (2023) Out-of-the-box parameter control for evolutionary and swarm-based algorithms with distributed reinforcement learning. Swarm Intell (01 2023) 12. Eiben A, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141 13. Skakov E, Malysh V (2018) Parameter meta-optimization of metaheuristics of solving specific np-hard facility location problem. J Phys: Conf Ser 973(03 2018):012063 14. Keller, E.F.: Organisms, machines, and thunderstorms: a history of self-organization, part ii. complexity, emergence, and stable attractors. Histor Stud Nat Sci 39(1):1–31 15. Phan H, Ellis K, Barca J, Dorin A (2020) A survey of dynamic parameter setting methods for nature-inspired swarm intelligence algorithms. Neural Comput Appl 32(2):567–588 January 16. Huang C, Li Y, Yao X (2020) A survey of automatic parameter tuning methods for metaheuristics. IEEE Trans Evol Comput 24(2):201–216 17. Trindade, A.R., Campelo, F.: Tuning metaheuristics by sequential optimisation of regression models. Appl Soft Comput 85(C) (dec 2019) 18. Shadkam E (2021) Parameter setting of meta-heuristic algorithms: a new hybrid method based on DEA and RSM. Environ Sci Pollut Res 29(11 2021):1–23 19. Talbi EG (2013) A unified taxonomy of hybrid metaheuristics with mathematical programming, constraint programming and machine learning. Stud Comput Intell 434(01 2013):3–76 20. Harrison K, Ombuki-Berman B, Engelbrecht A (2019) A parameter-free particle swarm optimization algorithm using performance classifiers. Inf Sci 503(07 2019) 21. Sababha M, Zohdy M, Kafafy M (2018) The enhanced firefly algorithm based on modified exploitation and exploration mechanism. Electronics 7(8):132

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22. Hutter F, Hoos HH, Stützle T (2007) Automatic algorithm configuration based on local search. In: AAAI conference on artificial intelligence 23. Eryolda¸s Y, Durmu¸soglu A (2022) A literature survey on offline automatic algorithm configuration. Appl Sci 12(13) 24. Birattari M (2009) Tuning metaheuristics—a machine learning perspective. Springer, Heidelberg (01 2009) 25. Tatsis V, Parsopoulos K (2020) Reinforced online parameter adaptation method for populationbased metaheuristics. In: IEEE symposium series on computational intelligence (SSCI2020), Canberra, Australia, (12 2020), pp 360–367 26. Hutter F, Hoos HH, Leyton-Brown K (2011) Sequential model-based optimization for general algorithm configuration. In: Coello CAC (ed) Learning and intelligent optimization. Springer, Berlin, Heidelberg, pp 507–523 27. Hoos HH (2012) Automated algorithm configuration and parameter tuning. In: Hamadi Y, Monfroy E, Saubion F (eds) Autonomous search. Springer, Berlin, Heidelberg, pp 37–71 28. Birattari M, Yuan Z, Balaprakash P, Stützle T (2010) F-race and iterated f-race: an overview. In: Bartz-Beielstein T, Chiarandini M, Paquete L, Preuss M (eds) Experimental methods for the analysis of optimization algorithms. Springer, Berlin, Heidelberg, pp 311–336 29. Bartz-Beielstein T, Preuss M (2007) Experimental research in evolutionary computation. In: Proceedings of the 9th annual conference companion on genetic and evolutionary computation, pp 3001–3020 30. Duque Gallego J, Múnera D, Diaz D, Abreu S: In: Solving QAP with auto-parameterization in parallel hybrid metaheuristics, vol 1443. Springer, Cham (08 2021), pp 294–309 31. Eryolda¸s Y, Durmu¸so˘glu A (2022) An efficient parameter tuning method based on the Latin hypercube hammersley sampling and fuzzy c-means clustering methods. J King Saud Univ— Comput Inf Sci 34(10):8307–8322 32. Tatsis V, Parsopoulos K (2019) Dynamic parameter adaptation in metaheuristics using gradient approximation and line search. Appl Soft Computg 74(1 2019):368–384 33. Tatsis V, Parsopoulos K (2017) Differential evolution with grid-based parameter adaptation. Soft Comput 21(8):2105–2127 34. Dzalbs I, Kalganova T (2020) Simple generate-evaluate strategy for tight-budget parameter tuning problems. In: IEEE symposium series on computational intelligence (SSCI2020), Canberra, Australia (12 2020):783–790 35. Santos AS, Madureira AM, Varela LR (2022) A self-parametrization framework for metaheuristics. Mathematics 10(3):475 36. Ferrari A, Leandro G, Coelho L, Gouvea C, Lima E, Chaves C (2019) Tuning of control parameters of grey wolf optimizer using fuzzy inference. IEEE Latin Am Trans 17:1191–1198 37. Bezdek J, Ehrlich R, Full W (1984) Fcm-the fuzzy c-means clustering-algorithm. Comput Geosci 10(12 1984):191–203 38. Wang R, Diwekar U, Padró C (2004) Efficient sampling techniques for uncertainties in risk analysis. Environ Prog 23(07 2004):141–157 39. Dillen W, Lombaert G, Schevenels M (2021) Performance assessment of metaheuristic algorithms for structural optimization taking into account the influence of algorithmic control parameters. Front Built Environ 7(03 2021):618851 40. Eggensperger K, Lindauer M, Hutter F (2017) Pitfalls and best practices in algorithm configuration. J Artif Intell Res 64(05 2017) 41. Tan CG, Siang Choong S, Wong LP (2021) A machine-learning-based approach for parameter control in bee colony optimization for traveling salesman problem. In: 2021 international conference on technologies and applications of artificial intelligence (TAAI), pp 54–59 42. Lessmann S, Caserta M, Montalvo I (2011) Tuning metaheuristics: a data mining based approach for particle swarm optimization. Expert Syst Appl 38(09 2011):12826–12838 43. Hekmatinia A, Shanghooshabad AM, Motevali MM, Almasi M (2019) Tuning parameter via a new rapid, accurate and parameter-less method using meta-learning. Int J Data Mining Model Manag 11(4):366–390

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Chapter 4

QOPTLib: A Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems Eneko Osaba and Esther Villar-Rodriguez

1 Introduction Quantum Computing is expected to provide researchers and practitioners with a novel and revolutionary paradigm for dealing with complex problems in a more efficient way [1]. This kind of computation leverages quantum phenomena to find competent solutions via Quantum Processing Units (QPU). The potential of quantum computing has become apparent in several examples such as the Shor factorization algorithm [2] and the Grover quantum search algorithm [3]. So far, there have been several research areas in which quantum computing has shown its potential, such as cryptography [4], simulation [5], machine learning [6], or optimization [7]. This paper is focused on the last of this research streams. Quantum optimization has generated a profound impact in recent years. How to implement novel quantum solvers or how to introduce quantum methods in already existing classical pipelines or algorithms are currently widespread concerns in the community. In this regard, the fast advances in hardware technology [8] and the democratization in its access [9] have made research take off, especially in the optimization branch. Regarding applications fields, transportation [10], finance [11], energy [8], or medicine [12] are some examples of how quantum optimization can contribute to the development of notable scientific advancements. Even so, research cannot circumvent the state of the hardware. Current quantum computers suffer from certain limitations that directly affect their capability and performance. The current state of quantum computing is known as noisy intermediateE. Osaba (B) · E. Villar-Rodriguez TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain e-mail: [email protected] E. Villar-Rodriguez e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_4

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scale quantum (NISQ, [13]) era. Quantum devices available in this NISQ era are characterized by not being completely prepared to reliable deal with large problems. This situation hinders the evaluation of quantum or hybrid methods being the researchers building their own benchmarks for each scientific proposal. In these very first steps in the quantum algorithmic design a benchmark helps researchers to fairly assess their contributions. Iris dataset [14] or ImageNet [15] are excellent representatives of how a benchmark can be a cornerstone to gain momentum. Thus, this circumstance pushes researchers to generate their own testing benchmarks whenever they try to solve a particular problem using a quantum computer. This is the case even when dealing with well-known optimization problems, as can be seen in studies such as [16–19], where authors built ad-hoc problem instances adapted to the limited capacity of quantum computers. This situation directly affects the replicability and comparison of technical approaches. Taking this situation as main motivation, we present in this paper a quantum computing oriented benchmark for combinatorial optimization problems. This benchmark, coined as QOPTLib, is composed of 40 different instances equally distributed among four problems: the Traveling Salesman Problem (TSP, [20]), the Vehicle Routing Problem (VRP, [21]), the one-dimensional Bin Packing Problem (BPP, [22]), and the Maximum Cut Problem (MCP, [23]). Characteristics of each dataset are described in upcoming sections. Also, we conduct a first experimentation in order to extract a preliminary baseline of results. For conducting these tests, two commercial solvers provided by DWAVE have been employed: a pure QPU based Advantage_system6.1, and the quantum-classical LeapHybridBQMSampler. For each instance of QOPTLib, the best solution found by both solvers after 10 independent runs is given. Our main objective with this study is to propose a benchmark of well-known combinatorial optimization problems as the key element of a testbed in quantum optimization. The rest of this paper is organized as follows: in Sect. 2, we introduce the problems that have been considered in QOPTLib, highlighting briefly the related work done in each of them in the field of quantum computing. After that, Sect. 3 deeply describes QOPTLib. We conduct in Sect. 4 a preliminary experimentation with a pure QPU and a quantum-classical solver. This paper finishes in Sect. 5 with conclusions and further work.

2 Description of the Problems As mentioned in the introduction, QOPTLib contemplates instances regarding four combinatorial optimization problems. This section is devoted to briefly describe each of these problems.

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2.1 Traveling Salesman Problem The TSP is one of the most widely studied problems in operations research and computer science. Despite being a classical optimization algorithm, the TSP is the focus of many research works even today [24, 25], since transportation problems are still in the hype, and because of the analogy between many real-world problems and the TSP formulation. As a result of this interest, the TSP is frequently used as benchmarking problem for testing the quality of newly proposed techniques and solvers [26, 27]; and even for tackling real-world oriented transportation problems [28, 29]. The TSP is defined as a complete graph G = (V, A), where V = {v1 , v2 , . . . , vn } is the group of nodes and A = {(vi , v j ) : vi , v j ∈ V, i = j} is the set of links among these nodes. Additionally, traveling from one node to another has an associated cost ci j . This cost is the same regardless of the direction, i.e., ci j = c ji . Thus, the objective is to find a path which visits each and every node once while minimizing the total cost of the route. Also, the trip must start and finish at the same point. The TSP can be mathematically formulated as follows: minimize f (X) = X

subject to

n j=1 i= j n i=1 i= j



i∈S j∈S i= j

n  n 

ci j xi j

(1a)

xi j = 1, ∀ j ∈ {1, . . . , n}

(1b)

xi j = 1, ∀i ∈ {1, . . . , n}

(1c)

xi j ≥ 1, ∀S ⊂ V,

(1d)

i=1 j=1 i= j

where xi j ∈ {0, 1} takes value 1 if edge (i, j) is used in the solution. Additionally, the objective function is depicted in Formula (1a) as the sum of all costs associated with the edges that compose the route. Furthermore, Restrictions (1b) and (1c) represent that each node must be visited once and only once. Finally, (1d) assures the nonexistence of sub-tours, requiring that any subset of nodes S has to be abandoned at least once. Being such an interesting problem, the TSP has been one of the first combinatorial optimization problems to be solved by a QPU [10], and many works have followed the lead in exploring new solving schemes [30, 31]; improving the formulation or proposing novel variants [32, 33]; or making use of the TSP to solve similar, from the mathematical perspective, real-world use cases [34, 35]. Despite this interest, few advances have been made to create a TSP benchmarking, complicating the replicability and fair evaluation of the research published.

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2.2 Vehicle Routing Problem Like the TSP, the VRP is one of the most renowned and intensively studied problems in artificial intelligence field. In a nutshell, the VRP is an extension of the TSP, in which the objective is to find the optimal route planning for a fleet of vehicles, given the demands of a set of n client. Thus, the problem can be defined in a similar way to the TSP, as a complete G = (V, A) where V represent the set of clients and A the set of connections among them, having each edge (vi , v j ) an associated cost ci j (in this case, also ci j = c ji ). Additionally, in the case of the VRP, the node v0 represents a depot, in which all vehicles should start and end their route. The rest of nodes represent the clients to serve according to their demands qi , which are grouped in Q = {q1 , q2 , . . . , qn }. Lastly, each VRP instance counts with a fleet of vehicles K . Each available vehicle has a limited C capacity. Depending on the VRP variant, the size of K could be limited or unlimited, and the use of a certain vehicle could imply an additional cost to the route. In any case, in the majority of the VRP formulations, the fleet is composed of an unlimited number of free-using identical vehicles. With all this, the main objective of the canonical VRP is to find a number of routes minimizing the total cost, considering that i) each trip must start and end at v0 , ii) each client must be visited once and iii) the accumulated demand satisfied by each route does not exceed the vehicle capacity [36]. Mathematically, the VRP can be formulated as follows [37]: minimize f (X) = X

subject to

p n n   

ci j xri j

(2a)

r =1 i=1 j=1 i= j n n  

xri j = 1, ∀ j ∈ {1, . . . , n}

(2b)

r =1 j=1,i= j n 

xr 1 j = 1, ∀r ∈ {1, . . . , p}

(2c)

j=1 n 

xri j =

i=1 i= j

n 

xr ji , ∀ j ∈ {1, . . . , n}, r ∈ {1, . . . , p}

(2d)

i=1

n n  

q j xri j < C, ∀r ∈ {1, . . . , p}

(2e)

i=1 j=1,i= j p    r =1 i∈S j∈S,i= j

xri j ≤ |S| − 1, ∀S ⊆ {1, . . . , n}

(2f)

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where the binary variable xri j is 1 if edge (i, j) is part of the route r , and p is the number of paths that compose the whole solution. Formula 2a represents the objective function. Restriction 2b guarantees that each customer is visited once. Constraints 2c and 2d assure that each vehicle leaves the deport, and that the number of vehicles arriving to each customer is equal to the amount of vehicles leaving it. Formula 2b regards the capacity restriction, while Constraint 2f ensures the non-existence of sub-tours. The research conducted on the VRP in last decades has been extraordinarily prolific [38, 39], mainly because of the flexibility of the problem to be adapted to a wide variety of real-world settings. As a result of this abundant activity, a plethora of VRP variants have been proposed in the literature, considering different realistic features such as time windows [40], heterogeneous vehicles [41], multiple depots [42], or pickup and deliveries [43]. In addition to that, a specific group of variants coined as Rich VRP [44, 45] has emerged, which refers to these VRP variants contemplating an elevated number of constraints [46]. One immediate consequence of this increasing community is the vast amount of ad-hoc benchmarks. Some of these VRP datasets have become standards for the community, and they are often used as baseline for testing the quality of newly proposed methods. Some examples are the benchmark of Solomon [47], Cordeau [48], Christofides and Eilon [49], or Fisher [50]. Turning our attention to quantum computing, some interesting research has also been conducted in this field, although practical studies are still scarce [10]. In [51], for example, authors present a two-step method consisting of a clustering algorithm to estimate the number of vehicles to later solve each route as a TSP problem by the DWAVE. Further hybrid solvers can be found in [52] or [53]. Also, pure quantum solvers have also been proposed in the last years, as can be seen in [16, 54] or [55]. In any case, it should be considered that, even for hybrid schemes such as the one proposed in [51], most works do the experimentation on small problems, and those targeting larger instances are just centered on formulating different kinds of VRP variants [56, 57] in a theoretical framework.

2.3 Bin Packing Problem The packing of items (or packages) into a minimum number of containers (or bins) is a common task in logistics and transportation systems. In the field of operation research, this problem, known as Bin Packing Problem (BPP), has been in the spotlight for the last years. Depending on the characteristics of both items to store and bins, different variants of this problem can be formulated. Arguably, the simplest BPP formulation is the so-called one-dimensional BPP (1dBPP, [58]), which consists of a set of items I ∈ {i 1 , i 2 , . . . , i n } only defined by their weights wi , and an unlimited number of bins with a maximum capacity C. On top of this simple formulation, more complex problems have been introduced in the literature [59]: such as the two-dimensional BPP (2dBPP, [60]) to define height

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and width of items and bins, and the three-dimensional BPP (3dBPP, [61]), in which the depth is also considered. Besides, all these BPP formulations can be extended to meet new requirements such as fragility [62], time windows [63], or compatibilities [64]. Anyway, even though BPP is still the kingpin of many industrial processes, it was not until 2022 that the first research purely focused on this kind of problem was conducted by the quantum community [65, 66]. Besides those two papers, in [67] we can find a study tackling the problem of filling spent nuclear fuel in deep-repository canisters. Authors formulate this problem as a 1dBPP, solving it using the D-Wave quantum annealer. More recently, authors in [68] explore the first solving algorithm for a 3dBPP through a hybrid quantum solver. Finally, similarly to what occurs with the aforementioned problems, no standard benchmarking for quantum solvers exists, in spite of the fact that there are public datasets such as the BPPLib [69]. This situation contributes to the value of QOPTLib, which includes 10 instances of the 1dBPP.

2.4 Maximum Cut Problem The Maximum Cut Problem, also known as Max-Cut, is a combinatorial optimization problem whose principal objective is to divide the vertices of a graph into two disjoint subsets, in such a way that the number (or the sum of weights in a weighted graph) of crossing edges between these two subgroups is maximum. Proven to be an NP-Hard [70] problem, the MCP has been applied up to now to diverse fields such as network science [71] or clustering [72]. The MCP can be formally defined as an undirected graph G = (V, A), where V is the set of nodes and A is the set of edges. Also, the weight of the edge linking vi and v j is defined as wi, j . Thus, a cut (S,S ) is a partition of V into two subgraphs S, S = V /S. The value of this cut is calculated as the sum of the weights wi j of the edges that connect the two disjoint subsets S and S . As explained before, the goal of the MCP is to maximize the value of a cut. The MCP has been the focus of a myriad number of works over the last decades [73], giving rise to a wide variety of datasets. In this context, the Stanford University published GSet as a standard format for creating problem instances.1 In addition, many quantum algorithms have been applied to the resolution of MCPs, like QAOA [74–76] and quantum annealers [77]. Due to the importance of MCP in the bibliography, it is a good practice to include it in our benchmark.

1

https://web.stanford.edu/~yyye/yyye/Gset/.

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3 Introducing the Generated QOPTLib Benchmarks With all this, we introduce QOPTLib in this paper, which is a benchmark comprised of 40 different instances, evenly distributed among the problems described in Sect. 2: TSP, VRP, 1dBPP, and MCP. QOPTLib is openly available under demand, or online at [78]. The problem sizes have been selected to comprehend both small toy samples and more complex, yet approachable, instances to be solved by a QPU. Furthermore, the biggest instances have been empirically designed according to the capacity of the hybrid methods provided by DWAVE and the practical problem size with a non-zero probability of achieving good results. In this regard, DWAVE has been considered for this study since it is the platform that accepts the largest problem sizes. Being more specific, it is known that current quantum annealers, such as DWAVE, can deal with larger problems in comparison with quantum gate-based methods, such as QAOA [79, 80]. Similarly, in the context of quantum annealers, commercial hybrid approaches can deal with even bigger problem with respect to purely quantum-based alternatives [81]. Thus, our goal is to create a benchmark with a number of instances able to evaluate any quantum solver in any QPU. In addition to this, the instances built should suppose a challenge for both the most restrictive and the most advanced algorithms. Now, we proceed to describe the four different datasets included in our benchmark. Benchmarking instances for the TSP: the dataset generated for the TSP is composed of 10 different instances with sizes ranging from 4 nodes to 25. For the generation of this dataset, two well-known TSPLib instances have been selected as base: wi29 and dj38. These original instances have been then reduced to produce 10 different use cases: wi4, wi5, wi6, wi7, wi25, dj8, dj9, dj10, dj15, and dj22. To keep track of the original instance in TSPLib, each instance has been named as djX and wiX, where X is the size of the problem. Regarding the format, it is TSPLib standard compliant, being readable by existent libraries, such as the Qiskit TSP.2 Figure 1 illustrates the structure of wi4 instance.

Fig. 1 Structure of wi4 TSP instance

2

https://qiskit.org/documentation/optimization/stubs/qiskit_optimization.applications.Tsp.html.

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Fig. 2 Structure of P-n5 VRP instance

Fig. 3 Structure of BPP_4 BPP instance

Benchmarking instances for the VRP: 10 newly created instances of the VRP have been included in QOPTLib, composed of 4 to 8 nodes. All these cases are reductions of the well-known P-n16-k8 and P-n23-k8 instances from the Augerat CVRP benchmark [82]. Furthermore, in order to relax the complexity of the problem, the demands q of all clients have been set to 1, and the vehicle capacity C has been chosen to ensure that the optimum solution contains only two routes. Each instance has been named as P-nX_Y, where X is the number of nodes and Y is the suffix to distinguish the set of instances with same X . Additionally, the VRP dataset built is CVRPLib3 compliant. We depict in Fig. 2 an example of instance, specifically focused on P-n5_1. Benchmarking instances for the 1dBPP: in QOPTLib 10 cases for the 1dBPP have been incorporated. In this case, these 10 instances have been crafted by the authors of this paper, following the format described in already published studies such as [65, 66]. They have been randomly configured while keeping set boundaries: from 3 to 14 for number of packages; {10,12,15} for bin capacities and 2 or 5 as for the values of package weights. Additionally, the number of bins available on each instance is the same as the number of packages that compose it. Finally, Fig. 3 shows the structure of the instance BPP_4, contemplating the number of items on the first line, the maximum capacity in the second one, and the randomly generated item weights in the rest of the file. Benchmarking instances for the MCP: the dataset included in QOPTLib for the MCP is composed of 10 instances with sizes ranging from 10 to 300 nodes. Each 3

http://vrp.galgos.inf.puc-rio.br/index.php/en/.

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Fig. 4 Structure of an MCP instance composed of 4 nodes

case has been coined as MaxCut_X, being X the cardinality of graph G. All these instances have been randomly generated through a Python script which has been implemented for this specific research. This instance generation script is also openly available in the Mendeley Data repository [78]. It is also interesting to mention that all use cases have the standard format GSet, which eases their automatic reading by already implemented libraries.4 Figure 4 describes the structure of an instance with these parameters: cardinality of G and total sum of weights (first line), edge {i, j, w} (the rest of the lines), where i is the origin node, j the destination node, and w the weight of this link.

4 Preliminary Experimentation Despite not being the main objective of this paper, we present in this section a first complete set of results for QOPTLib. For this purpose, we resort to the DWAVE system, embracing two different solving approaches. On the one hand, we use the Advantage_system6.1 as a quantum pure alternative. This computer has 5616 working qubits, which are distributed using a Pegasus topology. On the other hand, we employ the LeapHybridBQMSampler, which is a hybrid solver of DWAVE to deal with general, often larger, binary quadratic problems. Having said this, Table 1 shows the results obtained by both approaches. As mentioned, hybrid solver of leap allows addressing larger problems. Consequently, this hybrid scheme can deal with the whole QOPTLib, whereas the pure quantum Advantage_system6.1 can only cope with a smaller proportion of the entire benchmark due to its limited capacity. For each problem instance, 10 independent runs have been executed. For each case, we depict the best results obtained as a baseline for future studies. Furthermore, Symbol – represents “no outcome” when the instance is unprocessable for the pure quantum approach.

4

https://qiskit.org/documentation/optimization/stubs/qiskit_optimization.applications.Maxcut. html.

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Table 1 Best results obtained by Advantage_system6.1 (QPU) and LeapHybrid BQMSampler (Hybrid) for the whole QOptLib benchmark. – represents that the instance is unmanageable for the solver Traveling salesman problem Bin packing problem Instance Results Instance Results QPU Hybrid QPU Hybrid wi4 6700 wi5 6786 wi6 9815 wi7 7267 dj8 3269 dj9 – dj10 – dj15 – dj22 – wi25 – Vehicle routing problem Instance Results QPU P-n4_1 97 P-n4_2 121 P-n5_1 120 P-n5_2 315 P-n6_1 – P-n6_2 – P-n7_1 – P-n7_2 – P-n8_1 – P-n8_2 –

6700 6786 9815 7245 2794 2438 3155 5268 13005 83132

Hybrid 97 121 94 295 118 122 119 164 153 269

BPP_3 2 BPP_4 2 BPP_5 3 BPP_6 – BPP_7 – BPP_8 – BPP_9 – BPP_10 – BPP_12 – BPP_14 – Maximum cut problem Instance Results QPU MaxCut_10 25 MaxCut_20 97 MaxCut_40 355 MaxCut_50 560 MaxCut_60 756 MaxCut_100 – MaxCut_150 – MaxCut_200 – MaxCut_250 – MaxCut_300 –

2 2 2 3 4 4 4 6 7 7

Hybrid 25 97 355 602 852 2224 4899 8717 13460 19267

5 Conclusions and Further Work In the field of quantum optimization, the evaluation of novel resolution methods often faces the problem of the non-existence of benchmarks as standards for fair comparisons. The community working on TSP and BPP, for example, relies on wellknown libraries, such as TSPLib or the BPPLib. However, these benchmarks are not suitable for current quantum devices. This situation pushes researchers to create their own instances adapted to the quantum computers they are using. This has a significant impact on the replicability of the studies and the generation of common knowledge.

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With this motivation in mind, we have introduced QOPTLib in this paper, which is a quantum computing oriented benchmark for combinatorial optimization. QOPTLib includes 40 different instances, equally distributed among four well-known problems: Traveling Salesman Problem, Vehicle Routing Problem, one-dimensional Bin Packing Problem, and the Maximum Cut Problem. In addition to that, we have also presented a first complete solving of QOPTLib using two commercial solvers provided by DWAVE: the pure quantum Advantage_system6.1, and the LeapHybridBQMSampler. The principal objective is not to find the optimality of QOPTLib, but to provide with a baseline results, hoping that future works beat these outcomes with newly proposed algorithms. Our team has now the sights set on two main research lines. In the short-term, we plan to increase the scope of QOPTLib, aggregating further instances to accommodate additional combinatorial optimization problems, such as the Job-Shop Scheduling Problem [83] or other problems related with economics [84] or energy [85] fields. In the medium term, we will also propose new quantum procedures tested on OPtLib, with the main goal of assessing newly proposed quantum computing-based solvers. Acknowledgements This work was supported by the Basque Government through ELKARTEK program (BRTA-QUANTUM project, KK-2022/00041), and through HAZITEK program (Q4_Real project, ZE-2022/00033). This work was also supported by the Spanish CDTI through Plan complementario comunicación cuántica (EXP. 2022/01341)(A/20220551).

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Chapter 5

Benchmarking for Discrete Cuckoo Search: Three Case Studies Aziz Ouaarab

1 Introduction Optimization algorithm benchmarking is a tool to present the performance mechanisms of algorithms and allow the obtained experimental results of its implementation to be comparable. It has to consider several topics [3, 6] such as goal statement, problem specification, algorithm choice, performance measurement, reproducibility and result comparability. These topics serve the goal of making a useful guideline for future researchers working on combinatorial optimization. The objective of the chapter is to summarize three implementation case studies of DCS while solving combinatorial optimization problems. It describes the common and specific steps of solving each COP and gives the key metrics to reproduce and compare experimental results. Sections that compose the chapter are four. The first (second section) presents a general combinatorial optimization problem statement with definitions and objective functions. Section 3 shows the general side of Discrete Cuckoo Search. It gives a description of its main functions independently of the solved problem. Section 4 presents the adaptations made in DCS to solve each studied COP. These adaptations are solution design and move operator. Section 5 lists tuned parameters, the solved instances and performance of DCS, and the chapter concludes in last section.

A. Ouaarab (B) Cadi Ayyad University, Marrakesh, Morocco e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_5

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2 COPs Statements Combinatorial optimization problems are very different if we look at their fields of application or their constraints. However, the moment we start their abstraction, we observe that they show a great similarity in terms of how the solution can be presented, the moves from one solution to another. This similarity cannot avoid any free launch theorem, but when these problems are solved with metaheuristics we can keep the same strategies for a variety of problems. The only thing that is changed is the adaptation of these strategies to each problem. In this section, we will show the three benchmark case studies, their definitions and the objective function of each case.

2.1 Studied COPs The three studied COPs are the most resolved literature problems. They are taken from three different families. The first is QAP. It represents the family assignment problems [7] where a set of resources (tasks or facilities) are assigned to an equal number of activities (agents or sites) with the objective of maximizing or minimizing the assignment profits or costs. The second family is composed of scheduling problems [23] that launch a set of tasks on a constant number of idle machines under the precedence constraint. The last problem family regroups all routing problems that try to combine or permute a set of weighted edges to connect two points while optimizing the total path. This family will be represented by TSP. 2 1

3

6

4 5

The Quadratic Assignment problem has as an objective, the minimization of the total facility construction and operation cost. The constraint is that each facility has an economic activity and this activity depends on other facilities located in different sites. So, the global gain is related to the location of a facility regarding the others and to the economic activity.

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The Travelling salesman problem seeks the shortest path or the lowest travel cost (distance) while visiting all n cities once and only once and finishing in the first city. 1

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Including Job Shop Scheduling problem, the family of scheduling problems is commonly defined by the following components: • A number of jobs or operations J i to perform; • A number of machines or resources Mi to occupy by the predefined jobs; • An allocation relation between resources and operations that can be presented with the help of a Gantt chart.

2.2 Formal Definitions The three COPs have been defined formally in many research works [1, 12, 13, 15]. In this section, a terms and formula definition approach will be provided to explain the role of each term separately.

2.2.1

Quadratic Assignment Problem

A formal definition of QAP instance could be decomposed in terms as follows: • • • •

S: QAP solution φ: solution permutation Q = {1, 2, . . . , N }: set to be permuted that defines a solution N : instance dimension or the number of sites

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• • • •

a: flow matrix between facilities ai j : flow between a couple i and j of facilities b: matrix of distances between each couple of sites bφ(i)φ( j) : distance between a couple of sites φ(i) and φ( j) assigned to the facilities iand  j N N • i=1 j=1 ai j bφ (i)φ( j): objective function as shown in Algorithm 1. For a given solution, we have the following equations: • φ(i) = k: here we assign a facility i to the site k • φ = (φ(1), φ(2), . . . , φ(N )): one of the set Q permutations. The QAP objective function is to find the smallest value of products f low × distance sum [22]. Algorithm 1: Objective function of QAP Input: Solution Result: SolFitness for i = 0 to Solution length do for j = 0 to Solution length do Fitness=Fitness+ai j bφ (i)φ( j); end end

2.2.2

Job Shop Scheduling Problem

To give a formal definition of JSSP ([10]), a list of terms are defined as follows: • • • • • • • • •

m: number of the performed machines M: set of machines j: a selected job that runs in m machines J : set of jobs n: number of jobs O j1 : operation order of job j in machine 1 p ji : the time taken by the job j while occupying machine i C ji : O ji completion time Cmax : makespan or the time we need to finish jobs of all machines.

Each job j is run on each machine i in a given order of operations. In JSSP, the interdependence of operations is presented in two constraints as follows [1, 16]: • O ji cannot be executed in a machine i if this one is not idle • O ji cannot be executed in a machine i if its predecessor Oli did not complete. In relation to jobs and machines, we can cite another two constraints: • Each job is launched on each machine once

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• A given machine is occupied at a time by only one job and cannot be interrupted. The schedule fitness function of the job shop scheduling problem that can be minimized calculates the makespan value as follows: minimize Cmax = Cn×m

(1)

Regarding Eq. (1), the quality of a solution is calculated via the makespan in Algorithm 2. Algorithm 2: JSSP fitness Input: Schedule Result: Completion time Machine is to update the maximum machines’ time; J ob is to update the maximum jobs’ time; J ind is an index of the operation of current machine; /* Initialization: Machine = 0, J obs = 0 and J ind = 0 */ /* N for numbers of jobs */ /* M for numbers of machines */ for i = 0 to N × M do From Sol(i), find j the current job ; From J ind( j), find m the current machine operation ; Calculate the max(Machine(m),Job( j)); Update Machine, J ob and J ind; end Calculate max of machines’ completion time;

2.2.3

Travelling Salesman Problem

The following statements composed the formal definition of TSP [9]: • C = {c1 , . . . , cn }: set of cities • E = {(ci , c j ) : i, j ∈ {1, . . . , n}}: set of all possible arcs that connect each couple of cites ci and c j • dci c j : arc associated cost between two cities • (ci x , ci y ): coordinates of the city ci . The problem is to minimize a Hamiltonian tour that passes through each city once. The following equations prepare the calculation of the objective function:  • dci c j = (ci x − c j x )2 + (ci y − c j y )2 : the Euclidean distance from city ci to city cj • π = (π(1), π(2), . . . , π(n)): a given permutation of n cities n−1  • f (π) = dπ(i)π(i+1) + dπ(n)π(1) : the cost of a permutation. It is then the objective i=1

function of our problem.

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So the solution fitness is a quality value that is assigned to each TSP solution, and it implements Algorithm 3. Algorithm 3: TSP tour Fitness Input: tour Result: Fitness Fit = 0; for i = 0 to Dimension − 1 do Fitness + = Distance from tour (i) to tour (i + 1); end return Fitness

3 DCS Common Resolution 3.1 General Algorithm All metaheuristics have mechanisms that balance between different strategies of seeking the optimum solution [24]. They try to balance between global and local searches, between exact and stochastic methods. In this context, we will present in this section the main strategies of DCS [17] to find the best balance between intensification and diversification. As shown in Algorithm 4, DCS makes global and local searches by implementing three methods: GetCuckoo, SmartCuckoo and WorstCuckoo. Algorithm 4: Discrete Cuckoo Search 1: Objective function f (x), x = (x1 , . . . , xd )T 2: Generation of the n nests xi (= 1, 2, . . . , n) as the initial population 3: while (t σ, 0 otherwise

(1)

in which σ ∼ U (0, 1), and T () stands for a transfer function described as follows: T (x) =

1 . 1 + e−x

(2)

After the optimization procedure, the metaheuristic best agent’s (lowest fitness/highest validation accuracy) features are used to compose the new sets and hence used to train and test a new classifier.2 Each full-pass on the algorithm mentioned above depicts a so-called “run". Therefore, to provide a more robust analysis, we conduct 20 runs with different seeds (different splits) for each (metaheuristic, dataset) pair, followed by a statistical analysis according to the Friedman test [8, 9] with a significance of 0.05 (5%), followed by a Nemenyi post-hoc test [17]. Finally, we used Opytimizer [26] as the metaheuristic package and hosted the paper’s source code at GitHub.3

4.2 Experiments In this section, we present the obtained results guided by the methodology presented in Sect. 4.1. Also, we conducted two statistical tests to confirm the robustness of our results. Figures 2 and 3 illustrate the convergence of each metaheuristic algorithm applied to the datasets presented in Table 1. It should be noted that this process phase is represented by Fig. 1a. The CS technique, represented by the orange line, obtained the best convergence in all datasets compared to the other metaheuristics. The FA algorithm obtained the worst convergence in all datasets while PSO and FPA alternated between the second-best performance. Figures 4 and 5 illustrate the mean of selected features in each dataset. When analyzing the FA technique, it can be noticed that it selected fewer features in the Arcene and Sonar datasets. In contrast, in the BASEHOCK, Caltech101, Coil20, Madelon, ORL, PCMAC, Semeion, Spambase, Vehicle, and Wine datasets, FA was the technique that performed the worst. The BA technique obtained the best results by selecting fewer features in the BASEHOCK, Caltech101, Lung, Phishing, and 2

Note that the final evaluation discards the validation set and uses only the training and testing ones. 3 The source code is available at https://github.com/gugarosa/mh_feature_selection.

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Fig. 2 Convergence of metaheuristic algorithms on a Arcene, b BASEHOCK, c Caltech101, d Coil20, e Isolet, f Lung, g Madelon, and h ORL datasets

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Fig. 3 Convergence of metaheuristic algorithms on a PCMAC, b Phishing, c Segment, d Semeion, e Sonar, f Spambase, g Vehicle, and h Wine datasets

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Fig. 4 Average selected features considering each metaheuristic algorithm on a Arcene, b BASEHOCK, c Caltech101, d Coil20, e Isolet, f Lung, g Madelon, and h ORL datasets

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Fig. 5 Average selected features considering each metaheuristic algorithm on a PCMAC, b Phishing, c Segment, d Semeion, e Sonar, f Spambase, g Vehicle, and h Wine datasets

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Table 2 Results concerning the test set over all datasets Datasets

BA

Arcene

57.59 ± 10.32 57.47 ± 8.26

CS

FA

FPA

PSO

59.87 ± 9.23

57.75 ± 8.55

59.28 ± 11.38 53.68 ± 9.56

NB

BASEHOCK 94.02 ± 0.88

94.36 ± 0.98

95.79 ± 0.98

94.07 ± 1.18

93.95 ± 0.98

Caltech101

34.09 ± 1.39

35.67 ± 1.52

34.78 ± 1.61

34.86 ± 1.65

34.37 ± 1.68

95.79 ± 0.98 34.89 ± 1.53

Coil20

83.95 ± 4.95

86.92 ± 5.24

82.85 ± 4.96

84.93 ± 5.02

84.70 ± 4.88

79.52 ± 4.69

Isolet

78.85 ± 3.07

83.53 ± 2.67

77.61 ± 3.05

81.01 ± 2.01

80.09 ± 3.08

75.45 ± 2.90

Lung

71.89 ± 6.70

74.15 ± 7.87

71.84 ± 6.67

73.59 ± 8.79

72.24 ± 7.04

67.23 ± 7.14

ORL

38.73 ± 5.14

40.48 ± 5.84

38.66 ± 5.39

39.34 ± 5.66

38.86 ± 4.92

35.42 ± 4.80

PCMAC

82.49 ± 1.86

84.26 ± 2.12

85.01 ± 2.16

82.84 ± 2.19

82.48 ± 2.20

85.29 ± 2.01

Phishing

91.39 ± 0.59

92.26 ± 0.54

91.16 ± 0.62

91.84 ± 0.60

91.60 ± 0.61

69.20 ± 1.08

Segment

85.77 ± 4.15

89.75 ± 1.68

84.69 ± 3.95

89.52 ± 1.43

86.99 ± 3.90

77.23 ± 2.77

Semeion

78.34 ± 2.91

81.00 ± 2.37

76.21 ± 2.36

78.17 ± 2.88

78.37 ± 2.91

75.43 ± 3.14

Sonar

70.09 ± 6.99

73.22 ± 5.61

69.63 ± 5.74

71.31 ± 6.41

69.58 ± 6.71

69.55 ± 4.28

Spambase

88.12 ± 1.67

90.23 ± 0.78

87.74 ± 1.61

89.57 ± 1.23

88.82 ± 1.92

78.95 ± 3.71

Vehicle

51.31 ± 6.84

54.34 ± 5.06

50.31 ± 6.30

53.85 ± 5.21

51.43 ± 7.17

43.58 ± 5.77

Wine

94.02 ± 5.14

94.28 ± 4.45

93.71 ± 4.98

94.56 ± 4.54

94.00 ± 3.98

97.06 ± 3.13

Wine datasets obtaining a tie with the CS technique. The CS technique selected fewer features in the Coil20, Isolet, Segment, Semeion, and Vehicle datasets, tying with the FPA technique. Next, the FPA technique selected fewer features in the Madelon, ORL, and PCMAC datasets. Finally, the PSO technique achieved the best performance in the feature selection task in the Spambase dataset. Table 2 presents the final evaluation of the metaheuristics obtained in the test set in each dataset. This process is illustrated in Fig. 1b. It is worth noting that the values in the table represent the mean and standard deviation considering 20 independent rounds. Note, too, that the top performers are highlighted in bold. The CS technique obtained the best results in the final evaluation, except for the Arcene and BASEHOCK datasets that had the best performance achieved by the FA technique and in the Madelon, PCMAC, and Wine datasets where the Naïve Bayes classifier obtained the best performance. We used two statistical tests to test the results’ robustness: the Friedman, post-hoc Nemenyi, and Wilcoxon Signed-Rank tests. For the first test, on our null hypothesis H0 , we assume that all metaheuristics are equal. However, in the alternative hypothesis Ha , we assume that there are differences among the metaheuristics. For the Arcene (0.3841), Madelon (0.7348), ORL (0.2191), Sonar (0.0974), and Wine (0.6949) datasets, the p-value, shown in parentheses, is greater than the adopted significance level. Therefore, we assume H0 that all metaheuristics performed statistically the same in these datasets. The p-value was lower than the significance level for the other datasets. That is, H0 is rejected, and we assume Ha . However, for those datasets where the Friedman test showed a difference between the metaheuristic approaches, we employed the Nemenyi post-hoc test, illustrated in Fig. 6. The top

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

Fig. 6 Nemenyi test on a BASEHOCK, b Caltech101, c Coil20, d Isolet, e Lung, f PCMAC, g Phishing, h Segment, i Semeion, j Spambase, and k Vehicle datasets

6 Metaheuristics for Feature Selection: A Comprehensive … Table 3 Results concerning the test set over all datasets Datasets BA CS FA Arcene BASEHOCK Caltech101 Coil20 Isolet Lung Madelon ORL PCMAC Phishing Segment Semeion Sonar Spambase Vehicle Wine

= = = = = = = = = = = = = = = =

= = = = = = = = = = = = = = = =

= = = = = = = = = = = = = = = =

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FPA

PSO

= = = = = = = = = = = = = = = =

= = = = = = = = = = = = = = = =

line in the diagram is the axis along which each metaheuristic ranks average, from the most important ones located further to the left side to the least important ones located to the right side. Groups of metaheuristics that are statistically similar to each other are connected. The critical difference (CD) is shown above the graph. Following, we perform the Wilcoxon Signed-Rank test where in the null hypothesis H0 , we assume that the result obtained by the Naïve Bayes classifier is equal to the result obtained using feature selection for each of the metaheuristics and in contrast, in Ha , we assume that there is a difference between the results obtained. In Table 3, it can be seen that the symbol = represents that the performance of the Naïve Bayes classifier using the respective technique for feature selection was similar to the performance of the classifier without feature selection, i.e., the null hypothesis H0 is assumed. In contrast, the symbol = represents that H0 was rejected and, therefore, the alternative hypothesis is accepted.

5 Conclusions In this chapter, we study the use of metaheuristic algorithms with regard to the feature selection task. At first, a literature review was conducted, surveying works using different metaheuristics for the feature selection task. Following, we demonstrate how a hands-on, employing well-established and easy-to-use tool, the Opytimizer [26] library, can be used for the feature selection task. Furthermore, following the

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hands-on demonstration, an experiment was carried out. We chose five metaheuristics, BA, CS, FA, FPA, and PSO, for the feature selection task in sixteen benchmark datasets. The experimental results showed that CS was superior to the other metaheuristics regarding convergence. Regarding the number of selected features, both BA and CS performed similarly. The experimental results also demonstrated superiority in the performance of all metaheuristics concerning the Naïve Bayes classifier, emphasizing CS, which obtained the best performance. However, the study also demonstrated that each metaheuristic has internal mechanisms that must be studied for each task in which they are used. Therefore, we conclude that using metaheuristics is an excellent alternative for the feature selection task.

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Chapter 7

AL4SLEO: An Active Learning Solution for the Semantic Labelling of Earth Observation Satellite Images—Part 1 Corneliu Octavian Dumitru, Gottfried Schwarz, and Mihai Datcu

1 Introduction One of the most demanding aspects in Machine Learning (ML) image classification is the necessity for large volumes of already labelled data. So far, most of the labelled reference data has been created manually [1]. In the last years, another topic that has become more and more prominent in ML is Active Learning (AL), which provides automated or semi-automated methods for identifying and labelling new data. AL promises great savings by radically reducing the amount of manual labelling required from the users. Generally, AL methods call for some interaction between the ML classifier and expert users. Usually, with only a few training examples provided by a user, an AL method can classify and label a data set of millions of samples (or image patches) with high accuracy (of about 90%, a result obtained by the ExtremeEarth project, [2], and detailed in the conclusion section of Part 2). The main purpose of this chapter is to introduce and use an AL method for the semantic labelling of various types of SAR (Synthetic Aperture Radar) and multispectral images acquired by various sensors (e.g., TerraSAR-X, Sentinel-1, WorldView-2, Sentinel-2). Here, the focus is on the extraction of semantic classes and not necessarily on the accuracy with which these classes are classified (for our first accuracy evaluations, see [3]). The method was successfully applied during the ExtremeEarth project for the generation of large semantic benchmark data sets for polar areas. What is Active Learning? “Active Learning is a special case of machine learning in which a learning algorithm can interactively query a user (or some other information source) to label new data with the desired outputs. There are cases in which the volume of unlabelled data is very large and the manual labelling is expensive. In C. O. Dumitru (B) · G. Schwarz · M. Datcu Remote Sensing Technology Institute, German Aerospace Center (DLR), 82234 Wessling, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_7

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such a case, learning algorithms can actively query the user for labels. This type of iterative supervised learning is called active learning. Since the learner chooses the examples, the number of examples to learn a class can often be much lower than the number required in normal supervised learning ...” [4]. AL has important advantages when compared with Shallow Machine Learning (SML) or Deep Learning (DL) methods, as shown in [5]. This comparison can be made from the point of selected training data, volume of data to be trained, number of generated classes, classification accuracy, and speed of the training. The clear advantage of AL that we propose here is that, in only a few minutes and with a very small number of training samples (with 7 to 10 representative patches tiled from EO images given by the users, typically comprising 1 KB of data), we can train large volumes of data (GB or TB representing the volume of data to be analysed) with a classification accuracy (e.g., precision/recall) of 85-90% (results obtained by the CANDELA project, [6]). Another important point is its adaptability to user conjectures where the user can discover and understand the reality on the ground, while extracting the best classes and providing the number of classes he/she considers. In summary, the goals of labelling with such techniques are as follows: (1) Analysis of small and large sets of images with many classes that can be defined by the users; (2) Analysis of land cover/use images, but also ocean surfaces and cloud cover (in the case of optical sensors); (3) Assignment of general or fine semantic labels depending on the sensor resolution; (4) Assignment of single labels or weighted multi-labels (depending on the study case); (5) Inclusion of user knowledge in the semantic labelling; (6) Inclusion of the attainable classification accuracy (expert opinions, but also precision/recall metrics); and (7) Application to single images but also to image time series for label generation. In the following, we describe three study cases using a Cascaded Active Learning (C-AL) method [5, 7–9] for semantic labelling of Earth observation (EO) satellite images. Semantic multi-level labelling represents our first study case that analyses the impact of the patch size on the semantic labelling and the reduction of the processed volume of data that is obtained when changing the patch size. The results are given for several TerraSAR-X images of urban areas acquired all over the globe. Semantic multi-sensor labelling is the second study case that investigates the impact of various satellites on the semantic labels that can be obtained. This analysis was performed with three satellites (WorldView-2, TerraSAR-X, and Sentinel-1) covering two cities (Munich, Germany, and Venice, Italy). Semantic multi-temporal labelling is the third study case that examines the temporal evolution of an area in terms of changes that the semantic labels undergo. We analysed three different areas using three satellites: Sendai in Japan based on TerraSAR-X images, Belgica Bank in Greenland based on Sentinel-1, and the Danube Delta in Romania based on Sentinel-2. Then the main contributions of Part 1 and Part 2 can be described by the following three bullets:

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• Semantic labelling of Earth observation images on different levels. • Joint semantic labelling of different types of sensor images. • Understanding of image time series. This Part 1 is organised as follows: Section 2 summarises a short state of the art in terms of AL initiatives for EO. Section 3 contains the characteristics of each data set compiled for each study case. Section 4 presents the implementation details of a cascaded active learning approach, while Sect. 5 describes the main modules of the proposed workflow needed for each study case. Section 6 gives a conclusion about the theoretical framework of the AL method and the data sets. In Part 2, Sect. 1 details the results by discussing typical examples for each individual study case using the methodology and data sets from Part 1. The conclusions of both parts (Part 1 and Part 2) are given in Sect. 2.

2 State of the Art As for the AL methods applied to Earth observation images, a number of approaches presented in [7, 10–13] have to be mentioned. These AL methods were applied at pixel level in [10–12], at patch level in [7], and at parcel level in [13] and also deal with classification uncertainties depending on the image diversity. In [10], Demir et al. describe several batch-mode AL strategies in order to apply AL methods to multiclass learning when using a Support Vector Machine (SVM). The main idea of this approach is based on the use of two criteria: uncertainty and diversity. The uncertainty criterion is linked to the classification confidence of the selected supervised algorithm. In contrast, the diversity criterion has as objective the selection of unlabelled samples comprising a large diversity of samples, thereby reducing the redundancy of the selected samples. A robust validation was made by exploiting very high-resolution multispectral QuickBird images as well as hyperspectral images [10]. The resulting number of classes depends on the images and varies between six semantic classes for the first image and eight or thirteen semantic classes for the second and third images. In [11], Débonnaire et al. study the use of AL and other standard ML methods for change detection of Satellite Image Time Series (SITS). The methods comprise random-forest-based heuristics that use a combination of uncertainty and diversity criteria, and a classic SVM breaking heuristic ties. The validation of the methods was made on multispectral SPOT images for a period of more than 20 years but considering only four semantic classes. In [12], Güttler et al. present an active transductive learning method for object classification of satellite images. The method is based on three components: a transductive setting, the required label propagation, and the applied AL strategy. The transductive approach considers both labelled and unlabelled image objects to perform the classification as they are all available at training time, while the AL strategy smartly guides the compilation of the training set being employed by the user. The

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validation of the method was made with multispectral RapidEye images considering nine semantic classes. In [7], Blanchart et al. propose a multistage active learning process, namely a cascade of classifiers working each at a certain scale on a patch-based representation of images. At each scale, the nonrelevant parts of the image patches are discarded, thus reducing the volume of the data to be analysed. By reducing the size of each patch (going from one scale to another scale), this operation captures the properties of a target object quite well. A validation was made with QuickBird images and SAR images using 10 semantic classes for the former images and six classes for the latter images. In [13], Slimene et al. propose an AL technique based on random forests and a mean-shift classifier. This technique is a parcel-based AL method, suitable for cultivated agricultural areas. As agricultural areas in France are measured in parcels and these are catalogued accordingly, the AL classification is made at parcel level and not at pixel level. A validation of the method was made with a multispectral SPOT 6 image. In general, recent trends in AL are related to multi-label AL, hybrid AL, AL for classification with abstention, and AL in a single-pass context. For further details, see [14] and [15]. Moreover, in [16], Khanna proposes a Deep-Learning-based AL strategy that determines which data points should be labelled.

3 Data Set Description The overall data set being used in this chapter is structured in three parts that correspond to the three study cases. The first data set contains images of the single-band TerraSAR-X sensor [17] acquired in multi-look ground range detected mode, as high-resolution (HS) spotlight products after being radiometrically enhanced. The selected products are horizontally polarised (HH) and were acquired during ascending or descending passes. In this case, the resolution of the images is 2.9 m, and their pixel spacing is 1.25 m. For evaluation, we chose from the entire data set described in [18] a set of images (one image per city) that covers (a) Ten North American cities (Ciudad Juarez, Los Angeles, North San Diego, South San Diego, Poway, Sun Lakes, Tijuana, Tucson, San Francisco, and Santa Clarita); (b) Fourteen European cities (Porto in Portugal, Garmisch in Germany, Naples in Italy, London in the UK, Barcelona in Spain, Strasbourg in France, Belgrade in Serbia, Helsinki in Finland, East of Amsterdam in the Netherlands, Kassel in Germany, Zeebrugge in Belgium, Venice in Italy, Bydgoszcz in Poland, and Thessaloniki in Greece); and (c) Seven Middle Eastern cities (Ashdod in Israel, Beirut in Lebanon, Baghdad in Iraq, Cairo in Egypt, Abu Nakhlah in Qatar, Dubai in the United Arab Emirates, and Riffa in Bahrain). The quick-look images of the first ten studied cities are shown in Fig. 1. The second data set contains pairs of multi-sensor images (one image acquired by TerraSAR-X [17], by Sentinel-1 [19], and by WorldView-2 [20]) covering two

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Fig. 1 TerraSAR-X quick-look images of ten US cities (from left to right, top to bottom): Ciudad Juarez, Los Angeles, North San Diego, South San Diego, Poway, Sun Lakes, Tijuana, Tucson, San Francisco, and Santa Clarita

European cities, namely Munich, Germany, and Venice, Italy. The TerraSAR-X images are in enhanced ellipsoid-corrected mode, are high-resolution spotlight products, and radiometrically enhanced. They are in VV polarisation with a resolution of 2.9 m, while their pixel spacing is 1.25 m. The second sensor is the single Cband Sentinel-1 imager in interferometric wide swath mode generating ground range detected products. For land areas, the Sentinel-1 sensor provides two polarisations, namely VV and VH. However, in order to obtain image data being comparable to TerraSAR-X, we only selected VV data. Their resolution is 20 m with a pixel spacing of 10 m. For the third sensor, namely WorldView-2, its images were acquired with a resolution of 1.87 m for the multispectral images (from the available eight bands only the RGB bands were used) and with 0.46 m for the panchromatic images. The images were resampled in order to co-align them properly [21, 22]. The quick-look images of the two selected target areas are shown in Fig. 2. The last data set contains acquisitions of a selected area over a period of time made by the same sensor. The first case is the area of Sendai, Japan, affected by a tsunami in 2011 [23]. These acquisitions were made using the TerraSAR-X sensor between March 12th, 2011 and June 19th, 2011 to which we added two images acquired (prior to the tsunami) on September 21st, 2008 and October 20th, 2010. These two were the only available images for this area that had been taken with the same parameters like the ones from 2011. All these nine TerraSAR-X images are StripMap products that were geo-coded with ellipsoid correction and radiometrically enhanced. Their polarisation is HH with a resolution of 5.77 m and a pixel spacing of 2.5 m. The second case is the area of Belgica Bank in Greenland [24], an area that was affected by the melting of local ice in 2018 and 2019. For the analysis of this area, the Sentinel-1

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Fig. 2 (Top) Quick-look images of the city of Munich, Germany, and their multi-sensor images: (from left to right) TerraSAR-X, Sentinel-1, WorldView-2 multispectral, and WorldView-2 panchromatic. (Bottom) Quick-look images of the city of Venice, Italy, and their multi-sensor images: (from left to right) TerraSAR-X, Sentinel-1, WorldView-2 multispectral, and WorldView-2 panchromatic

SAR sensors (comprising both Sentinel-1A and Sentinel-1B) were used to obtain one image per month between January, 2018 and December, 2019. These images were taken in interferometric wide swath mode yielding ground range detected products. For the polar areas, the Sentinel-1A/B sensors provide images with HH and HV polarisations. Their pixel spacing is 10 m with a resolution of 20 m. In the last case, the scanned area is the Romanian part of the Danube Delta [25]. For this area, the Sentinel-2 optical sensors (comprising both Sentinel-2A and Sentinel-2B) [26] were used with 13 multispectral bands and sampling distances between 10 m and 60 m (depending on the selected bands). For demonstration, we only selected the RGB bands with 10 m sampling distance (a study of band impact is contained in [27]). The analysis was made for a period of almost one year (between April, 2016 and June, 2017) selecting only Sentinel-2 images with low cloud level. In total, there are 10 images. The quick-look images of this last selection are shown in Fig. 3.

Fig. 3 Quick-look examples from the series of images analysed for each location: (left) Sendai in Japan, (centre) Belgica Bank in Greenland, and (right) the Danube Delta in Romania

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Table 1 Most important parameters of the used sensors Study case

Instrument

Type

Number of bands/selected bands for the experiments

Resolution (m)

Pixel spacing (m)

Polarisation

First case

TerraSAR-X

SAR X-band

1/1

2.9

1.25

HH

Second case

TerraSAR-X

SAR X-band

1/1

2.9

1.25

VV

Sentinel-1

SAR C-band

1/1

20

10

VV and HH

WorldView-2

Multispectral

8/3

1.87

–

–

WorldView-2

Panchromatic

1/1

0.46

–

–

TerraSAR-X

SAR X-band

1/1

5.77

2.5

HH

Sentinel-1

SAR C-band

1/1

20

10

HH and HV

Sentinel-2

Multispectral

13/3

10/20/60

–

–

Third case

Table 1 shows, as a synthesis, the parameters of the image data for the three study cases. For the multispectral images, only the RGB bands were selected. A detailed study of the band selection and the types of semantic labels to be identified is given in [27]. For the second study case, the multi-sensor case, the choice of locations was based on the availability of multispectral images and the closeness of their acquisition times.

4 Active Learning Different cascaded learning methods have already been proposed and applied to object detection in computer vision [28, 29]—in contrast to Earth observation where until recently, this domain was not widely exploited [5, 7, 9]. As already reported in the literature, Support Vector Machines (SVMs) [30] are one of the best and commonly used supervised classifiers because they can accommodate high-dimensional feature vectors with good generalisation capability, while preserving high classification accuracy. For the SVM, we selected a χ 2 kernel and a one-against-all approach. To train an efficient SVM, sufficient patch examples are needed [8]. In many cases, the SVM is associated with RF (Relevance Feedback) [31, 32], where RF has two iterative steps: the first step is to learn the class followed by the second step that provides the class selection. At every iteration, the classifier learns the desired class based on the feedback given by (expert) users who divide the features of the patches into two classes, the desired ones called relevant and the unwanted ones called irrelevant. In our case, the SVM approach is combined with a Random Forest (RF) concept. In addition, we applied a cascaded classification technique to optimise the required processing effort.

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Our Cascaded Active Learning (C-AL) method is based on a hierarchical topdown processing scheme for object retrieval from big volumes of satellite images [7]. The method learns a cascade of SVM-RF classifiers, each working at a certain scale/level on a patch-based set of images. The procedure starts by tiling the original image/images into patches with different sizes (e.g., 160 × 160 pixels, 80×80 pixels, or 40×40 pixels) to reduce their patch size; then the users can more easily identify a desired object class. The transition from one level to another one is made by keeping only the patches that are relevant. This automatically propagates the training examples from one level to the next one. The major advantage of the C-AL method is that it can learn a new mathematical class (or physical category) with extremely few training sample patches [9]. With only 4-5 examples of the desired class (relevant patches) and one example for the classes that are not desired (irrelevant patches), the accuracy of the classification may reach more than 90%. During the AL process, two goals are achieved: (1) Learn the targeted image category as accurately and as exhaustively as possible and (2) Minimise the number of iterations in the relevance feedback loop. The C-AL method achieves a reduction of the number of computations by two orders of magnitude and provides high accuracy when compared with other state-ofthe-art methods (e.g., standard SVMs). This C-AL method was successfully validated for benchmark data set generation without too much a priori knowledge about the area of investigation (e.g., polar areas).

5 Semantic Labelling The main modules of the proposed workflow are feature extraction, cascaded active learning based on SVM-RF for classification followed by semantic labelling, and analytics. The ingested data can be in the form of individual images (first study case), multi-sensor images (second study case), or multi-temporal images (last study case). The overall workflow is shown in Fig. 4 and has as its main goal the extraction of the content information from large data sets to be semantically labelled in a way as close as possible to the ground truth. The method was designed in order to easily work with all three cases and to generate semantic labels using a hierarchical semantical labelling scheme developed in [33] for high-resolution SAR images. This scheme was adapted also for lower resolution SAR images [34] by reducing the number of semantic labels (i.e., those that give details), and for multispectral images by adding the specific labels that correspond to these images (e.g., clouds, irrigation) [34]. The data to be analysed was stored in three data sets that correspond to each case. The next step was to cut the satellite images into patches (with various patch sizes depending on the desired resolution and sensor type), followed by the extraction of the individual features for each patch (e.g., via Gabor filters, Weber descriptors, or gold colour histograms [34]). The C-AL approach based on SVM-RF [7] was used

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Fig. 4 Our overall semantic labelling workflow being used for all three study cases: selection of one out of the three data sets, and processing of the images by tiling each image into patches with a size adapted to each set of images, and also for different patch levels (if necessary); generation of the quick-look images of each tiled patch and of the full image/images that are needed for visualisation; extraction of features from each tiled patch as feature descriptors (e.g., using Gabor filters); interactive selection of training samples and training of a SVM classifier with RF in order to group the patches into classes; semantic annotation of each retrieved category using the already predefined hierarchical semantic annotation scheme or annotations defined by the user/operator; generation of different statistical analytics based on the semantic classification results from the previous step

without supervision to retrieve the classes from a large data set and to semantically label them (based on the knowledge of an expert user). This labelling step was further followed by a data analytics stage, where the results are produced in various forms highlighting the extracted information in the form of semantics for each image/study case. For the first study case, the semantic labelling was performed in a single run for all selected images; in the second case, the semantic labelling was made sensor by sensor, while for the last case, the images from an extended period of time were jointly semantically labelled (however, separately for each sensor and area). When several images were jointly put together (i.e., for the first and third case), the semantic labelling was made via a concatenated feature arrangement. Figure 5 depicts an example of how the C-AL method works in practice. On the top left corner, one sees the image to be labelled semantically, and from this image (for exemplification), a subarea is cut out (see the lower left part of Fig. 5) that contains the class to be labelled (in this case, Windmills). The method starts from

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Fig. 5 C-AL approach [7]: The classification starts from a first level with a big patch size (e.g., with 160 × 160 pixels), to a second level with medium patch size (e.g., with 80 × 80 pixels), and—if needed—to a third level with a still smaller patch size (with 40 × 40 pixels). This approach reduces the computational effort when a large data set is to be processed, because at each transition from one level to another one, only the positive patches are kept, while the rest will be discarded. On the last level, the user selects the most appropriate label [33] from a predefined list or defines a new label

a first set of patches, namely the patches with the biggest size (e.g., with 160×160 pixels). By selecting relevant (positive “+”) and irrelevant patches (negative “-”), the C-AL procedure is trained. After a number of iterations (e.g., five to seven iterations depending on the user satisfaction), all patches of this set are classified as positive or negative. The positive patches usually contain some additional other classes or objects identified within the patches (see Fig. 6, top right; Windmills and Ocean), but all the patches being selected or retrieved by the method as positive are transferred to the next level, while all negative ones are discarded from the training process. This decision reduces the computational effort when a large data set is to be analysed. If necessary, the positive patches are classified further on the second level (e.g., with 80×80 pixels) or on the third level (e.g., with 40×40 pixels), to eliminate the irrelevant class/classes (in the example, the class Ocean). This classification and labelling step can be repeated until the user is satisfied with the results. If no training samples (with the defined class) are available on the finer level, the class can be inferred from the samples of the previous level [8]. Figure 5 also illustrates that the results obtained on the third level are the ones that contain only the desired class (here, Windmills) that is selected from an already defined list of semantic labels [33, 34] or can be defined by the user. The C-AL operation can be divided into two cases:

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Fig. 6 Three examples of patches that show how to apply the three-level C-AL method (upper part) in order to create semantic multi-labels (lower part)

1. Single-level learning When only a single level of patches (e.g., with 160×160 pixels) is used for classification, then only a single semantic label can be assigned to each patch, based on the majority of the patch content (more than 50% of the patch content dictates the assigned semantic label). Figure 6 shows three such examples for the first level where the semantic labels are Storage tanks, Ocean, and Tents. 2. Multi-level learning If the classification continues with finer levels (comprising levels 2 and 3), one can reach a classification where a patch will only contain one class object. In this case, an appropriate semantic label can be assigned (for example in Fig. 6: Storage tanks to its left side, Windmills to its centre, and Tents to its right side). Repeating this procedure for the unexplored content of a patch on level 1, one can do this on level 3 by assigning further semantic classes such as Sand, Chemical plants, and Ocean. Once this fine semantic labelling (at level 3) has been done for each patch (at level 1), one can create multiple semantic labels for the patch from level 1 that are more accurate. In Fig. 6, the three patches from level 1 are classified as semantic multi-labels: the patch (on the left side) then has the label 25% Storage tanks, 13% Sand, and 62% Chemical plants, the patch (in the centre part) then got the label 7% Windmills and 93% Ocean, and the patch (on the right part) has the label 80% Tents and 20% Sand.

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6 Conclusions This chapter presents the AL/C-AL method for semantic labelling in three different situations. The method will be applied, in Part 2 to multiple images acquired by the same sensor from different locations, to multi-sensor images where the same location is analysed with images from various sensors, and to multi-temporal images where the same location is analysed for a period of time with images from one sensor. When the AL/C-AL method was applied (see Part 2) to different study cases, the classification accuracy was around 90%. Particularly for EO image applications, AL with very few training samples allows a detailed verification of image contents; thus, we can trust the results without caring for potential data base biases. Another point to be noticed is its capability to follow the actual user conjectures. In our case, we concentrate on plausible image semantics that may differ from many other fields of applied geography and surveying, and we expect that an EO image clearly depicts the actual target characteristics allowing us to identify and understand the meaning of nearly every image patch. This results in highly reliable semantic image catalogues. The advantages and disadvantages of AL are mentioned in [5], and the comparisons are made between Shallow Machine Learning and Deep Learning methods. Researchers interested in data that contain TerrSAR-X images related to the first and second data set covering cities all over the world, and to the third data set covering the area affected by tsunami, should submit a scientific proposal to TerraSAR-X Science Service System in order to receive these data (see https://sss.terrasar-x.dlr.de/). For the second data set that contains World-View-2 images, a similar proposal should be submitted to ESA in order to get access to the World-View-2 data (see https:// earth.esa.int/eogateway/catalog/worldview-2-full-archive-and-tasking). Regarding the data that contain Sentinel-1 and Sentinel-2 images related to the second and third data set covering an area in Greenland and the Danube Delta, the data should be freely downloaded from the Copernicus Open Access Hub (see https://scihub.copernicus. eu/). In addition, for the polar area in Greenland, the semantically labelled data can be freely accessed from European Commission Zenodo website (see https://zenodo. org/record/5075448#.YOR7FxMzZdA). Acknowledgements The TerraSAR-X image data being used in this study were provided by the TerraSAR-X Science Service System (Proposals MTH 1118 and LAN-3156), while the WorldView2 image data was provided by European Space Imaging (EUSI). The Sentinel-1 and Sentinel-2 image data is freely available via the Copernicus Open Access Hub. This work was supported by different projects funded by the European Space Agency (KLAUS, EOLib, and C-TEP), by the European Commission under the FP7 Programmes (TELEIOS), and under the H2020 Programmes (ECOPOTENTIAL, CANDELA, and ExtremeEarth). The results were obtained during my work at DLR in the DIKD (Data Intelligence and Knowledge Discovery) team coordinated by Mihai Datcu. I would like to thank the project partners and the DLR colleagues from the team.

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References 1. Mjolsness E, DeCoste D (2001) Machine learning for science: state of the art and future prospects. Science 293:2051–2055. http://computableplant.ics.uci.edu/papers/2001/science_ viewpoint.pdf 2. ExtremeEarth (From Copernicus Big Data to Extreme Earth Analytics) Project. http:// earthanalytics.eu/index.html. Cited 25 March 2022 3. Dumitru CO, Datcu M (2013) Information content of very high-resolution SAR images: study of feature extraction and imaging parameters. IEEE Trans Geosci Remote Sens 51(8):4591– 4610 4. Definition of Active Learning from Wikipedia. https://en.wikipedia.org/wiki/Active_learning_ (machine_learning) Cited 20 Oct 2021 5. Dumitru CO, Schwarz G, Pulak-Siwiec A, Kulawik B, Albughdadi M, Lorenzo J, Datcu M (2020) Understanding satellite images: a data mining module for sentinel images. Big Earth Data 4(4):367–408 6. CANDELA (Copernicus Access Platform Intermediate Layers Small Scale Demonstrator) Project (2020) Deliverable D2.2 data mining version, vol 2. http://www.candela-h2020.eu/. Cited 25 March 2022 7. Blanchart P, Ferecatu M, Cui S, Datcu M (2014) Pattern retrieval in large image databases using multiscale coarse-to-fine cascaded active learning. IEEE J. Select. Top. Appl. Earth Obs. Remote Sens 7(4):1127–1141 8. Dumitru CO, Cui S, Datcu M (2015) Validation of cascaded active learning for TerraSAR-X images. In: Proceedings of Image Information Mining (IIM) Conference, Bucharest, Romania, pp 1–4 9. Datcu M, Grivei AC, Espinoza-Molina D, Dumitru CO, Reck C, Manilici V, Schwarz G (2020) The digital earth observation librarian: a data mining approach for large satellite images archives. Big Earth Data 4(3):265–294 10. Demir B, Persello C, Bruzzone L (2011) Batch-mode active-learning methods for the interactive classification of remote sensing images. IEEE Trans Geosci Remote Sens 49(3):1014–1031 11. Débonnaire N, Stumpf A, Puissant A (2016) Spatio-temporal clustering and active learning for change classification in satellite image time series. IEEE J Select Top Appl Earth Obs Remote Sens 9(8):3642–3650 12. Güttler FN, Ienco D, Poncelet P, Teisseire M (2016) Combining transductive and active learning to improve object-based classification of remote sensing images. IEEE Remote Sens Lett 7(4):358–367 13. Ben Slimene Ben Amor I, Chehata N, Bailly J-S, Farah IR, Lagacherie P (2018) Parcel-based active learning for large extent cultivated area mapping. IEEE J Select Top Appl Earth Obs Remote Sens 11(1):79–88 14. Lughofer E (2012) Hybrid active learning for reducing the annotation effort of operators in classification systems. Pattern Recogn 45(2):884–896 15. Lughofer E (2012) Single-pass active learning with conflict and ignorance. Evol Syst 3(4):251– 271 16. Khanna S (2021) Learning to learn: a dual network approach to multi-class active learning. CS230, Stanford University, Palo Alto, California, USA, pp 1–7. http://cs230.stanford.edu/ projects_winter_2021/reports/70769927.pdf. Cited 20 Oct 2021 17. TerrSAR-X mission (2021). https://earth.esa.int/web/eoportal/satellite-missions/t/terrasar-x. Cited 20 Oct 2021 18. Dumitru CO, Schwarz G, Datcu M (2021) Semantic labelling of globally distributed urban and non-urban satellite images using high-resolution SAR data. IEEE J Select Top Appl Earth Obs Remote Sens 14:6009–6068 19. Sentinel-1 mission. https://earth.esa.int/web/eoportal/satellite-missions/c-missions/ copernicus-sentinel-1. Cited 20 Oct 2021 20. WorldView mission. https://earth.esa.int/web/eoportal/satellite-missions/v-w-x-y-z/ worldview-2. Cited 20 Oct 2021

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21. Dumitru CO, Cui S, Datcu M (2015) A study of multi-sensor satellite image indexing. In: Proceedings of JURSE 2015, Lausanne, Switzerland, pp 1–4 22. Dumitru CO, Schwarz G, Cui S, Datcu M (2016) Improved image classification by proper patch size selection: TerraSAR-X vs. sentinel-1A. In: Proceedings of IWSSIP 2016, Bratislava, Slovak Republic, pp 1–4 23. Dumitru CO, Cui S, Faur D, Datcu M (2015) Data analytics for rapid mapping: case study of a flooding event in Germany and the Tsunami in Japan using very high-resolution SAR images. IEEE J Select Top Appl Earth Obs Remote Sens 8(1):114–129 24. Karmakar C, Dumitru CO, Hughes N, Datcu M (2023) Latent analysis and knowledge extraction using SAR image time series for polar areas. IEEE J Select Top Appl Earth Obs Remote Sens 1–16. (under review) 25. Dumitru CO, Dax G, Schwarz G, Cazacu C, Adamescu MC, Datcu M (2019) Accurate monitoring of the danube delta dynamics using copernicus data. In: Proceedings of SPIE remote sensing, Strasbourg, France, pp 1–12 26. Sentinel-2 mission. https://earth.esa.int/web/eoportal/satellite-missions/c-missions/ copernicus-sentinel-2. Cited 20 Oct 2021 27. Dumitru CO, Schwarz G, Datcu M (2021) Machine learning techniques for knowledge extraction from satellite images: application to specific area types. In: Proceedings of ISPRS 2021, Nice, France, vol XLIII-B3-2021, pp 455–462 28. Viola P, Jones M (2001) Robust real-time face detection. In: Proceedings of eighth IEEE international conference on computer vision (ICCV), Seoul, South Korea, pp 747 29. Wu J, Brubaker SC, Mullin MD, Rehg JM (2008) Fast asymmetric learning for cascaded face detection. IEEE Trans Pattern Anal Mach Intell 30(3):369–382 30. Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press, Cambridge, MA, USA 31. Ferecatu M, Crucianu M, Boujemaa N (2004) Retrieval of difficult image classes using SVMbased relevance feedback. In: Proceedings of the 6th ACM SIGMM international workshop on multimedia information retrieval (MIR), New York, USA, pp 23–30 32. Costache M, Datcu M (2007) Learning-unlearning for mining high-resolution EO images. In: Proceedings of IGARSS, Barcelona, Spain, pp 4761–4764 33. Dumitru CO, Schwarz G, Datcu M (2016) Land cover semantic annotation derived from highresolution SAR images. IEEE J Select Top Appl Earth Obs. Remote Sens 9(6):2215–2232 34. Dumitru CO, Schwarz G, Datcu M (2018) SAR image land cover datasets for classification benchmarking of temporal changes. IEEE J. Select. Top. Appl Earth Obs Remote Sens 11(5):1571–1592

Chapter 8

AL4SLEO: An Active Learning Solution for the Semantic Labelling of Earth Observation Satellite Images—Part 2 Corneliu Octavian Dumitru, Gottfried Schwarz, and Mihai Datcu

1 Typical Examples This section presents typical examples of the use of the C-AL (Cascaded Active Learning) method from Part 1 with one or more levels of patches for all three study cases. The first study case is one in which for the semantic labelling all three levels are used showing how the results are filtered on the last level keeping just the patches that contain the desired class. From one level to the next higher one, the patches belonging to the desired class increase, reaching up to 98% on the last level. The second study case deals with the semantic labelling of the same area of interest acquired by several sensors, such as TerraSAR-X, Sentinel-1, and WorldView-2. Here, we describe how the sensor type, the resolution, and the patch size influence the number of retrieved semantic classes (even the details describing the respective class). The last study case describes the semantic labelling of three time series acquired by three different sensors (e.g., TerraSAR-X, Sentinel-1, and Sentinel-2) covering areas where some changes took place. By analysing the data over an extended period of time, a number of semantic changes were noticed.

1.1 Semantic Multi-level Labelling For the first study case, the results of the semantic multi-level labelling are presented for each data set covering three continents. The idea of this subsection is to show the C. O. Dumitru (B) · G. Schwarz · M. Datcu Remote Sensing Technology Institute, German Aerospace Center (DLR), Wessling 82234, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_8

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Fig. 1 Examples of the reduction of the data volume during multi-level labelling when using the cascaded active learning method. The plot near the top-left corner is an example of multi-level labelling for the first data from North America. The plot near the top-right corner is a similar example, but this time for data acquired over Europe. Finally, the last plot near the bottom-centre part is another example of the Middle East area

impact of each patch level on the semantic classes, and the reduction of the volume of data to be processed at each level by the C-AL method. The first step was to tile the images of the TerraSAR-X sensor on three levels, namely 160 × 160 pixels, 80 × 80 pixels, and 40 × 40 pixels. Each image was semantically labelled by an expert user using the AL method; at each level only, the relevant patches for the next level are kept, i.e., those patches that belong to the desired class. Figure 1 shows a set of seven general semantic classes defined in [25] (namely Settlements, Industrial production areas, Transport, Agricultural areas, Bare ground, Natural vegetation, and Water bodies) the analysis results of each level, the initial number of patches for each class, and—after classification—the number of patches containing this class and which are used further for the next level. Based on the C-AL method, only the positive patches (i.e., this means, the patches containing the desired class) are kept and used for semantic labelling. Based on the results and the observations made, this method has the advantage of maintaining the accuracy of the classification for the selected classes. In addition, Fig. 2 shows the percentage of data being kept from the entire data set. Taking one out of the seven classes, namely Water bodies, in the first level (patches with 160 × 160 pixels) only about 12% of the entire number of patches are used, while the remaining patches are discarded from the training data set because they are belonging to other classes. The selected patches from the first level are subdivided

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Fig. 2 A synthesis example that shows the acquired locations from all over the world

again on the second level into patches of 80 × 80 pixels, then classified, and the ones with the desired class (about 65% from all patches) are kept, while the rest of the patches that do not belong to the desired class are removed from the training set again. On the third level (patches with a size of 40 × 40 pixels), the same procedure is applied again, and now about 94% of the patches belong to the Water bodies class. This procedure is repeated for all classes. The idea of this analysis from Fig. 1 is that the transition from one level to another (level 1 to level 2 and level 2 to level 3) has the effect of removing the patches that do not belong to the investigated class (for the class Transport, 95% of patches were removed) and at the next level only 5% will be maintained which will be divided into smaller patches. These are classified again, eliminating 60% of them in level 2, the remaining 40% are divided again into smaller patches. In this case, we will eliminate only 10% by classification, the remaining 90% being the correct ones belonging to the respective class. Regarding Fig. 2, this presents a synthesis of the results over all the images from the data set, choosing the most representative classes. The trend that was identified in Fig. 1, level by level, is also maintained for the entire data set. For an image selected from the Middle East data set, Fig. 3 depicts the typical data analysis steps taken for the semantic labelling. This figure shows the diversity of semantic classes identified from this image when using three levels of classification (see the example in Fig. 5 (in Part 1)). This plot is made in order to illustrate the evolution of the semantic labels from the first level (patches with a size of 160 × 160 pixels) to the last level (patches with a size of 40 × 40 pixels). One can observe a decreasing trend for most of the classes (e.g., Chemical plants, Windmills) and an increasing trend for some limited number of classes (e.g., Ocean, Sand). This can be justified when we take a look at the central part of Fig. 6 (in Part 1), where on

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Fig. 3 Diversity of semantic labels identified from an image belonging to the set of Middle East images using three levels (on the left side) together with the percentage of each semantic class on the first level for the same image (on the right side)

Fig. 4 Typical examples of patches semantically labelled as Storage tanks on all three levels. Examples of this patch: (top) on the first level with a size of 160 × 160 pixels; (centre) on the second level with a patch size of 80 × 80 pixels, and (bottom) on the third level with a patch size of 40 × 40 pixels

its right side, on the first level the patch is labelled as Windmills and this patch is further divided on the second level into four smaller patches. One of these patches is the “parent” label Windmills and the other three patches are annotated with another label; in this case, the patches are labelled as Ocean. On the last level the procedure is similar, one patch with the “parent” label Windmills and three “offspring” patches with the label Ocean. The classification accuracy (e.g., the precision/recall metric) for all semantic classes on each level remains constant, ranging from 85% to 98%, depending on the class [27]. Figure 4 depicts for an image from the Middle East (also being used in Fig. 3) a number of patches semantically labelled as Storage tanks on each of the three levels. Based on this, it can be seen how by reducing the patch size, the content of the patch only contains the desired class.

1.2 Semantic Multi-sensor Labelling For the second study case, the results of the semantic labelling are presented separately for each sensor. The idea of this subsection is to analyse the impact of the

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resolution and sensor type on the semantic classes identified by an expert user using the AL method. The first step was to tile the images of the three sensors (TerraSAR-X, Sentinel-1, and WorldView-2) in order to cover the same area on the ground. Each image was semantically labelled by an expert user using the AL method with only one level of patches. The size of the patch depends on the resolution of the sensor images [28]: 160 × 160 pixels for TerraSAR-X images, 26 × 26 pixels for the Sentinel-1 images, and 100 × 100 pixels for the WorldView-2 (multispectral and panchromatic) images. For labelling, the semantic labels were selected from the hierarchical schema defined in [25]. In the case of high-resolution sensors, like TerraSAR-X and WorldView-2, three levels of annotations are taken into account, while for the medium-resolution sensors such as Sentinel-1, only the two general levels are used (the third one, the detailed one, could not be used due to its resolution). Figures 5 and 7 present the semantic classification results for two cities in Europe, Munich in Germany, and Venice in Italy. Analysing the first location, Munich shows that in the case of SAR sensors, it was possible to identify nine semantic classes for TerraSAR-X and six semantic classes for Sentinel-1, while for the optical sensors, it was possible to identify ten semantic classes in the case of WorldView-2 (multispectral and panchromatic channels). Here, it can be said that the resolution is directly proportional to the number of semantic classes found when using the AL method. However, it is very difficult to compare these results because there were no corresponding high-resolution ground-truth data sets. In the case of the second location, Venice shows the same tendency of retrieved semantic classes being proportional to the resolution. For TerraSAR-X, we found eleven semantic classes, for Sentinel-1, there are five classes, while for WorldView2 (multispectral and panchromatic channels), there are twelve classes. Figures 6e, f and 8e, f show for comparison two of the existing reference data sets (Corine Land Cover [29] and Urban Atlas [30]) at European level, but for lowresolution maps. From the first evaluation, we observed that the semantic classes are very similar in the case of these two data sets and sometimes less classes can be found with the AL method. An important observation is that there are semantic classes that are specific to the sensor. For example, in the case of Munich, the class Clouds appears only in WorldView-2 images, and in the case of Venice, the Buoys class appears only in TerraSAR-X images. Another important factor in finding the attainable number of semantic classes is the patch size that needs to be adapted to the resolution of the images. Figure 9 shows a comparison of the number of classes found for TerraSAR-X images; when the patch size is 160 × 160 pixels, nine classes were identified, while for a patch size of 100 × 100 pixels, ten classes were identified. Similar to this, Fig. 10 illustrates the same comparison for the city of Venice, where, for both cases, the number of semantic classes is eleven. For both cities, in case of smaller patch sizes, the results are more detailed/granular and this result is closer to the results of WorldView-2 (except for the classes that are specific to each sensor).

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Fig. 5 City of Munich, Germany. The quick-look images of each sensor are shown in Fig. 2 in Part 1. The retrieved and semantically annotated classes together with their generated classification maps are presented for: a A TerraSAR-X image with a patch size of 160 × 160 pixels, b A Sentinel-1 image with a patch size of 26 × 26 pixels, c A multispectral WordView-2 image with a patch size of 100 × 100 pixels, and d A panchromatic WordView-2 image with a patch size of 160 × 160 pixels

For a detailed quantitative assessment, the precision/recall metric was computed for each semantic class by comparing the retrieved results of the AL with manually created ground-truth data. The precision varies between 70 and 87%, while the recall varies between 60 and 84%. By fusing optical and SAR sensors (World-View-2 and TerraSAR-X) it helps us to discriminate better and with higher accuracy the extracted semantic classes for both cities (Munich and Venice). Combining the information

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Fig. 6 (Continuation of Fig. 5) City of Munich, Germany. e Corine land cover classification map with its corresponding legend [29], f Urban Atlas classification map with its corresponding legend [30]. These last two maps cover an area slightly larger than the analysed one and were produced by the European Environment Agency (EEA) Illustration taken from the EEA website, courtesy of EEA [55]. The blue rectangle marks the analysed area

provided by the two sensors offers the possibility of more accurate detection and separation of the classes in the images [14].

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Fig. 7 City of Venice, Italy. The quick-look images of each sensor are shown in Fig. 2 in Part 1. The retrieved and semantically annotated classes together with their generated classification maps are shown for a A TerraSAR-X image with a patch size of 160 × 160 pixels, b A Sentinel-1 image with a patch size of 32 × 32 pixels, c A multispectral WordView-2 image with a patch size of 100 × 100 pixels, and d A panchromatic WordView-2 image with a patch size of 160 × 160 pixels

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Fig. 8 (Continuation of Fig. 7) City of Venice, Italy. e Corine land cover classification map with its corresponding legend [29], f Urban Atlas classification map with its corresponding legend [30]. The last two maps cover an area slightly larger than the analysed one and were produced by the European Environment Agency (EEA). Illustration taken from the EEA website, courtesy of EEA [55]. The blue rectangle marks the analysed area

1.3 Semantic Multi-temporal Labelling For the last study case, the results are split into three parts depending on the sensor: TerraSAR-X, Sentinel-1, and Sentinel-2. The idea of this subsection is to analyse the evolution of semantic classes, to identify their temporal changes, and to understand the origin of these changes [37].

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Fig. 9 City of Munich, Germany. Comparison of two semantic classification maps for TerraSAR-X images using different patch sizes. (left side) Classification results using patches with a size of 160 × 160 pixels. (right side) Classification results using patches with a size of 100 × 100 pixels. The colour legend is similar to the one from Fig. 5

Fig. 10 City of Venice, Italy. Comparison of semantic classification maps for TerraSAR-X images with different patch sizes. (left side) Classification results of patches with a size equal to 160 × 160 pixels. (right side) Classification results of patches with a size of 100 × 100 pixels. The colour legend is similar to the one from Fig. 7

1.3.1

TerraSAR-X Images

Our first example uses several images provided by the TerraSAR-X sensor. This series of images covers the area of Sendai, Japan, affected by the Tohoku earthquake and tsunami in March, 2011. The data set consists of nine images: two TerraSAR-X images acquired as pre-disaster data on September 21st, 2008 and on October 10th, 2010, and seven TerraSAR-X images acquired after the event as the post-disaster data. These last images were acquired in 2011 during the period of three months (March 12th, March 23rd, May 6th, May 17th, May 28th, June 8th, and June 19th). Processing all these selected images for this case and using the methodology described in Sect. 5 with a single level of patches (with a size of 160 × 160 pixels), an EO expert user applying the method mentioned above was able to group the patches tiled from these images into 12 classes and select from the already created hierarchical annotation scheme [25] 12 semantic labels (see Table 1).

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Table 1 Complete list of semantic labels together with their definition from [31]

Table 1 presents the retrieved and labelled classes from the processed images, by an expert in domain. Following Table 2 shows for four classes, Ploughed agricultural land, Runways, Aquaculture, and Channels their temporal evolution in time, as well as the changes in the semantic classes due to the effects of the tsunami. For a better understanding of these effects, Fig. 11 shows the diversity of the userdefined retrieved classes based on the cascaded learning method together with their

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Table 2 Temporal evolution of a number of classes with changing semantic labels. Each patch has attached a semantic label (as a colour) corresponding to the description listed in Table 1

associated percentages. From this figure, one can see the evolution of classes and their transition from one class to another class due to the tsunami. The class Others contains several classes (Industrial buildings, Medium-density residential areas, Mountains, and Shores) joined together because the variation of these classes is not so big and they have not been affected by the tsunami. In contrast, the most affected classes are Ploughed agricultural land, Aquaculture, Runways, and Bridges. The class Channels shows little variation during the event. In contrast, Fig. 12 gives an idea about the temporal evolution of the affected area before, during, and after a period of three months from the tsunami. The results are split into 3 plots: (1) the top-left plot presents the evolution of the stable classes over the entire analysed period; (2) the top-right plot presents the stable class Ocean that is separated from the previous ones because its contribution is very high compared to other classes and it would be difficult to compare this class with the ones with smaller contributions; (3) the bottom-centre plot presents the classes affected by the tsunami and the classes that appeared after the tsunami. From Fig. 13, it can be seen that the entire Aquaculture was totally destroyed on March 12th, 2011, and rebuilding the damaged area took some time (about 15% compared with October 2010). In terms of Debris, this class appeared immediately after the tsunami, and three months later, it was reduced (to 20% in June, 2010) or migrated from the ocean to other areas.

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Fig. 11 Semantic classes identified from the series of images acquired over Sendai, Japan. The left part shows the retrieved classes in the pre-event images (August 21st, 2008 and October 20th, 2010), while the central and the right part show the retrieved classes in the post-event images (from March 12th to June 19th, 2011). The class Others (marked in grey) contains the following classes: Industrial buildings, Medium-density residential areas, Mountains, and Shores

Fig. 12 Quantitative analysis of all semantic labels for the entire set of images. The plots show the evolution of each semantic class over the analysed time period

Finally, once the expert users had semantically labelled all the images (each patch belonging to the image was given a semantic label), the next step was to create classification maps or even change maps by analysing the transition from one class to another class (a change of the semantic labels). Figure 14 shows the classification maps of two images along with the change map that is depicted.

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Sentinel-1 Images

The second example uses the images of the Sentinel-1A/1B sensors. This series of images covers Belgica Bank in Greenland which was strongly affected by the melting of ice and a volume reduction of the ice in 2018 and 2019 [32]. The data set consists of twenty-four images acquired by Sentinel-1 between January 2018 and December 2019. An expert in polar areas identified and labelled 10 semantic classes (see Table 3) using the methodology described in Sect. 5 of Part 1 with one level. Here, the patches were cut into individual tiles with 256 × 256 pixels. Table 4 illustrates the evolution of two locations during two years. The first one is for the class Mountains, and the second one is for the class Icebergs. The colours behind each patch represent the evolution of the semantic class versus time. If a grey colour background appears, then this means that the semantic label is a combination of several semantic labels from the Water group. This is a group that combines four classes, namely Floating ice, Water body, Water/ice current, and Melted snow/ice. In addition, Fig. 15 shows the evolution of each semantic class during the 24 analysed months. During the summer period of 2018, an increase in the Water group class could be seen together with a reduction of the other classes due to the melting of snow and ice. However, in the summer of 2019, the changes are more complicated. There is a reduction of Old ice and an increase of Young ice. In 2018 and 2019, during July and August, the class Glaciers decreased a lot, and after that, it remained constant for the rest of the year. As for the class Icebergs, this class saw also a decrease during summer, while the class count of Mountains remained more or less constant throughout the two years.

Fig. 13 Statistical analysis of the classes affected by the tsunami when all images had been analysed. Here are shown the distribution of the most affected classes (Ploughed agricultural land, Runways, Aquaculture, and Bridges) and the classes that appear after the tsunami (Debris and Flooded areas). A percentage equal to 0% on the left side means that, prior to the tsunami, there were no Debris or Flooded areas

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Fig. 14 Comparative classification maps based on images acquired on October 10th, 2010 (before the tsunami—top left and central part) and on March 11th, 2011 (after the tsunami—bottom left and central part). The colours of the semantic labels and the classification map are the ones from Table 1. The right side depicts the resulting change map between the previous two images. Each change is mapped into a new class and encoded with a different meaning even if colours from the previous labelling have been reused. The areas which remained unaffected are marked (on the right side) in light orange [26]

Finally, in its upper part, Fig. 16 presents the classification maps of two out of twenty-four images acquired on April 17th and on August 9th, 2018. The classification was performed by an expert user using the AL method, and the retrieved classes (i.e., the background colours) are linked with the ones from Table 3. In August 2018, it could be observed that new classes can appear due to the melting of ice. By comparing the two images between them (see the bottom part of the figure), a change classification map was generated with different changes (transitions between classes). From this last figure, it can be seen that the change maps portray all kinds of possible transitions that are caused by the changing seasons [34].

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Sentinel-2 Images

The last example uses some images of the Sentinel-2A/2B sensors. This series of images cover the Danube Delta in Romania that has been observed for many years [38, 39]. We selected some images that were acquired in 2016 and 2017 that aroused some interest to monitor the evolution of the alluvial discharge and to investigate its impact, as well as the changes that took place in this period. The area of interest was already split by Sentinel-2 data handling into different quadrants, namely T35TPK and T35TQL [35]. Based on the knowledge of an expert user, twelve classes were identified by using the AL method during semantical labelling (see Table 5). The method is described in Sect. 5 of Part 1 for one level where the patches are cut into tiles of 120 × 120 pixels. Figures 17 and 19 depict the classification maps of three images from 2016 acquired on April 28th, September 5th, and December 14th, and one image from

Table 3 Complete list of semantic labels together with their definition from [31, 33]

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Table 4 Temporal evolution of a number of classes with changing semantic labels. Each patch has an attached semantic label (as a colour background) that corresponds to the descriptions given in Table 3

2017 acquired on June 2nd. The quantitative distribution of the semantic labels retrieved from both acquisitions (T35TPK and T35TQL) is shown in Figs. 18 and 20 for the same acquisition date. A time series analysis was made for a period of one year, and for demonstration, we chose the four most representative Sentinel-2 images available on the Copernicus Open Access Hub [36] (excluding any images with higher cloud coverage). For the first location (quadrant T35TPK), 12 classes were retrieved and semantically labelled, while for the second location (quadrant T35TQL) only 10 classes were retrieved. Figure 17 shows the results of the first area with 12 semantic classes, while Fig. 19 shows the same classes; the two classes (Mixed forest and Harbour infrastructures) that do not appear were marked as Not identified. In contrast, analysing the results we observed that the largest volumes of alluvium discharged by the Danube River into the Black Sea [49] were identified on June 2nd, 2017 and April 28th, 2016 but also on December 14th, 2016. This effect mentioned

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Fig. 15 Quantitative analysis of all semantic labels for the entire set of 24 images. The plots show the evolution of each semantic class over the analysed time period

above is due to the rain that fell in the respective period (and even floods), but also to the melting of the snow. When we analysed the results of the classification and semantic labelling of each image separately (T35TPK and T35TQL), a number of patches were identified with different semantic labelling during the acquisition period. A general observation, for both locations, is that the semantic classes that are changing over time were Clouds and alluvium Deposits. The class Clouds had some impact and generated changes for the following classes: Ploughed agricultural land, Deltas, Hills, Lakes, Mixed forest, Inhabited built-up areas, Harbour infrastructures, and Rivers, while the class alluvium Deposits also had some influence and generated changes for the Sea class.

1.4 Conclusions This chapter demonstrates the usefulness of the AL/C-AL method for semantic labelling in three different situations. The method was applied successfully to multiple images acquired by the same sensor from different locations, to multi-sensor images where the same location is analysed using the images from various sensors, and to multi-temporal images where the same location is analysed with images for a period of time with one sensor. In the first case, we considered the semantic labelling on several patch levels (e.g., here on three levels), which leads to a weighted multi-labelling for each patch [48]. In the second case, we could show that for the same area covered by more than one

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Fig. 16 Comparative classification maps based on images acquired on April 17th, 2018 (winter season—top part) and on August 9th, 2018 (summer season—central part). The colours of the semantic labels and the classification map are the ones from Table 3. The bottom view represents the resulting change map between the previous two images. Each change is mapped into a level of changes being encoded with a colour, standing for a different meaning (even if colours from the previous labelling were reused). The areas which remained unaffected are marked (on the right side) in light green [34]. The classes Floating ice and Water body belong to the class Water group

sensor, different classes can be extracted. We obtained different numbers of classes as well as different semantic meanings. In the third case (the multispectral temporal analysis), a semantic signature versus time could be generated for each patch and for each of its three selected sensors, all illustrating the changes that occurred in different periods. From the application point of view, these three cases cover the following:

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Table 5 List of semantic labels together with their definition [31]

• Application to urban analysis with two sub-applications: (a) Analysis of different cities all over the world to see what semantic classes can be obtained and (b) Analysis of the same city with two different sensors to see which sensor captures better the ground level; • Application to monitoring areas with diverse changes with three sub-applications. (a) Monitoring of an area affected by a natural disaster, (b) Monitoring of an area with changes due to climatic and seasonal effects, and (c) Monitoring of an area with natural changes over time. In order to show the power of the C-AL method, we compared the accuracy of the results with other methods. We selected a set of images covering an area in Greenland.

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Fig. 17 (Top) A Sentinel-2 RGB quick-look view using the bands 2, 3, and 4 and (Bottom) the semantic classification map created after the AL method has been applied to each image (from the T35TPK quadrant zone [36]). The study area was the Danube Delta, for which the images were acquired on April 28th, September 5th, December 14th, 2016, and June 2nd, 2017. The semantic labels are the same for all four images (see the colour legend at the bottom of the figure)

Fig. 18 Quantitative analysis of the semantically labelled classes within the area of interest (T35TPK) using four Sentinel-2 images acquired during one year. The colour legend corresponds to Table 5 and Fig. 17

For the comparison, we considered a set of methods [52–54] for which we calculated the accuracy of the classification. Table 6 shows the classification results; the best accuracy is obtained for the C-AL method, followed by the hybrid method, while the third rank was obtained by the CNN approach. As known from the literature, the classification of multispectral summer images is better than the classification of images from winter time [46]. This is one of the reasons why for the first and second study case the acquisition of images was avoided during the winter period. For the last study case, (the multi-temporal analysis) we

C-AL

90

Method

Accuracy (%)

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Table 6 Performance comparison

81

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80

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78

78

AutoAutoencoder+SVM encoder+ k-NN 75

Compressiondictionary+GMM

72

Compressiondictionary+ k-means

62

Gabor+SVM

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Gabor+k-NN

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Fig. 19 (Top) Sentinel-2 RGB quick-look views using the bands 2, 3, and 4 and (Bottom) The semantic classification map created after the active learning method was applied to each image (the T35TQL quadrant zone [36]). The analysed area was the Danube Delta, for which the images were acquired on April 28th, September 5th, December 14th, 2016, and June 2nd, 2017. The semantic labels are the same for all four images (see the colour legend at the bottom of the figure)

Fig. 20 Quantitative analysis of the semantically labelled classes within the area of interest (T35TQL) using four Sentinel-2 images acquired during one year. The colour legend corresponds to Table 5 and Fig. 19

analysed the full period of the selected year in order to observe all changes that occurred. All images being used for the analysis of the study cases are shown in Fig. 21. The selected images are based on their availability (for multispectral images: a low cloud coverage), their content being related to the cases, their class diversity, and their class changes over time. It is important to mention that there is usually a discrepancy between the user and computer interpretation of an image, called a semantic gap. The authors of [41] made some efforts to bridge this semantic gap by including different user perspectives to

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Fig. 21 Geographical locations of the cities analysed in this study projected on Google Maps [40]

make good for the individual subjective biases, and by increasing the diversity of the data sets being used for the specific domain. The extracted classes and their semantic labels were created by trustable experts in the field with a small intentional [47] percentage of noisy labels (3 to 5%). These semantically labelled semantic classes, after having been retrieved, classified, and annotated by the user with the C-AL method, can also be used to retrieve

Fig. 22 Results of a query applied to the city of Venice images using a multi-sensor data set

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Fig. 23 Knowledge graph representation compiled for the natural disaster management

still more information hidden in these classes to provide additional knowledge to the user. This information can be accessed in the form of queries [28], ontologies [11], knowledge graphs [11], etc. • Various queries can be based on the metadata of the sensors and the semantic labels generated by the users via the AL method. An example of such a query combining sensor metadata and semantically labelled patches could be: “Give me, for the multi-sensor data, that has the following coordinates latitude 45.438759 and longitude 12.327145, all the patches semantically labelled as Harbour infrastructures.” The result of such a query is presented in Fig. 22 for the city of Venice, Italy. • Knowledge graph representation adapted to the study cases after the AL concept has been applied. An example can be the knowledge graph created for the natural disaster which took place and caused a lot of damage to both infrastructure and natural vegetation. The damages are split into two groups: the first one is the destruction of some infrastructures of the analysed area (Runways, Bridges, and Channels), and the second one is the destruction of some areas providing food (Ploughed agricultural land and Aquaculture). Such a knowledge graph is depicted in Fig. 23 for the area of Sendai, Japan. Acknowledgements The acknowledgement corresponding to Part 2 is similar to the one for Part 1.

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Chapter 9

Deep Learning-Based Efficient Customer Segmentation for Online Retail Businesses Jayesh Soni, Nagarajan Prabakar, and Himanshu Upadhyay

1 Introduction The extensive use of data mining methods in finding valuable and strategic information hidden in an organization’s robust database has evolved with the ever-increasing race among big businesses to thrive in the market. Data mining is the procedure of mining significant information from a dataset and delivering it in a humanly comprehensible layout for complex decision support. The data mining methods comprise learning-based algorithms with database systems. Fraud revealing, bioinformatics, image analysis, weather prediction, financial exploration, and customer segmentation are a few data mining examples. Segmentation of customers is the grouping of the organization’s customers based on their similar characteristics, such as a particular product, area, etc. It helps businesses to market the appropriate programs to each customer group, such as products shared, decisions for credit card applicants, etc. Clustering has demonstrated efficiency in determining valuable information and relationship in unlabelled datasets. Such a procedure of learning is categorized as unsupervised learning. Data points in each cluster have similar patterns but diverge significantly from other clusters’ data points. Each organization has a wide variety

J. Soni (B) Applied Research Center, Florida International University, Miami, FL, USA e-mail: [email protected] N. Prabakar Knight Foundation School of Computing and Information Sciences, Florida International University, Miami, FL, USA e-mail: [email protected] H. Upadhyay Electrical and Computer Engineering, Florida International University, Miami, FL, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_9

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of customer data that contains numerous pieces of information. Not all information is needed to group the customers into segments. Principal Component Analysis and AutoEncoders are a few of the learning-based algorithms that can reduce the feature dimensionality of the dataset. Such algorithms can extract meaningful features which can be used further for clustering. To summarize the remainder of the chapter, Sect. 2 presents the literature review, while Sect. 3 provides a detailed overview of clustering algorithms and their evaluation metrics. Section 4 explains the different dimensionality reduction algorithms. In Sect. 5, the open-source library used in the study is discussed, and in Sect. 6, practical use cases of these algorithms in solving customer segmentation problems are presented using an open-source dataset. Finally, the chapter concludes in Sect. 7 with a discussion of future work in the field.

2 Literature Review Organizations are attentive to attaining insights about their consumers using business intelligence techniques. Time and seasons are among the fundamental constituents of such insights, in addition to sales patterns. This assists in discovering new trends and proper promotion campaigns which remain hidden from the retailer. Chen et al. [1] extract important customer segments using a K-Means clustering algorithm on an online retailer dataset. Next, they applied a decision tree algorithm for the final result. RFM (Recency, Frequency, and Monetary) is a technique to study customers’ shopping patterns. Time passed since the last purchase is recency, whereas frequency denotes purchases completed in a given time duration, and the total amount spent by the customer is denoted by monetary. Dogan et al. [2] designed a system for giving loyalty cards to the customer by applying K-Means clustering and RFM computations for a sports retail company. The dataset used by the author was developed by Hu and Yeh [3]. Sarvari et al. [4] used association rule mining and RFM study on a global food chain data set for examining customers’ buying patterns. Yeh et al. [5] enhanced the RFM model by adding the parameter that captures the time since the first purchase. Bloom [6] uses neural networks for customer segmentation in the global tourist business. Holmbom et al. [7] performed portfolio analysis using self-organizing maps. Authors in [8, 9] have analyzed several machine learning algorithms on numerous applications. Kiang et al. [10] applied self-organizing maps in the telecommunication service area. In statistics, data dimensionality refers to the number of attributes present in a dataset. Big data is a widely studied topic today, with techniques being applied across various industries, such as telecom, to support strategic decisions [11]. Clustering is a fundamental process used to analyze unsupervised data by grouping similar objects into clusters. Objects in one cluster are typically different from those grouped in another cluster. This process has a wide range of applications, including computer vision [12], natural language processing [13], and bioinformatics [14]. One solution to the challenge of analyzing high-dimensional data is to employ dimensionality reduction methods [15]. These methods aim to learn a simplified and

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appropriate representation of the data from the original dataset, which can provide more significant insights into large datasets. However, standard clustering techniques often need to be more efficient in dealing with high-dimensional data due to the limitations of similarity measures. Additionally, applying these techniques to largescale datasets can result in high computational complexity. To overcome these issues, researchers have extensively studied techniques for reducing dimensionality and transforming features to map the raw data into a new feature space. By transforming the features this way, clustering algorithms and data analysis techniques can be applied to representative features instead of the entire feature space. There are several techniques for data transformation, including linear transformation, such as Principal Component Analysis (PCA), and non-linear conversion techniques, such as kernel methods [16]. Furthermore, deep learning-based techniques have also been developed that have shown impressive results in eliminating irrelevant and redundant information from the data. Overall, employing these techniques can help to simplify the data and make it more manageable for analysis. Recent interest in deep learning has encouraged many researchers to use autoencoders. Autoencoders are a type of neural network that can learn efficient representations of input data by training the network to reconstruct the input from a reduced set of features. Clustering approaches are then applied to the learned representations to group similar data points. In summary, the challenges of analyzing high-dimensional data can be addressed through dimensionality reduction methods and data transformation techniques. By reducing the dimensionality of the data and transforming features, more efficient and accurate clustering algorithms can be applied to representative features. The use of deep learning-based techniques, such as autoencoders and clustering approaches, is an increasingly popular method for achieving this objective. We proposed a method that uses K-Means clustering and Autoencoder to segment the customers. Further, we optimize hyperparameters for these algorithms using advanced deep-learning frameworks.

3 Clustering Algorithms Machine learning algorithms [17] learn the patterns from the dataset for prediction. There are three types of machine learning algorithms, as defined below. Supervised Learning Supervised learning algorithms use input data that has been labeled for training purposes. These algorithms are divided into two main categories: classification and regression, depending on the type of target label value. When the output label is categorical, the problem is considered a classification task, whereas a regression task is when the output label is a real value. Several supervised learning algorithms have been developed, including Decision Trees, Random Forest, K Nearest Neighbor, Support Vector Machine, and linear regression.

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Unsupervised Learning Input data without the target label is used for training. Such algorithms learn the hidden structure from the unlabeled dataset. Clustering is one such type. It clusters the data into different groups. K-Means, Agglomerative, and Divisive are some of the unsupervised algorithms. Semi-Supervised Learning It contains a small part of the labeled dataset, with the majority of data being unlabeled. The algorithms learn from the labeled data to predict unknown samples. We restrict our focus to the K-Means clustering algorithm in this chapter.

3.1 K-Means Algorithm The data points are divided into different subgroups, as shown in Fig. 1 in clustering, so all the points in one group have the same characteristics. It clusters data points based on their similarities [18, 19]. With clustering, researchers can find inherent patterns or outliers in unlabeled datasets. There are no precise principles for good clustering. K-Means assigns centroid and computes the distance between the data points. The main goal is to categorize the data into K distinct groups. It assigns every point to a particular group iteratively, where gradually, the data points with identical characteristics are clustered into a group. To correctly locate the cluster for a particular data point, the algorithm minimizes the distance between the data point and its closest cluster centroid. How does K-Means work? Let us understand the working mechanism of the algorithm with a small example.

Fig. 1 K-Means clustering algorithm

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(1) Selecting the Value for K (the Number of Clusters) The first step is to specify the value for K for the algorithm to divide the dataset into K distinct clusters. Let us say K = 3. It means the algorithm will divide the dataset into three distinct groups. (2) Centroids Initialization The center of any cluster is the centroid. The precise centroid has yet to be discovered initially for the data points. Thus, we pick any data points randomly and state them as cluster centroids. We will initialize three centroids in the dataset. (3) Data Points Assigned to the Cluster During this step, each data point is assigned to its closest centroid. This is achieved by computing the Euclidean distance between the data point and all available centroids. The Euclidean distance is calculated using the following formula:   n  D(x, y) =  (x i − yi )2

(1)

i=1

(4) Re-Initialize Centroids Here, we calculate the average x and y coordinates of all the data points for each cluster to define the new centroids. Cx =

1  xi |Ni |

(2a)

Cy =

1  yi |Ni |

(2b)

Steps 3 and 4 are repeated until the change between the previous centroid location and to current centroid location converges.

3.2 K-Means++ algorithm K-Means++ [20] differs from K-Means in the initialization of the centroid. Instead of randomly assigning all the K centroids initially, K-Means++ spreads the initial location of the centroid. Its main goal is to allocate the centroid, which can be as far as possible from each other. The first centroid is selected randomly, and the remaining centroid location is decided based on the maximum square distance. Below are the steps to initialize centroids in the K-Means++ algorithm: 1. Select the first centroid randomly. 2. Compute the Euclidean distance between the centroid and all data points.

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 2 Di = max(g = 1 to k)  Pi − C g 

(3)

This indicates the calculated distance of a point Pi from the farthermost centroid Cg. 3. Set the new centroid as Pi Repeat steps 2 and 3 till all the clusters centroid are allocated.

3.3 Evaluation Metrics 3.3.1

The Elbow Method

The distance between a cluster and all the points that belong to it is known as the intercluster distance. In contrast, the distance between a pair of clusters is referred to as the intracluster distance. To determine the optimal number of clusters in a dataset, the elbow method [21] can be employed. This technique involves plotting the number of clusters (K) on the x-axis and the average intercluster distance among all clusters on the y-axis. Initially, the intercluster distance decreases rapidly as K increases, but eventually, it stabilizes with the shape of an elbow. The K value corresponding to the turning point of the elbow is considered the optimal cluster value. The elbow method is effective because it evaluates the trade-off between the number of clusters and the performance metric. As the number of clusters increases, the performance metric typically decreases since there are more cluster centers to assign data points. By selecting the value of K that represents the optimal trade-off, we can strike a balance between the number of clusters and the clustering quality. However, there is a point at which adding more clusters does not result in significant improvement in the performance metric, and this point is referred to as the “elbow” of the curve. The elbow method suggests that the optimal number of clusters is the point at which the performance metric stops improving significantly with adding more clusters. This point is identified by visually inspecting the curve and selecting the number of clusters at the elbow. The elbow method is essential because it provides a simple and intuitive way to determine a dataset’s appropriate number of clusters. It helps to avoid overfitting (using too many clusters) or underfitting (using too few clusters) the data, which can lead to suboptimal clustering results. Using the elbow method, data analysts can make more informed decisions when choosing the number of clusters for their analysis, leading to more accurate and valuable results.

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The Silhouette Score

The silhouette score is a metric that measures the distance between a data point’s cluster and its nearest cluster, as well as how close the data point is to its cluster. This score takes into account both the intercluster distance and intracluster distance. Its values range from −1 to +1, with a score of +1 indicating a good score and vice versa [22]. The silhouette coefficient for a given data point, denoted as sc(p), is calculated using the following formula: sc( p) =

m( p) − n( p) max{n( p), m( p)}

(4)

where n(p): the average distance between point p and all the points in its cluster. m(p): the least mean distance of point p to all other clusters p does not belong. The silhouette score is helpful in K-means for several reasons. First, it provides an objective measure of the quality of clustering results, allowing data analysts to compare different clustering solutions and choose the best one. Second, it helps identify cases where the K-means algorithm may have failed to produce meaningful clusters, such as when the clusters are too overlapping or sparse. Finally, the silhouette score can be used to fine-tune the parameters of the K-means algorithm, such as the number of clusters, by testing different values and selecting the one with the highest average silhouette score. Overall, the silhouette score is a valuable tool for evaluating the quality of clustering results in K-means and can help data analysts make more informed decisions when analyzing their data.

4 Dimensionality Reduction Algorithms In this section, we discuss PCA and AutoEncoder, which are widely used for dimensionality reduction purposes.

4.1 Principal Component Analysis (PCA) Principal Component Analysis [23] reduces the dimension (number of features) in an unsupervised learning fashion in machine learning. It is a statistical-based approach that uses the orthogonal conversion technique to transform the set of correlated features into an uncorrelated vector in a linear space. These altered features are known as the principal components depicted in Fig. 2. It

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Fig. 2 PCA

is widely used for visualization and data exploration purposes. It provides insights into the dataset with the high-dimensional feature vector. A good split among the different categories of target labels can be seen with the high variance features. Therefore, PCA reduces dimensionality by considering the variance of the feature. Image processing and recommendation of the movie are a few of the applications of PCA. The main objective is to extract the meaningful features and discard the less significant feature. Steps for Building the PCA Algorithm First, we denote our dataset into a two-dimensional matrix format where each row represents a feature vector for a data point, and each row column represents a feature value. The total dimension of the dataset is the number of columns. Data Standardization and Covariance Calculation The data is standardized by dividing each feature value by its corresponding standard deviation. Let us name this data matrix S. Next, the covariance is computed by first transposing the matrix S and multiplying it with S. Eigen Values and Eigen Vectors Eigenvalues and eigenvectors are computed using the covariance matrix. Eigenvectors are the vectors that point toward meaningful patterns, whereas the coefficient of these vectors is known as eigenvalues. Next, we sort all the eigenvectors in decreasing order. Let us name the final matrix J*. Deriving the New Features or Principal Components To get the final principal components, we multiply S with J*. This resultant matrix contains a linear combination of original features with the reduced feature, where each column is uncorrelated from the other.

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T-Distributed Stochastic Neighbor Embedding (t-SNE) [24] is another technique widely used for visualizing high-dimensional data.

4.2 AutoEncoders AutoEncoders [25, 26] are deep learning-based neural networks where the output is similar to the input, as described in Fig. 3. It comprises three modules: encoder, latent space, and decoder. The input is compressed to a lower-dimensional subspace by the encoder, then reconstructed as the output by the decoder. The compressed or encoded dimension is known as the latent space representation. There are three hyperparameters to tune for training the AutoEncoder algorithm. Latent Space size: Total number of middle layer nodes. The number of layers: The above figure has one layer in the encoder and decoder. The number of nodes per layer: With each subsequent layer of the encoder, the nodes per layer decrease and vice versa in the decoder. In terms of architecture, the decoder structure is symmetric to the encoder. One of the critical advantages of Autoencoder is its ability to learn features from the data in an unsupervised manner. By learning to compress the data into a lowerdimensional representation and then reconstructing it, the Autoencoder can learn to identify the essential features of the data. This makes it an effective tool for dimensionality reduction and feature learning in applications such as computer vision and natural language processing.

Fig. 3 AutoEncoder

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Another important feature of Autoencoder is its ability to generate new data. By sampling from the latent space representation learned by the encoder network, it is possible to generate new data points similar to the original data. This makes Autoencoder a powerful data generation and synthesis tool, which is useful in many applications, such as image and speech synthesis. There are several variations of Autoencoder that have been developed over the years, each with its strengths and weaknesses. Some popular variations include denoising autoencoder, variational Autoencoder, and convolutional Autoencoder, designed for specific types of data and applications. Autoencoder is a powerful tool for data compression, feature learning, and generation. Its ability to learn features from the data in an unsupervised manner and generate new data points makes it a versatile tool that can be applied in many domains. As the field of deep learning continues to evolve, Autoencoder and its variants will likely remain an important tool for many data analysis tasks.

5 Libraries Tensorflow: TensorFlow is a powerful tool that can be used for customer segmentation, which is the process of dividing customers into distinct groups based on their characteristics and behavior. TensorFlow is a popular deep-learning framework that allows data analysts to build and train complex neural networks for various applications, including customer segmentation. Using TensorFlow to build a neural network model, data analysts can leverage the power of deep learning to identify patterns in customer data and create meaningful customer segments. These segments can target marketing campaigns, personalize customer experiences, and improve customer retention. TensorFlow’s flexibility and scalability make it an ideal tool for customer segmentation. It can easily handle large and complex datasets, enabling data analysts to extract insights and create value from customer data [27]. Keras: Keras is a high-level API that simplifies the process of building and training neural networks, making it an ideal tool for data analysts new to deep learning [28]. By using Keras to build a neural network model, data analysts can leverage the power of deep learning to identify patterns in customer data and create meaningful customer segments. These segments can target marketing campaigns, personalize customer experiences, and improve customer retention. Keras’s user-friendly interface and intuitive syntax make it an ideal tool for customer segmentation, allowing data analysts to quickly and easily build complex models and extract valuable insights from customer data. Scikit-learn: Scikit-learn [29] provides various tools for data preprocessing, feature selection, and model evaluation, making it easy to build robust and accurate customer segmentation models. Scikit-learn’s user-friendly interface and extensive documentation make it an ideal tool for data analysts new to machine learning. In contrast, its powerful algorithms and scalability make it suitable for large and

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complex datasets. With Scikit-learn, data analysts can gain valuable insights into customer behavior, improve marketing campaigns, and ultimately increase customer satisfaction and retention.

6 Proposed Approach This section provides a practical implementation of customer segmentation. The primary objective is to analyze the data and use unsupervised algorithms to cluster the customers into a distinct group for launching a targeted marketing ad campaign. The proposed framework shown in Fig. 4 consists of three modules, namely data collection, data preprocessing, and cluster detection. Stage 1: Data Collection The dataset is collected from Kaggle [30]. It consists of information on credit cardholders during the last six months. The dataset has 9000 rows and 18 behavioral features. Table 1 describes the features of the dataset. Stage-2: Data Preprocessing In this stage, we perform the following data preprocessing task: (1) Impute the feature vector with null values (2) Scaling the dataset to have a common scale among various features. Stage-3: Cluster Detection This is the main stage of the whole framework, where we perform the following operations: (1) Use AutoEncoder to reduce the features of the dataset

Fig. 4 Proposed framework

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Table 1 Dataset features Index

Feature name

Description

1

CustID

Unique customer ID

2

Balance

Amount left

3

BalanceFrequency

Frequency of balance update

4

Purchases

The total amount of purchases

5

OneOffpurchases

Maximum purchase in one-go

6

InstallmentPurchases

The total amount of installment purchases

7

CashAdvance

Advance cash by user

8

PurchaseFrequency

Frequency of purchase

9

OneOffPurchaseFrequency

Frequency of purchases in one-go

10

PurchaseInstallmentFrequency

Frequency of purchases in installments

11

CashAdvanceFrequency

Frequency of cases paid in advance

12

CashAdvanceTRX

Total transactions with cash in advance

13

PurchasesTRX

Total purchases in transactions

14

credit limit

Limit of credit

15

Payments

Total payment made

16

Minimum_Payments

Min amount paid

17

PrcFullPayment

Percent of paid payment in full

18

Tenure

Tenure of the service

(2) (3) (4) (5)

Apply the K-Means + + algorithm to find the clusters Use the Elbow method to find the optimal number of clusters (K) Perform K-Means + + for that optimal K value and label the dataset Use PCA to visualize the clusters in a two-dimensional subspace.

We use the AutoEncoder algorithm to reduce the dimensionality of the dataset. Figure 5 depicts the model architecture. The stacked AutoEncoder used in this study has multiple hidden layers, specifically two hidden layers. The first hidden layer consists of 500 neurons, while the Fig. 5 Model architecture

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second layer has 250 neurons. The AutoEncoder aims to reduce the dimensionality of the input data from 17 features to only ten features in the latent space. The Rectifier Linear Unit (ReLu) activation function trains the model, which helps overcome the vanishing gradient problem during backpropagation. To optimize the gradient for weight calculation, the adam optimizer is employed with a mini-batch value of 64. To find the optimal values of the hyperparameters, the Gridsearch optimization technique is used. The model is trained for 40 epochs, and the loss value at each epoch is plotted in Fig. 6. The total loss achieved by the model is 0.06, indicating that the model can accurately reconstruct the input data. Overall, the stacked AutoEncoder with ReLu activation and adam optimizer has proven to be a powerful tool for reducing dimensionality and extracting meaningful features from high-dimensional data. After obtaining the reduced feature set from the AutoEncoder, the next step in the analysis is to use this data as input for the K-Means++ algorithm. This algorithm is used to identify patterns or clusters within the data by partitioning it into a set of K clusters. In order to determine the optimal number of clusters, we run the K-Means++ algorithm for several K values ranging from 1 to 30. The K-Means++ algorithm uses a centroid-based clustering approach to group the data points into clusters. By running the K-Means++ algorithm for various K values, we can identify the optimal number of clusters that best represents the structure of the data. This is typically done by evaluating the performance of the clustering algorithm for each value of K, using a metric such as the silhouette score or the elbow method. The silhouette score measures how well each data point is clustered, while the elbow method identifies the point of diminishing returns in terms of clustering performance. Overall, using the reduced feature set obtained from the AutoEncoder as input to the K-Means++ algorithm can help to identify meaningful clusters within the data.

Fig. 6 Loss w.r.t Epoch

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By running the algorithm for multiple K values, we can select the optimal number of clusters and gain insights into the underlying structure of the data. Once the K-Means++ algorithm has been run for several K values, the next step is determining the optimal number of clusters using a performance metric such as the elbow method. This method involves plotting the number of clusters on the Xaxis and a relevant performance metric on the Y-axis, such as the sum of squared distances between data points and their assigned cluster centers. The point at which the performance metric experiences diminishing returns is identified as the “elbow” in the curve. Figure 7 shows the elbow curve for our data, with the number of clusters on the X-axis and the performance score on the Y-axis. By analyzing the curve, we can see that the elbow point is located at 7 clusters, which is the optimal value for our data. With this information, we now have seven features and a target column for our analysis. To visualize these features in a two-dimensional space, we use Principal Component Analysis (PCA), which is a technique for dimensionality reduction. We can plot the data points on a two-dimensional graph by reducing the seven features to two principal components. The resulting visualization is shown in Fig. 8. Each data point is plotted as a single point on the graph, and the color of the point corresponds to the cluster it belongs to. By examining the plot, we can gain insights into the underlying structure of the data and how it is partitioned into clusters. This visualization can help identify patterns and trends within the data and inform decision-making in various domains, such as marketing and customer segmentation. After identifying the optimal number of clusters and visualizing the data using PCA, we can see that our approach has successfully clustered the data into several

Fig. 7 Elbow method score

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Fig. 8. 2-Dimensional view of clustered data

distinct groups where customers in the same group share similar behavioral characteristics. This clustering can inform targeted marketing campaigns, allowing us to identify and target customers more likely to respond to specific messaging or offers. For example, if we identify a cluster of price-sensitive and value-conscious customers, we could develop targeted ad campaigns emphasizing value and savings. Similarly, if we identify a cluster of customers who are early adopters of new technology, we could develop campaigns focusing on the latest products or features. By targeting specific groups of customers with relevant messaging and offers, we can improve the effectiveness of our marketing campaigns and increase customer engagement and loyalty. This can lead to increased sales and revenue and a more substantial brand reputation and customer base. Overall, the clustering approach we have employed can be a valuable tool for businesses looking to improve their marketing strategies and better understand their customers. By leveraging the power of data analytics and machine learning, we can gain insights into customer behavior and preferences and use this information to drive targeted marketing campaigns and ultimately achieve business success.

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7 Conclusion The traditional approach of mass marketing products to a large audience, assuming everyone will be motivated to buy the product, is now more effective in today’s digital age. This approach is time-consuming and inefficient and often leads to poor results. Instead, companies are now turning to customer segmentation to drive personalized tactics and dynamic content based on behavioral characteristics. By dividing their customer base into several groups, companies can better understand their customer’s preferences and behaviors and tailor their marketing strategies accordingly. This approach improves the effectiveness of marketing campaigns and drives customer loyalty and business growth. This chapter has discussed various unsupervised learning-based algorithms, such as K-Means, PCA, and AutoEncoder, which can be used for customer segmentation. These algorithms help to identify patterns and trends within the data and partition customers into distinct groups based on their behavioral characteristics. By leveraging these algorithms, businesses can gain insights into their customer base and develop targeted marketing campaigns more likely to resonate with their customers. Furthermore, we have presented a practical implementation of applying these algorithms to solve the customer segmentation problem using a real-world Kaggle dataset. By using a stacked AutoEncoder with ReLu activation and adam optimizer, we could reduce the dimensionality of the data and extract meaningful features that were then used as input to the K-Means++ algorithm. By analyzing the resulting clusters, we gained insights into the underlying structure of the data and identified meaningful customer segments. While the implementation of stacked AutoEncoder and K-Means++ for customer segmentation has yielded promising results, the approach can be further extended and improved by employing an ensemble approach with additional algorithms. One such algorithm is the Self-Organizing Map (SOM), a type of neural network that can learn to represent high-dimensional data in a low-dimensional space. By using SOM along with stacked AutoEncoder and K-Means++, we can further reduce the data’s dimensionality and improve the clustering’s accuracy. Another algorithm that can be employed is the Restricted Boltzmann Machine (RBM), a type of neural network that can learn to represent complex probability distributions. By using RBM along with the other algorithms, we can further improve the accuracy of the clustering and gain deeper insights into the underlying structure of the data. In addition, we can also explore the use of Convolutional Neural Networks (CNN) for further dimensionality reduction. CNNs are robust neural networks commonly used in image recognition tasks. By applying CNN to the customer data, we can reduce the dimensionality even further and improve the accuracy of the clustering. Overall, by employing an ensemble approach with additional algorithms such as SOM, RBM, and CNN, we can further enhance the accuracy and efficiency of the customer segmentation process. This can help businesses to better understand their customers and develop targeted marketing campaigns that drive growth and success.

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Chapter 10

Optimization of Water Use in the Washing Process of Industrial Orange Juice Extractors for a Circular Economy Approach Amaury Nabor-Lagunes, Alberto Ochoa-Zezzatti, and Luis Sandoval

1 Introduction The raw materials used by the food industry are very complex and have very high microbiological and safety requirements, so any process must guarantee that the transformations that take place as it goes through the different operations will lead to a final product that meets the strictest sanitary requirements. Microbial contamination of the materials and machinery required for the packaging and production of goods can lead to product deterioration and have a significant economic impact due to product recalls. It is essential to have a preventive process of sanitization of containers and equipment before filling and during the process to ensure their use and avoid complications. The optimization of energy resources such as electrical energy and water consumption is leading to the development of new processes with low energy consumption, while each company studies how to eliminate energy losses and how to rationalize their use. The industrial machinery washing system in companies uses chemical compounds, in addition to using the water resource as a base, respecting the physicochemical characteristics of the water, without changing its conductivity or pH, or precipitating salts. Proper water management in the process can also lead to enormous economic savings in consumption and discharge quotas, based on efficient reuse. Naturally, the sanitary and environmental aspects are unquestionable. A. Nabor-Lagunes · A. Ochoa-Zezzatti (B) Instituto Tecnológico Superior de Misantla, Misantla, Mexico e-mail: [email protected] L. Sandoval Instituto de Ingeniería Y Tecnología (UACJ), Chihuahua, Mexico A. Ochoa-Zezzatti Facultad de Ingeniería, Universidad Anáhuac México, Huixquilucan, Mexico © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_10

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This system is highly effective against the main pathogenic microorganisms, among which we can find Alcaligenes, Bacillus, Clostridium, Cryptosporidium, Enterobacter, E. Coli, Giardia Lamblia, Legionella, Micrococua, Mycobacteria, Pseudomonas, Salmonella, Staphylococcus, Streptococcus, Vibrio, etc. [1]. In Mexico, water consumption in companies is regulated by the Secretaría de Medio Ambiente y Recursos Naturales (SEMARNAT), which establishes how industries must return the water they use in their processes and sets the maximum permissible limits for contaminants in wastewater discharges to urban or municipal sewage systems, in accordance with NOM-011-SSA1-1993 [2]. The state of Veracruz is an agricultural entity of national interest in citrus production and is considered the most important orange-producing region. In the north of the state, there are 3 areas that are dedicated to the cultivation and exploitation of tangerine; the municipalities that comprise them are Alamo, Tihuatlán, Tuxpan, Gutiérrez Zamora, Papantla, Tecolutla, Martínez de la Torre, Tlapacoyan and Misantla. It is precisely in this region where the municipality of Alamo Temapache is located, which stands out above all others for being the most important in terms of surface area and volume of orange production, even at the national level. Due to the abundant citrus production in the region, it is to be expected that citrus companies dedicated to the export of fruit and derivatives, such as juice, have been established. Such is the case of the company “Internacional Química de Cobre, S.A. De C.V.”, which for more than 25 years has been dedicated to the production and marketing of products for the field, nationally and internationally, and which in the mid-1980s expanded, founding a food division IQCitrus—Citrus Division [3]. Specifically, this company produces frozen juice concentrate, essential oil and dehydrated orange, lemon, mandarin and grapefruit peel [4] in their analysis of the competitiveness of small agroindustrial enterprises (SMEs) in Alamo Temapache, Veracruz. In terms of demand conditions, the companies’ clients demand product and packaging quality, as well as that the companies have HACCP and ISO certifications, respect delivery times and comply with customs and tariff administrative procedures. Some of the significant problems faced by small and medium-sized enterprises are management deficiencies, low employee participation in the planning of the company’s activities, insufficient attention to the personnel selection and induction process, lack of employee motivation, insufficient information and knowledge of current issues, no application of production planning techniques and lack of tools to control environmental pollution. The last point is the area of opportunity to develop an improvement, since the problem lies in the deviations from the maximum permissible limits of pollutants in wastewater discharges to sewage systems. That is why we intend to implement an industrial optimization model to maximize water consumption performance for the washing process of industrial orange juice extractors for the company “Internacional Química de Cobre, S.A. De C.V.”. On the other hand, unrestricted water use has grown globally at more than twice the rate of population growth in the twentieth century, to such an extent that in many regions it is no longer possible to provide reliable water service. Population pressure, the pace of economic development, urbanization and pollution are putting unprecedented pressure on a renewable but finite resource, especially in arid and semi-arid

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regions. Water use in agriculture and agribusiness continues to be determined by the steady growth in demand for agricultural products to meet the needs of a growing population. Although the rate of world population growth has slowed since the 1980s, population numbers continue to grow rapidly, particularly in developing countries. The net result of all this is that water use for these economic sectors is increasing the severity of water scarcity in some areas, and causing shortages even in areas with a relatively good level of water resources [5]. Evidently, one of the most used resources throughout the agroindustrial process of orange juice extraction is water; for such reason in the different activities that take place within the citrus industry, wastewater is generated both from fruit processing and cleaning operations. The water used by the industry to carry out its manufacturing process is called industrial wastewater, and as such cannot be disposed of directly into the sewage system, so it is important to implement a treatment system and take action to reduce contamination. A viable alternative is the implementation of a wastewater discharge control program, which refers to the organization of works and activities with the purpose of regulating the high concentration of pollutants in the water that is discharged. In addition, integrating physical, chemical and biological operations and processes is needed in order to purify them to a level that allows them to reach the required quality for final disposal or reuse. On the other hand, the purpose of the washing and cleaning process as such in the food industry, in this case agribusiness, is to leave a surface and/or machine free of dirt to reduce the number of microorganisms present and limit their growth. In this way, it contributes to compliance with official standards governing food safety and health, such as NOM-251-SSA1-2009 [6], which includes the control of water that is in direct contact with food, beverages, raw materials, packaging and surfaces that come into contact with it, to cite a few examples. Cleaning is a critical factor, fundamental in the activities that measure the quality of the process; since residues and dirt can alter the functions and safety of the products, it also improves efficiency and increases the useful life of the equipment. The treatment used to carry out the cleaning and washing of the machines should not affect the equipment or its devices; for this, it is important to use food-grade substances and cleaning products that meet the required specifications to disinfect the equipment and even the water itself, as stated in NOM-127-SSA1-1994 [7]; at the end of the washing process activities, final sanitation is performed using antibacterial solutions in order to minimize the presence of microbes. Thus, a proposal for improvement is proposed, which will be developed later in the content of this work, whose objective is to achieve the optimization of the washing process of industrial orange juice extractors using industrial engineering tools in order to obtain an approach to a circular economy model.

2 Methodology This research seeks the implementation of an approximate circular economy system for the recovery of water generated as waste in the process of washing industrial orange juice extractors in the company “Internacional Química de Cobre, S.A. De

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C.V.” by measuring and evaluating the process variables involved (volume of juice extracted, extraction pressure, juice alkalinity, biomass generated and wastewater generated) through industrial engineering tools, in order to optimize the water consumption required in the industrial extractor washing process and generate an improvement proposal for decision-making by the company’s managers. It is important to mention that the fulfillment of these objectives would be bringing us closer to a circular economy model, which aims to reduce both the input of virgin materials and the production of waste, closing the economic and ecological flows of resources to circulate in a socioeconomic system through reuse and technical recycling as a key strategy [8]. In environmental matters, it is of utmost importance that companies carry out emissions of wastewater discharges with pollutants to drainage systems based on legal regulations, depending on what the case may be: national (SEMARNAT), state and even municipal. Otherwise, they may be subject to fines for noncompliance and damage to the environment, restrictions and temporary or permanent closure. The scope of this research is to provide a theoretical solution to the decision makers of the company IQCitrus, to the problem of the lack of optimization of the washing process of industrial orange juice extractors. Subsequently, the steps to follow would be the implementation of corrective actions necessary in the actual process, in order to measure and monitor the changes that occur in the course. The research presents a type of exploratory-correlational study, since throughout the work the problem of the lack of control in water consumption for the washing process of industrial orange juice extractors is examined; an area of opportunity for improvement little studied, in turn, relates to operating variables such as volume of juice extracted, extraction pressure, juice alkalinity, biomass formed (orange peel and bagasse) and residual water generated, to carry out an investigation and evaluation of the process with the objective of determining how much affectation the lack of control of the variables generates, in addition to its impact on the efficiency of the machine when producing the juice extraction, and to carry out the work we will rely on the operating parameters of different literature consulted, fieldwork and the applicable regulations, as the case may be. The exploration will be carried out with the objective of identifying the main variables that have a direct impact on the efficiency of the industrial equipment and consequently generate a higher water consumption in the process; for this search for information, two tools will be used to support a probabilistic sampling, so that all elements of the population have the same possibility of being selected. The first will be an instrument for data collection that will help to obtain the variables that affect the functionality of the equipment, applied to a group of engineers (process manager, process engineer and production supervisors) of the company IQCitrus, and the second will be the access to the company’s database, to obtain information regarding the indicators of water consumption over time, used in the production process (Fig. 1). Once the data from the instrument is obtained, first an index of process efficiency will be made, evaluated based on the Likert scale, relating the impact of the variables found with the process operation throughout 2020, thus being able to detect the days with higher and lower efficiency index for the analysis of the root cause of

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Fig. 1 Research scheme, own elaboration

the impact problem and the subsequent decision-making for the implementation of corrective actions. Meanwhile, with the data obtained from the water consumption information base for the year 2020 in the citrus plant, these will be subjected to a sample size calculation using STATS® software to subsequently choose the days of operation, randomly selected (probabilistic sample), and analyze the respective water consumption for each one. Finally, by obtaining the two indexes provided through the data selection tools, the trends and behavior of both indicators will be studied and analyzed in a single graph, relating water consumption over time with the variables that reduce the operating efficiency of the industrial extractor. The sampling units to be analyzed in this work are as follows • The variables that reduce the operating efficiency of the industrial orange juice extractor. • The water expenditure required in the washing process of industrial orange juice extractors over one year of operation (the year 2020). Since we are analyzing data from one year of operation of the production process for the IQCitrus company, it can be deduced that we will work with the 366 days of the referred period, which is proportional to the number of data obtained from the water consumption of the process, and through it we will be able to calculate an indicator of water consumption over time. Since we will be working with a sample larger than 100 units, we will apply the central limit theorem to our information to fit the data to a normal distribution graph, with the purpose of making inferences in the analysis of the orange juice extractor washing process, as is analyzed in our proposal Objective Function, in Eq. 1.

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2.1 Objective Function of this Research The citrus industry is a very important economic sector in many countries due to the high demand for citrus juices and products derived from citrus fruits. One of the key processes in this industry is juice extraction, for which a significant amount of water is required. In this section of our research, we will discuss the use of water in juice extraction in the citrus industry and some of the challenges and solutions associated with its use. Juice extraction is a process that involves the separation of juice from the pulp and peel of citrus fruits. The extraction process is usually performed in a machine called a juicer or juice extractor. This process requires a significant amount of water, both to clean the citrus prior to extraction and to cool the machine and juice after extraction. The water used in the citrus industry for juice extraction can have various origins, such as well water, surface water, municipal water and recycled water. The use of water of adequate quality is important to ensure the food safety of the final product and to avoid contamination of the environment. In addition, the quality of the water used can affect the quality and yield of the juice. However, the use of water in juice extraction also presents significant challenges. One of the biggest challenges is the excessive use of water in the process of cleaning citrus fruit prior to extraction. Often, an excessive amount of water is used to wash citrus, which can be costly and contribute to water waste. In addition, wastewater contamination can be a major problem if not properly managed. Another challenge associated with water use in juice extraction is the limited availability of water in some regions. In many countries, water scarcity is a critical problem, and excessive water use in the citrus industry can exacerbate this problem. Therefore, it is important for the citrus industry to adopt sustainable water management practices to minimize water use and reduce environmental impact. Fortunately, practical solutions exist to address these challenges. One solution is the use of more efficient and sustainable technologies in juice extraction, such as more efficient cleaning systems and the use of water recycling techniques. Another solution is the adoption of sustainable water management practices, such as rainwater harvesting and storage, drip irrigation and the implementation of water conservation programs. There is an indicator in the literature that allows us to know the amount of water used in the creation of a product through industrial processes called water footprint, and refers to the rate of use of this resource through the set of products or services that it consumes (Nadal, 2021). And in the case of orange juice that addresses this research work, the relationship of water footprint that is cited to the CONAGUA (2007) and the work of Arreguín-Cortés et al. (2007) called virtual water in Mexico, it is 170 L of water used to produce 200 ml of orange juice, which is equivalent to an average glass of juice. So, the use of indicators can be useful as a tool for measuring the level of performance of a process and allow us to analyze the variables involved in operations through a performance index; overall, with the data mining method, more accurate

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results can be obtained in the face of industrial process optimization problems and resource management. Therefore, water management must be a concern in all organizations and in any productive activity, the responsibility of companies with the environment must go before the regulatory duty, through the implementation of a cleaner production plan, control of water quality and optimal use of the resource, in favor of sustainable development. In conclusion, water use in juice extraction is a critical process in the citrus industry. However, excessive water use and limited water availability are major challenges that need to be addressed to ensure the sustainability of the industry. The adoption of more efficient and sustainable technologies is necessary to ensure sustainable water management practice. An objective function that considers the different variables to optimize water in the juice extraction process in the citrus industry could have the following form: f(x) = α1∗ (Cw) + α2∗ (Ce) + α3∗ (Cr) + α4∗ (Cp) + α5∗ (Ct)

(1)

where Cw is the amount of water used to wash citrus before extraction. Ce is the amount of water used in the extraction process. Cr is the amount of wastewater generated during the extraction process. Cp is the cost of water used in the process. Ct is the total cost of production. Variables α1, α2, α3, α4 and α5 represent the relative weights assigned to each variable in the objective function and can be determined by the company or user based on specific needs and priorities. Each variable used in the objective function is detailed below. Amount of water used to wash citrus prior to extraction (Cw): This variable refers to the amount of water used to clean citrus prior to extraction. The objective is to minimize the amount of water used in this process, as this can reduce the cost and environmental impact of the extraction process. To optimize this variable, more efficient cleaning techniques and water recycling systems can be used. Amount of water used in the extraction process (Ce): This variable refers to the amount of water used in the extraction process itself. The objective is to minimize the amount of water used in this process, as this can reduce the cost and environmental impact of the process. To optimize this variable, more efficient technologies and water recycling systems can be used. Amount of wastewater generated during the extraction process (Cr): This variable refers to the amount of wastewater generated during the extraction process. The objective is to minimize the amount of wastewater generated, as this can reduce the cost and environmental impact of the process. Wastewater treatment systems and water recycling techniques can be used to optimize this variable.

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Cost of water used in the process (Cp): This variable refers to the cost of water used in the extraction process. The objective is to minimize the cost of water used in the process, as this can reduce the total cost of production. To optimize this variable, more economical water sources and more efficient water management systems can be used. Total cost of production (Ct): This variable refers to the total cost of production, including the cost of water used in the extraction process. The objective is to minimize the total cost of production, as this can improve the profitability of the company. To optimize this variable, more efficient production techniques, more efficient water management systems and more economical water sources can be used. In conclusion, an objective function that considers the different variables to optimize water in the juice extraction process in the citrus industry can help companies improve the efficiency and sustainability of their processes considering the uncertainty of this process.

3 Results A. Data collection through the creation of an instrument With the help of a questionnaire designed to be applied to professional personnel in the production area, this preliminary exercise was carried out with the support of 50 engineers in the areas of specialization competent with the orange juice extraction production process, obtaining the following data (Figs. 2, 3, 4, 5, 6, 7, 8, 9 and 10). Based on the weighting of the following variables according to the Likert scale, an index is formulated to present the results obtained (Fig. 11).

Fig. 2 Questionnaire I graph

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Fig. 3 Questionnaire II graph

Fig. 4 Questionnaire III graph

In the following images, an example of the Excel data is presented, taking a sample of the first 30 days of operation of the year 2020; the rest of the calendar and variables are shown completely in the spreadsheet. It can also be seen that for 5 variables, a minimization is performed and for the rest it is maximized (Figs. 12 and 13).

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Fig. 5 Questionnaire IV graph

Fig. 6 Questionnaire V graph

By calculating all the data and making a general summation of variables per day of operation for the year 2020, as a result we obtain an index where the 366 dates that the company operated are ranked. The measurement of the variables and their subsequent evaluation allowed us to observe their daily behavior and assess their impact on the efficiency of the industrial orange juice extractor. The following image shows the main dates that the extractor operated with greater functionality, according to the evaluation of the work performed (Fig. 14).

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Fig. 7 Questionnaire VI graph

Fig. 8 Questionnaire VII graph

Subsequently, a statistical analysis was made of the index resulting from the measurement of the variables, with the data corresponding to 366 days of operation. As a result, it was obtained that the index has an average of 0.64618 representing the mean value of the process efficiency = 65%, and a standard deviation of 0.13595 with respect to the mean = 14%, being a considerable value of dispersion among the analyzed values, but it is justified since the operation process is not continuous (Fig. 15).

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Fig. 9 Questionnaire VIII graph

Fig. 10 Questionnaire IX graph

The following histogram graphically represents the frequencies of the data analyzed (Fig. 16). In addition, a probability plot for the efficiency index values, fitted to a normal distribution, is presented (Fig. 17). The top high 10 and top bottom 10 of the dates of operation, in relation to the efficiency ranking, are presented below (Fig. 18).

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Fig. 11 Operationalization of the research variables, own elaboration

Fig. 12 Spreadsheet with estimated values for each variable, part I

It is evident that the date with the highest efficiency index was position 177 of the year 2020 with an adherence of 94%; on the other hand, the date with the lowest tendency was position 120 with a percentage of 34%. The result of this ranking was based on the values assigned and evaluated in Excel for each date; the following table shows the values of each variable for the day with the highest percentage of index; in it, we can see the calculated weights that led it to be in the top 1 (Fig. 19).

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Fig. 13 Spreadsheet with estimated values for each variable, part II Fig. 14 Top 40 most efficient 2020 dates

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Fig. 15 Statistical analysis performed in Minitab

Fig. 16 Histogram performed in Minitab

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Fig. 17 Probability plot performed in Minitab

Fig. 18 List of dates with the highest and lowest percentages of adherence to the efficiency of the process

Fig. 19 Values of the variables calculated for the top

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4 Discussion of Results Using Eq. 1, it is possible to analyze a specific benchmark and the Python code is given below. The following is an example of a benchmark of variables for the objective function that considers the different variables to optimize water in the juice extraction process in the citrus industry : • Amount of water used to wash citrus fruit before extraction (Cw): 5–10 L per 100 kg of citrus fruit. • Amount of water used in the extraction process (Ce): 200–400 L per 1000 kg of citrus. • Amount of wastewater generated during the extraction process (Cr): 50–100 L per 1000 kg of citrus. • Cost of water used in the process (Cp): 0.5–1 USD per cubic meter. • Total cost of production (Ct): 500–1000 USD per 1000 kg of citrus. Based on the variable benchmark, the objective function can be programmed in Python as follows:

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Suppose the Citrus fruits company wishes to minimize the proposed objective function, assigning the following relative weights to each variable: α1 = 0.2 (Cw) α2 = 0.2 (Ce) α3 = 0.2 (Cr) α4 = 0.2 (Cp) α5 = 0.2 (Ct) The resulting objective function in this case would be

The function optimize_water() takes as input the variables Cw, Ce, Cr, Cp and Ct, and returns the value of the objective function F. In this example, the relative weights for each variable are assumed to be equal (0.2). To plot the objective function, the Python matplotlib library can be used as follows:

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In this code, a 3D plot is generated showing how the objective function F varies as a function of the variables Cw, Ce and Cr. The constant values for Cp and Ct are set to 0.75 and 750, respectively. The values for Cw, Ce and Cr are generated using NumPy’s linspace() function to create a range of equidistant values. The result of the plotting will be a 3D figure showing how the objective function behaves as a function of the variables Cw, Ce and Cr. Depending on the relative weights assigned to each variable and the specific values of each variable, different optimal combinations of variables can be found to optimize the use of water in the juice extraction process required to meet the demand in a Smart City. A.–Data collection through the company´s information base. Population: Volume of water (hectoliters) used in the washing process of all machinery required for the manufacture of orange juice and cleaning activities of the areas in general throughout the year 2020, of the company IQCitrus. Sampling elements or units: volume of water (hectoliters) used in the washing process of industrial orange juice extractors throughout 2020. Sample: probabilistic sample, estimated through the STATS ® program. Data: n, Sample = ? N, Population = 366. Z, Statistical parameter depending on confidence level = 95% = 1.96.

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Fig. 20 Sample size calculation, verified by the STATS® program

e, Maximum accepted estimation error = 3%. p, Probability of occurrence of the studied event (success) = 50% q = (1-p), Probability that the studied event does not occur (failure) = 50%. q = (1-p), Probability that the studied event does not occur (failure) = 50%. This sample number represents the 273 days in 2020 that I must randomly select in order to construct the process efficiency index for subsequent analysis (Fig. 20). The sample number required to work (n = 273) was obtained with a confidence level of 95% and a margin of error of 3%. With the help of Table 6-3 of random digits, from the book Statistics for Management and Economics by Levin et al., we proceeded to select the data randomly as indicated in the reference (Fig. 21). The data obtained are presented in the following table (Fig. 22). Subsequently, a statistical analysis was performed on the data selected for the sample size, corresponding to the volumes of water consumption for the 273 days sampled (Figs. 23, 24 and 25). The following histogram graphically represents the frequencies of the data analyzed (Fig. 26). In addition, a probability plot for the sample values of water consumption in hl, fitted to a normal distribution, is presented. Once the sample number required to work (n = 273) was obtained with a confidence level of 95% and a margin of error of 3%. With the help of Table 6-3 of random digits, from the book Statistics for Management and Economics by Levin et al. We proceeded to select the data randomly as indicated in the reference (Fig. 27).

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Fig. 21 Table of random digits Fig. 22 Table of volumetric water consumption

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Fig. 23 Table of statistics of central tendency

Fig. 24 Table of dispersion statistics

Fig. 25 Statistical analysis performed in Minitab

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Fig. 26 Histogram performed in Minitab

Fig. 27 Probability plot performed in Minitab

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5 Conclusions It can be concluded that the analyzed data (sample of 273 data, randomly selected), corresponding to the daily volumes of water consumption used in the process of washing orange extractors, have an average equal to 553. 7 hectoliters; this means that the company IQCitrus on average has an expenditure greater than 500 hl only in the washing of industrial machinery; this value alerts me about a possible surplus of water consumption since we do not consider the washing process in other areas and water consumption in general of the plant, so it is important to compare this indicator with the internal goals of the company, to make a more efficient decision-making on how to optimize this expenditure. On the other hand, the analysis of this data showed a standard deviation of 250 hl with respect to the mean, being a considerable value of dispersion between the values because when considering the daily water consumption, it must be taken into account that there are holidays and weekends in which the consumption of water resources decreases significantly compared to the dates when the master plan for cleaning, maintenance and other activities that increase the activity of the machinery washing process and areas in general are scheduled.

6 Future Research Finally, with the data obtained through the two data collection instruments presented above, it is feasible to construct a graph showing the trends of both indicators and to analyze the relationship between the variables that affect the efficiency of the orange juice extractor washing process [9, 10] and the consumption of water resources in the production process of the company “Internacional Química de Cobre, S.A. De C.V.”, as can be seen in Fig. 28.

Fig. 28 Annual trend graph expressed as a percentage, comparing the efficiency index of the washing process in relation to water expenditure during the year 2020

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Fig. 29 Representation of an intelligent avatar that by means of a conversational agent can adequately identify changes in the information to be analyzed

Another relevant aspect to be realized is an intelligent avatar to be a conversational agent that can accurately indicate a paradigm shift in the information collected and the appropriate visualization of it (Fig. 29).

References 1. Díaz Peralta R, Ontoria Y, Alcaíz Escribano I (2011) Limpieza e higiene, piezas clave para la industria. Revista Tecnifood. La revista de la tecnología alimentaria. Madrid, España. MayoJunio, pp 94 y 100 de 101 2. Norma Oficial Mexicana NOM-002-SEMARNAT-1996. “Limites máximos permisibles de contaminantes en las descargas de aguas residuales a los sistemas de alcantarillado urbano o municipal”. Diario Oficial de la Federación, México, 3 de Junio de 1998 3. Internacional Química de Cobre, S.A. De C.V. IQCitrus División Cítricos (2008) COPYRIGHT © 2021 IQCITRUS-MÉXICO. Recuperado el 07 de Marzo de 2021. http://www.iqcitrus.com/ nosotros/historia 4. Bada Carbajal LM, Ramírez Hernández Z, López Velázquez MA (2013) Competitividad de las pequeñas y medianas empresas (pymes) agroindustriales en cítricos de Álamo, Veracruz. IA. Investigación Administrativa. México. ISSN 1870-6614. vol 42 (no111), pp 78 y 79 de 81. (Enero-Junio 2013) 5. Burchi S (2013) Afrontar la escasez de agua. Un marco de acción para la agricultura y la seguridad alimentaria. FAO. Informe sobre temas hídricos. Organización de las naciones unidas para la alimentación y la agricultura. Roma, Italia. ISSN: 1020-1556, pp 19 y 20 de 97. 6. Norma Oficial Mexicana NOM-251-SSA1-2009. Prácticas de higiene para el proceso de alimentos, bebidas o suplementos alimenticios. Diario Oficial de la Federación, México, 1 de Marzo de 2010 7. Norma Oficial Mexicana NOM-127-SSA1-1994. Salud ambiental, agua para uso y consumo humano. Límites permisibles de calidad y tratamientos a que debe someterse el agua para su potabilización. Diario Oficial de la Federación, México, 15 de Agosto de 1994 8. Haas W, Krausmann F, Wiedenhofer D, Heinz M (1 de octubre de 2015) How circular is the global economy?: An assessment of material flows, waste production, and recycling in the

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European Union and the World in 2005. J Ind Ecol, published by Wiley Periodicals, Inc., on behalf of Yale University, vol 19, no 5, pp 165 de 177. ISSN: 1530-9290. https://doi.org/10. 1111/jiec.12244 9. CONAGUA (Comisión Nacional del Agua) (2014) Inventario Nacional de Plantas Municipales de Potabilización y de Tratamiento de Aguas Residuales en Operación. http://www.conagua. gob.mx/CONAGUA07/Publicaciones/Publicaciones/In-ventario_Nacional_Plantas1.pdf 10. Pérez López O, Nava Tablada ME (2021) Evolution of Mexican citriculture (1993–2018). The case of the municipality of Gutiérrez Zamora, Veracruz. Revista de Geografía Agrícola, pp. 64 y 65 de 71. Universidad Autónoma de Chapingo. Número 67. Septiembre. ISSN-e: 2448-7368. https://doi.org/10.5154/r.rga.2021.67.01

Chapter 11

Optimizing ROVs in Metaverse for Marine Oil Pipeline Maintenance Using Gorilla Troops Optimizer Algorithm Irving Azuara, Roberto Contreras-Masse, Alberto Ochoa-Zezzatti, and Lucia Sada-Elizondo

1 Introduction Metaverse is a digital multiuser environment with multiple technologies converging in a single environment. These technologies can be virtual reality (VR) and augmented reality (AR) that allow recreating physical scenarios in a digital environment where the physical laws that govern our existence are programmed so that a computer can simulate the real environment [21]. When performing the calculations of these laws, the accuracy of the simulation depends on the mathematical optimizations and in the detail included in the code, so approximations are necessary and justified, and the user or system can obtain realistic simulations. Currently, there are high-capacity graphics engines, also named as virtual reality environment (VRE) such as Unity and Unreal Engine; a graphics engine is software specialized for the creation of virtual environments; its main task is the rendering of graphics, the simulation of the physical laws of the virtual environment that are configured according to the developer’s criteria, the animation of elements that make up the virtual environment, and the reproduction of audio that corresponds to the

I. Azuara UPITTA, IPN, Av Instituto Politécnico Nacional 2580, La Laguna Ticoman, Gustavo A. Madero, 07340 Ciudad de México, CDMX, Mexico R. Contreras-Masse (B) TECNM Campus ITCJ, Ciudad Juárez, CH, Mexico e-mail: [email protected] A. Ochoa-Zezzatti UACJ, Ciudad Juárez, CH, Mexico e-mail: [email protected] L. Sada-Elizondo UDEM, Monterrey, NL, Mexico © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_11

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actions that are taken in the virtual environment such as the sound of a flow of water or the breeze, among others [9]. The level of detail in the textures and physics of a virtual environment depends on the skill of the developer, as well as the computing power hardware to run the graphics engine, including a dedicated graphic processing unit (GPU); with the computing power that we currently have, physical environments can be simulated with great accuracy [15], which makes it possible to generate reliable simulators for real systems where their construction is costly and temporary, or where their operation is dangerous and there is little margin of error in the maneuvers. The simulator of a system can be used to perform performance or operation tests, create failure and catastrophe scenarios, or train people to operate the system properly without the need to put the investment, infrastructure, and the integrity of the operators at risk [19]. A clear example of what was described above is detailed in this paper; the extraction of hydrocarbons at the submarine level presents a great environmental risk due to failures in the transportation system that is based on pipelines to transport the material extracted from the submarine extraction zone to the storage area on the surface. It is common to find leaks in pipelines caused by the high pressures they must withstand when located in the depths of the sea and by the viscous characteristic of hydrocarbons. To carry out the repair of the leaks present in the oil pipelines, the use of Remotely Operated Vehicles (ROV) is a good option, due to the health risk that working in high sea depths represents for humans while working collaboratively to carry out all the required maneuvers [6]. The ROVs are operated remotely by a human operator from the surface, who communicates with the unit through a cable or line. This same cable also provides energy to ROV. A few important characteristics to consider for the ROVs for repairing leaks are the length of its arms, the number and type of maneuvers that can be performed with them, as well as its stability in the presence of sea currents [24]. In the last 50 years, the Remotely Operated Vehicle (ROV) technology has been advanced through research in military, oil, and gas industries, and, more recently, by commercial enterprises who have taken advantage of cost reductions to create affordable underwater vehicles. Inspection-class ROVs are linked to the surface user by an umbilical cord, and can be employed as a substitute for divers in hazardous or deep-sea conditions. ROVs can improve the efficiency of underwater operations through 24 h operations, real-time video feedback, and continuous relay of scientific data to the surface operator [8]. ROVs are often classified by duty or purpose. The intervention-class ROVs, or work-class ROVs, are used in the offshore oil and gas industry for heavy-duty work such as cleaning, drilling, and construction. They can operate at depths of up to 6000 m and weigh up to 5000 kg. They require a Launch and Recovery System and Tether Management System, resulting in high operational costs. For less demanding applications, inspection-class ROVs can be used to reduce costs and complexity. Inspection-class remotely operated vehicles (ROVs) are smaller and less expensive than intervention-class ROVs, and they are subdivided into medium-sized and handheld/micro-sized ROVs. Medium-sized inspection ROVs are typically openframe models that weigh between 30 and 120 kg, have accurate navigation systems,

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and high-resolution imaging capabilities that enable them to carry out underwater mapping and surveys. Micro- or handheld inspection ROVs weigh between 3 and 20 kg, and are often used to reduce operational costs and system complexity. The depth rating of this ROV category is generally less than 300 m [8]. Although it is vitally important to repair leaks in oil pipelines and ROVs, they are capable of operating in underwater conditions; their operation requires a lot of practice on the part of the operator to be able to carry out the necessary repair maneuvers and avoid losing control of the unit at all costs, since the failure of a unit represents potential risks such as the appearance of new leaks in the pipelines when presenting impacts with the unit, the shock of the ROV out of control with others ROVs which are collaborating to repair the leak, or loss of communication with the unit by breaking the communication cable [6]. In either case, economic losses are high due to the high acquisition cost of a ROV unit. Finally, there are low-cost ROVs entering the market as an option to make available higher quantity of these devices for a large number of applications. Low-cost ROVs typically consist of a central air-sealed unit with a camera and control electronics, with 3–5 propellers for propulsion. The operator controls the device using a tether for video and data signals. Adapting these vehicles for deep-sea scientific surveys or tasks is challenging due to crushing pressures, long-distance communication, and freezing temperatures [25]. The use of ROVs for dangerous tasks have become popular. Submarine exploration, mining, and repairs are some of the fields where ROVs can be used. There are oceans and areas where the conditions are more dangerous than others and have more activity than others. Gulf of Mexico is a good example of those two features. It has a large oil industry deployed and the natural behavior is challenging. In addition, according to statistical data from the NOAA’s (National Oceanic and Atmospheric Administration) Atlantic Oceanographic and Meteorological Laboratory, the Gulf of Mexico presents a particular behavior in its maritime currents that are part of the Atlantic current system, which have great variation both in the angle of direction and in the magnitude of their speed and drag force [12, 16, 26]; this being a factor more than hinders the operation of ROVs for the execution of the maneuvers, while for its transfer to the place of the escape it represents a priority data, since it is completely preferable that the ROV move diagonally to the sea currents that are against or totally in favor of it to ensure its stability. For the purposes of this work, the system will be named the set of ROVs working collaboratively to carry out the repair of leaks in pipelines, due to the care and experience required to manually operate the system, as well as the economic cost it represents. The National Institute of Electricity and Clean Energies (INEEL) has developed a virtual reality metaverse environment that recreates the underwater environment of the Gulf of Mexico with the aim of training operators without jeopardizing the infrastructure and equipment that national companies that are dedicated to the extraction of hydrocarbons have. Metaheuristics are commonly used for optimization problems because they offer a flexible and efficient approach to finding near-optimal solutions in complex and large-scale problems where traditional optimization methods may not be feasible.

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Metaheuristics are able to explore a wide range of solutions and search spaces by using intelligent search strategies and heuristic rules, making them a powerful tool for optimization in diverse fields such as engineering, finance, and operations research [17]. Metaheuristics are useful for optimizing ROV operations because they can efficiently search for near-optimal solutions in complex, high-dimensional search spaces. ROVs often face complex, uncertain, and dynamic operational environments that require continuous adaptation to changing conditions. Metaheuristic algorithms can adapt to these changing conditions and optimize ROV operations by exploring different solutions, evaluating their performance, and refining them over time. They can also handle constraints and uncertainty, such as limited power or communication, which are common in ROV operations. Overall, metaheuristics offer a powerful tool for optimizing ROV operations and improving their efficiency, safety, and effectiveness [18, 19, 30]. The objective of this work is to implement the algorithm Gorilla Troops Optimizer to support decision-making in the collaborative work of the ROVs. In this way, it is ensured that the repair of leaks in the oil pipelines is resolved in the least number of maneuvers possible, which is reflected in a lower economic and temporary cost and less damage to the environment, applied to virtual reality metaverse model. This work is organized by sections. Section two covers the description of the metaverse created by INEEL. The next section discusses the metaheuristics, their classification, and the implementation of the Gorilla Troop Optimization algorithm (GTO). Next, the results of GTO applied to ROVs model are presented. The last section shares conclusions and future work.

2 Metaverse Environment Where the Project Is Implemented The virtual reality environment developed by INEEL is powered by Unity graphic engine version 2018.3.14f1. In the present work, the configurations simulating the underwater environment are reused to corroborate the operation of the system with the implemented algorithm. There are pipelines where the leak in the pipeline is simulated and represents the hydrocarbon extraction plant. The environment supports the existence of several leaks at the same time in different pipeline segments. Within the metaverse, there is a 3D model of a ROV including all it’s mobile parts, such as the six propellers to move forward, backward, and laterally, which when combined produces diagonal movement. It also has an arm with a clamp to the end; this arm allows it to be fixed to the pipes to have greater stability when carrying out maneuvers against the sea currents. When the sea currents are strong, the arm clamps to the pipe to ensure the ROV don’t be swept away by the current. Also, the ROV has a multi-functional arm that allows it to perform other maneuvers required

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Fig. 1 Development of radar in the virtual reality metaverse environment. Schematic view. Source Own creation

to repair leaks in oil pipelines. At the top of the ROV, there are two lanterns that illuminate the view so the operator can see through a video camera installed at the top of the ROV in the front and back. Knowing the ROV architecture, the most important characteristics of ROV are defined to carry out different maneuvers. Since not all the units are equal to each other, common variables are defined such as the maximum current that each ROV supports to navigate, the number of clamping arms to the pipe available, the number of maneuvering arms, the extension of each clamping arm, the extension of each maneuvering arm, and the type of maneuvers the unit can perform. Figure 1 shows the development of a radar, a vital instrument used in deep water navigation to know the proximity with the objects that surround each ROV, especially with the other ROV units. It is very important to know the distance between the units and the leak in the pipeline to define roles in the collaborative work they carry out. In addition to this, it must be remembered that the behavior of marine currents is another important variable for the navigation of the ROVs and that, together with the distance, are part of the criteria to select which units should move toward the place of failure. Currently, the virtual reality environment developed by INEEL has a multi-user interface that allows an instructor and the person being trained to interact with the simulator at the same time, so that the instructor supervises the operator’s learning process. Also, the instructor is capable of activating leaks in the pipelines, which the

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person in training must repair. In addition, it is possible to configure changes in the sea current such as the angle of incidence as well as the intensity. On the other side, the operator can manipulate the ROV. It is important that the person being trained becomes familiar with the movement of the unit; the simple fact of manipulating a moving object within a fluid with a higher density than air is complicated due to the paradigm shift in the sensation of inertia, combined with the presence of sea current results in a complex experience to operate a ROV. On the user interface designed for the role of the operator, the available navigation tools for operators are a compass that indicates their position in the area of interest and the radar that was shown previously in Fig. 1, where the hearts represent other ROVs close with which you will work collaboratively. It must be remembered that the view for the operator on the surface is reduced and totally depends on the angle of view of the cameras incorporated in the unit, as well as their quality, along with illumination. To fully recreate the experience, the operator will only be able to see from the background the movement of the arms of the 3D model of the ROV with the purpose of generating the ability to size the extension of the arms and avoid making mistakes when having a bad perspective. In addition to the front camera, the unit has a rear camera, necessary to carry out certain maneuvers and to return the unit to the station on the surface. The main screen of the application in which the initial menu is located to select the role of the user and where the hydrocarbon extraction plant can be seen in the background. In this menu, a new button is implemented that redirects the flow of the program to a new scene where the virtual reality metaverse environment for the incorporation of the intelligent assistant is configured to optimize the collaborative work of the ROVs. In this stage of leak repairs, the carried-out maneuvers use the algorithm Gorilla Troops Optimizer determined as the best solution to minimize temporary and economic costs. By metaverse simulation, it is possible to verify if the repair process has the minimum amount of movements and maneuvers. When starting the scene of the intelligent mode, a random distribution of the objects is generated. ROVs in the virtual reality metaverse environment are placed, as shown in Fig. 2, which is usually a common use case in real-life operation. Please note Fig. 2 is a sample representation of the environment as it cannot be reproduced from the production system. During the simulation, the appearance of a leak in the pipeline occurs (either randomly or by a predefined scenario), for which the algorithm must determine the best procedure to solve the failure. The animation of leak appearance at a certain point of the pipeline and the required displacement of the ROVs to deal with the incident are calculated with the bioinspired metaheuristics. Figure 2 shows an oil leak on the first pipeline at position −65.21, −34.73 of intensity 2. The metaverse environment developed allows to have an accurate notion of the performance that the system will have in the real world due to all the physical constraint as they are taken in the behavior of the system.

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Fig. 2 Random distribution of the ROVs in intelligent mode. Schematic view. Source Own creation

3 Implementation of Gorillas Nature-Inspired Metaheuristics The term heuristic is used for procedures that produce solutions with good performance regarding the use of resources. Generally, these procedures arise from specific knowledge of the tasks that need to be carried out and not from a rigorous formal analysis. The advantage of metaheuristic methods is the flexibility, which enables solving a large number of problems from different branches due to the design based on the solution of combinatorial optimization problems; another characteristic of the metaheuristic methods is the decision-making based on learning to search for the solution of the optimization problem in regions called search space in a random way, obtaining results in reasonable times and with an acceptable consumption of computing resources. Due to their random nature, metaheuristic methods require iterations to find the best solution to the problem [27]. Metaheuristics are not new. One of the first metaheuristics known is the proposed genetic algorithm by Holland in 1962. At this time, there are more than two hundred algorithms, and they are often classified into five big groups: (i) Bioinspired; (ii) Swarm-based; (iii) Evolutionary-based; (iv) Nature-inspired; (v) Population-based [7, 11, 13, 22]. Figure 3 shows this classification with some examples. The Gorilla Troops Optimizer (GTO) is a novel metaheuristic optimizer, but several authors differ in its classification. At this moment, GTO has been classified as bioinspired [3, 23], nature-inspired [1, 29], and swarm-inspired [28]. In this paper,

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Fig. 3 Classification of metaheuristic methods with examples on each group

GTO is considered as a nature-inspired metaheuristic method because it arises from observing and imitating the behavior of gorilla herds regarding their social hierarchy and the way they organize themselves to make group decisions. Gorilla societies are based on the division by groups called troops; these are made up of a group of male gorillas called silverbacks and a larger group of female gorillas, as well as their offspring. The average life of the silverback gorilla is 12 years, and it is distinguished by presenting a change in its fur that turns silver during puberty; another of its characteristics is the growth of its canines. Gorillas are constantly on the move as they have a nomadic lifestyle; this is how they are accustomed to migrating both from the geographical site and their troops from their birth. Male gorillas are the main ones to migrate to new groups and form their own troops by attracting female gorillas. In the case of not migrating, generally, male gorillas are integrated into the main group called silverbacks. Within the group of male gorillas, there is a leading gorilla; when this gorilla dies, the other gorillas fight among themselves to determine who the new leader is. As in most animal species, in addition to the fight to define who leads the pack, it is common for male gorillas to fight to increase the number of female members of the group. In the event that all male gorillas die or only one survives, the trend indicates that the troop is diluted to reintegrate into other nearby troops. The leading silverback gorilla has responsibility for the safety of the troop and makes decisions about the route the group will follow to find food sources. Male gorillas that follow

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Fig. 4 Phases of the algorithm Gorilla Troops Optimizer. Source Own creation

the commands of the main silverback gorilla are called blackbacks and support the troop by keeping it safe; these are aged 8–12 years. The core that keeps the troop together is the relationship between the silverback gorilla and the female gorillas; their relationship is close, staying physically close, as well as showing affection through grooming; for female gorillas, maintaining a close relationship with the silverback gorilla ensures protection from predators. On the other hand, black-backed gorillas have volatile relationships with female gorillas; however, they form friendly relationships through play, grooming, and closeness. When one gorilla troop confronts another, only the silverback gorillas fight, so only one survives, while the other gorillas adapt to the outcome. Once the general social panorama of the social life of gorillas has been raised, two major decisions are identified within the silverback group: the first is to follow the leading silverback, and the second is to compete to form a new troop by attracting female gorillas to it. On the other hand, the leading silverback gorilla decides among three options the fate of the troop. The first is to migrate to unknown places in search of new sources of food and spaces to make nests, the second is to migrate to known places where they remember their existence of the resources, and the third is to approach a neighboring troop. In GTO, five operators are identified to carry out the optimization operations (exploration—exploitation); the decisions that the silverback gorilla can make about the destination of the troop are called operators for exploration in the algorithm, while the decisions that can be made by the black-backed gorillas about their future are called operators for exploitation as shown in Fig. 4. The diagram corresponds to the analogy that relates the algorithm to the social behavior of gorillas. The operators proposed for the exploration phase are as follows: migration to unknown places increases the exploration of the algorithm, while movement toward other gorillas increases the balance between exploration and exploitation. Finally,

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migration to known places increases the capacity to search in different optimization spaces. The operators proposed for the exploitation phase improve the search. The GTO follow the following rules to find the solution: • The optimization space contains three types of solutions, where the X is the position vector of the gorillas, G X is the position vector of the candidate gorilla created in each phase for the operators to work better, and, finally, the α represents silverback gorilla, which is the best solution found in each iteration. • There should be only one silverback gorilla among the entire population when considering the number of search agents selected to carry out the optimization operations. • The three types of solution (X, G X, α) simulate the social behavior of gorillas. • Gorillas can increase their search power by finding better food sources or by increasing their troop size; for the algorithm, this means that the value of X is fed back from the value of G X . • The social behavior of gorillas avoids the solitary life of an individual. Community life is always sought subjected to the decisions of the silverback gorilla. For the algorithm, this means that the worst solution within the population is the weakest gorilla; the other gorillas seek to move away from the weak gorilla and remain close to the silverback gorilla, improving their conditions, that is, they approach toward the best solution. As mentioned above, male gorillas may attempt to become silverback gorillas by moving away from their troop and forming their own group; in the algorithm, this translates to all gorillas as possible solutions, with the best solution being the silverback gorilla; thus, this way the possible solutions are not excluded. The random part of the algorithm is found in a parameter called p that defines the destination of the troop migration. When the random number called φ meets the condition φ < p, gorillas migrate to an unknown place, while if φ ≥ 0.5, gorillas move closer to other gorillas. Finally, if it is true that φ < 0.5, gorillas move to familiar locations. The migration to unknown places feature allows the algorithm to observe the entire problem space, the move near other gorillas feature improves algorithm exploration, and, in the end, the migration to known places feature causes the algorithm to move from local optimum solutions. These scenarios are contemplated in the design set of Eq. 1: G X (t + 1) =

⎧ ⎨

(U B − L B) × φ1 + L B ;φ < p ; φ ≥ 0.5 (φ2 − C) × X φ (t) + L × H ⎩ X (i) − L × (L × (X (t) − G X φ (t)) + φ3 × (X (t) − G X φ (t))) ; φ < 0.5

(1) where G X (t + 1) corresponds to the position vector of the candidate gorilla in the next iteration; X (t) is the current position vector of gorillas, the values of φx and φ correspond to random numbers with values between 0 and 1 updated at each iteration (please note that φ could have a sub-index that means the number of iterations, e.g. φ4 means the random number at iteration number 4), and p is a value that must be

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initialized prior to the optimization operations; its value must be between 0 and 1. This parameter determines the probability of selecting a certain type of migration. U B and L B are the upper and lower bounds of the variables. X φ represents a member of the gorillas randomly selected from the total population. Similarly, G X φ is a position vector of the randomly selected candidate gorilla and includes the updated position in each phase. The values of C, L, and H are calculated with Eqs. 2, 5, and 6.  Ii is the total value of the In Eq. 2, It is the value of the current iteration and iterations to perform the optimization operations; F is calculated as indicated in Eq. 3. Due to the nature of Eq. 2, in the first iterations of the optimization operations, abrupt changes are generated; however, the more the iterations are carried out, the changes end up being small: C = F × (1 − n

It

i=1 Ii )

F = cos(2φ4 ) + 1

)

(2) (3)

The calculation of L is performed as indicated in Eq. 4, where the values of l are random in a range of −1 to 1 updated on each iteration. This simulates silverback gorilla leadership, as it is not natural for the leader to always make the right decisions from the start to find food, protect the group, and stay at bay. The head, varying randomly the value of the risk of making a bad decision, is represented, which decreases with the acquisition of experience over time: L = C ×l

(4)

For parameter H calculation, Eq. 5 is used. In turn, the value of Z required in Eq. 5 is a random number calculated as shown in Eq. 6: H = Z × X (t)

(5)

Z = [−C, C]

(6)

Regarding the exploitation phase, there are two scenarios: the black-backed gorilla decides to follow the silverback gorilla to assimilate his life under the protection of the leader and assuming his orders until he dies thus having the opportunity to become the new leader, or compete for the female gorillas and form its own troop. These two scenarios are represented in the algorithm with the parameter C as follows: if C ≥ W , the gorilla chooses to follow the silverback gorilla; if C < W , then it has selected to compete to form its own troop. W is a parameter initialized before performing optimization operations. When the gorilla chooses to follow the silverback gorilla (α), it is only dedicated to following the orders that the lead gorilla chooses; Eq. 7 describes this scenario:

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G X (t + 1) = L × M × (X (t) − X α ) + X (t)

(7)

To determine the unknown parameter M, Eq. 8 is used. The other parameters are already known. In Eq. 8, the parameter g is given by Eq. 9 and N represents the total number of gorillas: g g1  N 1     G X i (t)) (8) M=  N  i=1

g = 2L

(9)

On the other hand, the other gorilla choice scenario is to compete for the female gorillas against the other male gorillas, usually against the silverback gorilla; Eq. 10 mathematically describes these implications: G X (i) = X α − (X α × (Q − X (t)) × Q)) × A

(10)

The unknown parameters in Eq. 10 are Q and A, which are obtained with Eqs. 11 and 12. In turn, the unknown parameter E from Eq. 12 is estimated as shown in Eq. 13: (11) Q = 2 × φ5 − 1 A=β×E

E=

N1 , φ ≥ 0.5 N2 , φ < 0.5

(12) (13)

In Eq. 10, the function of Q is to simulate the impact force of the gorilla; as this factor can vary according to the characteristics of the individual, a random parameter with values from 0 to 1 are required; on the other hand, A represents a vector of coefficients that determines the degree of violence in conflicts. To calculate A, it is needed to initialize the value of β before performing the optimization operations. Finally, E is a parameter that simulates the effect of violence in the solution space. At the end of the exploitation phase, the reintegration of groups is carried out, where the cost of all the solutions is estimated and if the cost meets the following characteristic G X (t) < X (t)G X (t) < X (t), G X (t)G X (t), it is used as the new solution X (t)X (t) and the best solution within this group is called the silverback gorilla. Once the design of the algorithm based on the analogy of the social behavior of gorillas has been exposed, the flowchart of the GTO algorithm is shown as in Fig. 5 for better understanding. Based on the state of the art present in the development of the algorithm Gorilla Troops Optimizer over a little more than a year from the first publication that mentions it in the magazine Wiley, the algorithm presents a better performance in terms of execution time needed to find the best solution, as well as the amount of computing

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Fig. 5 Gorilla Troops Optimizer flowchart. Source Own creation

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resources used, compared to its bioinspired analogues such as the Spider Monkey Optimizer (SMO), Shark Smell Optimizer (SSO), and Spotted Hyena Optimizer (SHO), [2, 4, 10, 20, 31], among others. Also, the comparative results present in the state of the art and those mentioned in the references of this work show that the algorithm Gorilla Troops Optimizer gets more precise and similar results by running it multiple times. In addition to the above, there are two previous works where other artificial intelligence techniques are implemented to improve the collaborative work of the ROVs in the repair of leaks in marine oil pipelines; the first of them implements the Harmony Search Algorithm [19] and the second makes use of Horse Herd Optimizer (HHO), which is another bioinspired metaheuristic method in the behavior of horses [5], where the results obtained with these two strategies are observed. Thus, the selected Gorilla Troops Optimizer is used to observe the behavior of the system with the latest generation algorithm that has shown the best results according to the literature and, in future works, to compare the results obtained for this system against the results obtained with other metaheuristics.

4 GTO Algorithm with ROV System Datasets Using datasets coming from metaverse simulation to test the effectiveness of GTO, it is required to introduce the needed repairs as the objective function. This function is modeled as in Eq. 14 K = DF × ε × M F × P F (14) where K is known as the performance of the hydrocarbon network; its value depends on the amount and type of leaks that the network presents. The parameters are defined as follows: Leakage Reduction (D F) that has a value from 0 to 1—when this parameter is equal to 1, it indicates that there are no leaks. There is also the Magnitude of Fire (M F) parameter with a value between 0 and 1. M F indicates the presence of fire, which accelerates hydrocarbon consumption, as well as increases the risk and operating time of the maneuvers to repair the leak; finally, there is the Leak Propagation (P F) parameter with a value from 0 to 1. In addition to the objective function, the number of leaks to be repaired is taken into account; the virtual reality environment supports up to 8, hence the value of this parameter is defined from 0 to 8. And it must be taken into account for the result of the amount of ROVs available to deal with the failure; generally, there are seven ROVs in total, to carry out the repair maneuvers. It is considered that the existence of the units does not translate into having them always available to carry out actions with them. The structure of the variables in the dataset starts from left to right with the D F factor, followed by the number of explosions ε, the M F factor, the P F factor, and finally to the extreme right the number of ROVs available for maneuvers. The dataset consists of datasets from multiple scenarios, with the objective that the algorithm can

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Table 1 Example of a dataset for multiple system scenarios Leakage Explosions (ε) Magnitude of fire Leak propagation Available ROVs reduction [0, 1] [0, 1] [0, 1] [1, 7] 0.09 0.19 0.95 0.44 0.24 1.00 0.31 0.08 0.59 0.48 0.63 0.75 0.49 0.63 0.46 0.31 0.63 0.20 0.18

3 0 6 5 2 6 7 5 4 8 6 1 2 3 2 3 5 6 6

0.59 0.86 0.18 0.17 0.96 0.70 0.10 0.81 0.70 0.52 0.08 0.91 0.52 0.49 0.68 0.18 0.43 0.76 0.18

0.99 0.88 0.28 0.80 0.97 0.17 0.49 0.50 0.16 0.48 0.93 0.28 0.64 0.64 0.60 0.62 0.54 0.10 0.92

4 2 2 1 5 3 0 5 1 5 4 4 3 2 3 2 0 1 3

learn properly by performing multiple iterations to obtain the best solution. Table 1 shows an example of the data structure and available ROVs. Once the datasets have been formed and the algorithm is ready for execution, the results are obtained and visualized as in Fig. 6. It can be observed the number of ROVs in use decreases as well as the leaks, magnitude of fire, and leak propagation. This is a promising result showing the GTO calculates and selects the right number of workers needed to attend and fix the leaks. The simulation shows also how the number of ROVs can be saved due to optimization. This is interpreted as the efficiency to fix a leak as the closest ROV will be pulled to fix a leak. The more leaks you can fix, the less propagation will happen, and the less number of ROVs needed. It is observed that, by increasing the number of iterations (x-axis), the parameters decrease to their minimum values, which means that the best solution will be obtained by causing the failure parameters to decrease their value. The green points represent the amount of ROVs necessary to repair the failure and it can be seen how they decrease each time, so that in the end the most economical solution is found, which means deploying the minimum number of units at risk to carry out the repair. In order to have a better visualization of the results, the values of the y-axis are modified, so that its minimum value is 0, eliminating the negative part of the

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Fig. 6 Gorilla Troops Optimizer results with sample simulation in metaverse

Fig. 7 Gorilla Troops Optimizer results with positive number of ROV units deployed during sample simulation in metaverse

results. This is required due to the nature of the system where negative solutions are impossible solutions. The adjusted visualization can be seen in Fig. 7. By having a better visualization, it is observed how at the beginning of the iterations there are sudden changes, which is explained by the nature of the GTO design. As optimization progresses, there are smooth changes. In order to have a better observation of relevant variables values, another adjustment is made on the y-axis, leaving this at the value of one unit. The result can be seen in Fig. 8. Figure 8 focuses on the relevant variables with system leaks. The Leakage Decrease (DF) parameter is observed in yellow, which for the last iteration is close

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Fig. 8 Adjusted results in one unit scale

to the value of one, while the other variables present low values. This shows that the algorithm not only delivers the most optimal solution in terms of the number of ROVs required to carry out the repair maneuvers, the optimization work of the algorithm is also reflected in the variables that indicate performance of the hydrocarbon network.

5 Conclusions and Future Work Metaverse (Virtual reality) combined with simulation is a powerful tool that makes it possible for anyone to ensure the operation of a system and perform tests on it without the risk of manipulating it directly without knowing the possible failure scenarios. This paper showed the development of an underwater virtual reality environment that can transmit the sensation of navigating in the depths of the ocean for the operators of the ROVs thus achieving their training in the management of remote units within a fluid and all that this implies such as the difference in the sensation of inertia, the absence of light, as well as the restrictions in movement. It is clearly observed that with the developed environment, it is possible to carry out navigation tests of the ROVs. With the objective of providing intelligent assistance at work, in the real world having navigation assistance represents a powerful tool, especially in moments of crisis, moments where making an incorrect decision can result in a major catastrophe. It is clear the importance of the work that is developed in the INEEL with the simulator shown in the present work providing assistance to the operators with correct training to avoid environmental catastrophes due to hydrocarbon leaks. Another benefit perceived is the savings due to using simulation by avoiding risks to the ROVs that can be costly.

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On the other hand, the application of artificial intelligence techniques for the optimization of processes is a wise decision since it allows better solutions to be reached quicker, which in the real world translates into increasing the productivity of a system, either economically or with respect to production times; in addition to artificial intelligence techniques, learning to observe nature to imitate its processes is a powerful methodology since it means taking up the work that nature has been developing for thousands of years and whose results can be observed in nature itself. This is how nature-inspired algorithms (as well as other inspired optimization techniques) have such good results to solve engineering problems, especially in combinatorial problems. Particularly, the metaheuristic method Gorilla Troops Optimizer provided good results to optimize the system proposed in the present work, obtaining from it relevant information to assist the operators of the ROVs and thus ensure the repair of failures in marine oil pipelines in the best possible way. Furthermore, it is observed that the execution time of the algorithm is relatively short, which allows the operator to wait for intelligent assistance before making any decision. Taking up the work carried out in the virtual reality metaverse environment and adding the metaheuristic method, better visual results are obtained, being able to observe in the simulation of the underwater environment the movement of the ROVs according to the response obtained from the Gorilla Troops Optimizer implementation. It is left as future work to compare the results obtained in the present work with the works carried out previously using different metaheuristic and optimization methods, with the objective of determining which algorithm is the one indicated to solve the problem that is posed in the present work, like Multi Objective GTO [14]. Additionally, as with any technology today, updates to the metaverse environment are required in order for the system to be able to operate on upcoming operating systems, on top of having the current configurations required for multiplayer applications over the network and can be active longer. Updating the application will also facilitate the incorporation of intelligent functions programmed in different programming languages such as Python and R, languages in which the algorithm of this work is developed.

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Chapter 12

Parameter Identification of the Combined Battery Model Using Embedded PSO-GA Elmahdi Fadlaoui and Noureddine Masaif

1 Introduction Global warming and the energy crisis have become a real danger to humanity. The transportation sector generated in 2020 approximately 29% of greenhouse gas emissions [1]; for this reason, electric vehicles (EVs) powered by lithium-ion batteries (LiB) are becoming favored in many countries because of the characteristics of environmental protection, high efficiency, and energy saving. Therefore, developing an effective battery management system (BMS) is considered as an important task to control the battery’s state for security and reliability. For EVs, the accurate state of charge (SOC) that indicates a battery’s remaining capacity of the (LiB) is significant for the diagnosis and prognosis of the battery behavior. This can prevent overcharging/discharging and ensure cell balancing, which increases the battery’s useful life. To improve this estimation performance, a battery model must be established. Many battery models in the literature have been proposed, such as Thevenin equivalent circuit model, the Electrochemical model, and the Combined battery model. The Thevenin equivalent circuit model is used to estimate the dynamic battery behavior; it is represented as multiple parallel RC circuit branches; with regard to its simplicity, this method is implementable for online applications [2]. The electrochemical model reflects the intercalation in the electrodes inside the lithium-ion battery; to make this model implementable in (BMS), they should be simplified for real-time systems [3]. And the combined battery model consists of three sub-models: The Shepherd model, the Unnewehr universal model, and the Nernst model. The Shepherd model and the Unnewehr Universal model, both consider the battery cell model E. Fadlaoui (B) · N. Masaif Electronic Systems, Information Processing, Mechanics and Energy, Faculty of Science, Ibn Tofail University, B.P 133-14000 Kenitra, Morocco e-mail: [email protected] N. Masaif e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_12

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composed of an internal resistance (R) and the initial cell voltage (E 0 ). This model describes the mathematical relationship between voltage (yk ) and current i(t) [4]. These two models are widely used for battery modeling; they are relatively simple to implement and can accurately predict the battery’s behavior under different operating conditions. While it has some limitations, one limitation is that the model does not take into account the complex electrochemical reactions that occur during battery operation. The Nernst model [5] is based on the Nernst equation, which describes the relationship between the equilibrium potential of an electrochemical cell and the concentrations of the reactants. In battery modeling, the Nernst model is used to predict the open-circuit voltage (OCV)—which is the battery’s voltage when it is not connected to any load of a battery—based on the concentrations of the reactants in the cell. However, the Nernst model has some limitations that should be considered; one limitation is that it only considers the equilibrium potential of the battery and does not account for the kinetics of the electrochemical reactions. Therefore, it may not accurately predict the battery’s behavior under certain conditions, such as high current rates or fast transients [6]. By combining these three sub-models, a more comprehensive model of the battery system can be created that accurately predicts the battery’s behavior under different operating conditions [7]. This model is easy to implement in real-time applications on a (BMS), however, it needs suitable tuning parameters [8]. Several studies have been proposed to identify the parameters of different mathematical battery functions. The main optimization process is to minimize the mismatch between the optimized experimental models. Ala Al-Haj et al. [9] suggested the least squares method to predict the parameters of the generic battery models; Ryan et al. [10] compared different metaheuristic optimization algorithms like differential evolution (DE), harmony search algorithm (HSA), particle swarm optimization (PSO), evolutionary particle swarm optimization (E-PSO), and Genetic Algorithm (GA), to predict the parameters of the combined battery model. However, it is important to develop a rapid and robust optimization algorithm. In this paper, the Embedded PSO-GA is proposed to identify the combined battery model parameters. The studied data is extracted from Lithium Polymer 5.4 Ah; the root mean square error (RMSE) and the simulation time consumption are used to evaluate this method by comparing it with PSO and GA. The results show that by applying the Embedded PSO-GA, the parameter identification system start to be more accurate and faster. The layout of this paper is as follows: Sect. 2 defines the combined battery model; Sects. 3 and 4 describe the two evolutionary optimization methods: GA, PSO, and the embedded PSO-GA, respectively. Section 5 presents the parameter identification system. The simulation results and the evaluation of the proposed method are illustrated in Sect. 6, and the conclusions of this study are made in Sect. 7.

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2 Combined Battery Model Battery models are mathematical representations of a battery’s behavior, which help predict the battery’s response to different conditions, such as state of charge (SOC), current, and temperature. The accuracy of the battery model is crucial in battery management systems (BMS), as it helps to optimize the performance, extend the life, and ensure the safety of the battery. Battery terminal voltage refers to the electric potential difference between the positive and negative terminals of a battery. It is measured in volts and is a function of the internal resistance of the battery, the state of charge, and the load connected to the battery. As a battery discharges, its terminal voltage decreases, and as it charges, the voltage increases. The terminal voltage is an important parameter in battery management systems as it can provide information about the state of charge of the battery. The combined battery model aims to address the limitations of Shepherd, Unnewehr universal, and Nernst models by integrating the advantages of the three approaches to describe the battery terminal voltage [11]: • Shepherd model:

yk = E 0 − Ri k − K 1 /z k

(1)

yk = E 0 − Ri k − K 1 z k

(2)

yk = E 0 − Ri k − K 1ln(z k ) + K 2 ln(1 − z k )

(3)

• Unnewehr universal model:

• Nernst model:

The combined model is defined as yk = K 0 − Ri k − K 1 /z k − K 2 z k + K 3ln(z k ) + K 4 ln(1 − z k ) z k = z k−1 − (

ηt )i k Cn

(4) (5)

where • yk : battery terminal voltage. • i k : battery input current. • z k : the battery state of charge (SOC) at time step (k), with (z k−1 ) representing the battery SOC at time step (k − 1), (Cn )—the nominal capacity, and (η)—the Coulombic efficiency Eq. 5. • R: the internal resistance changed when charging or discharging, which needs to be estimated with the parameters (K 0 , K 1 , K 2 , K 3 , K 4 ). The objective function used for this purpose is the cumulative sum of the squared voltage (CSSV): 

T

min 0

(V (t) − V˜ (t, θ ))2 dt

(6)

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that minimizes the error between the experimental V (t) and the optimized terminal voltage V˜ (t).

3 Evolutionary Method Evolutionary algorithms (EAs) are a family of optimization algorithms inspired by biological evolution and natural selection and are divided into three main processes: initialization, evaluation, and generation of a new population [12]. The process begins with initialization, where the initial population of solutions is arbitrarily generated according to the problem’s constraints. Then the second process evaluates each solution according to a fitness function, and, finally, the generation of a new population based on the fitness of the last population. EAs have been applied to a wide range of optimization problems, including engineering design, data mining, and machine learning. Cuckoo Search (CS) [13] is a recently developed metaheuristic optimization algorithm based on the brood parasitism behavior of some cuckoo species. CS was first introduced by Yang and Deb in 2009. In CS, a population of candidate solutions is represented by a set of nests, and the algorithm simulates the breeding and brood parasitism behavior of cuckoos to update the nests. CS has been used in various engineering applications such as antenna design optimization, image segmentation, and power system optimization. Firefly Algorithm (FA) [14] is another recently developed metaheuristic optimization algorithm based on the social behavior of fireflies. FA was first introduced by Yang in 2008. In FA, a population of candidate solutions is represented by a set of fireflies, and the algorithm simulates the flashing behavior of fireflies to update the positions of the fireflies. FA has been used in various engineering applications such as control system design, mechanical design optimization, and image segmentation. Other metaheuristic algorithms such as Artificial Bee Colony (ABC) [15], Gray Wolf Optimization (GWO) [16], Harmony Search (HS) [17], and Differential Evolution (DE) [18] have also gained attention in recent years due to their effectiveness in solving complex optimization problems. ABC is inspired by the foraging behavior of honeybees, while GWO is inspired by the social hierarchy and hunting behavior of gray wolves. HS is inspired by the musical improvisation process, while DE is based on the difference between the two solutions in the population. These algorithms have been used in various engineering applications such as data clustering, image processing, and control system design. The genetic algorithm (GA) and the particle swarm optimization (PSO) are the most popular evolutionary algorithms.

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3.1 Genetic Algorithm (GA) The idea of (GA) is to simulate Charles Darwin’s theory of natural evolution that occurs in living ecosystems, where a genetic operator is used to combine two parents to produce a new generation that could be better than the parents [19]. The algorithm begins by initializing a random population and computing the fitness value of each individual, after that, the Roulette Wheel selection mechanism is utilized to establish the selection of each particle due to its fitness; the best fitness is the most likely to be chosen; then the crossover operator occurs between two parents from the population; there are different techniques used to select them; in this paper, we choose the uniform crossover, which is presented as follows:  y1i = αi ∗ x1i + (1 − αi ) ∗ x2i (7) y2i = αi ∗ x2i + (1 − αi ) ∗ x1i   where α is a random variable uniformly distributed between −γ , γ + 1 and γ is a constant variable. Finally, the mutation operator is applied to randomly mutate some children based on mutation probability μ to maintain diversity and avoid convergence.

3.2 Particle Swarm Optimization (PSO) The particle swarm optimization is a swarm-based intelligent algorithm; it simulates the behavior of looking for the food of a bird swarm. After the initialization, the algorithm searches for optimal solutions using Eqs. 8 and 9; the personal best (Pbest ) indicate the individual historical best position, and (G best ) indicate the global best position. x and V represent respectively the position and velocity vectors of the particle’s swarm to adjust its direction to the optimal solution, where t denotes the current iteration’s number, and i is the particle’s index. C1 and C2 represent acceleration coefficients; r1 and r2 are two variables randomly distributed between between 0 and 1: Vi (t) = Vi (t − 1) + C1r1 (Pbest − xi (t − 1)) + C2 r2 (G best − xi (t − 1)) xi (t) = xi (t − 1) + Vi (t)

(8) (9)

Clerc and Kennedy developed an improved PSO [20] by adding the Constriction Coefficient to make the algorithm converge quickly to the best solution: χ=

2k  |2 − φ − φ 2 − 4φ|

(10)

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where • φ = φ1 + φ 2 • φ1 = C 1 r 1 • φ2 = C 2 r 2 . Equation 10 is used under the constrictions with k ∈ [0, 1] and φ ≥ 4; this modification helped to improve the performance of PSO, making it more effective at finding high-quality solutions for a wide range of optimization problems. As a result, the Improved PSO has become a widely used optimization technique in many fields, including engineering, economics, and computer science.

4 Embedded PSO-GA In addition to the low convergence speed of (GA), the (PSO) algorithms suffer from getting stuck on the local minimum in solving some problems; the proposed solution to resolve this issue is to combine these two evolutionary optimization algorithms, Fig. 1, using the following steps: • Step (1): Set swarm size, initial parameters, and iteration times, also crossover and mutation probability of the genetic algorithm, and inertia and acceleration coefficients of (PSO). • Step (2): Calculate the fitness function of the initial population. • Step (3): Update the velocity and position of each using Eqs. (8) and (9). t ) best of each particle. • Step (4): Update the personal (Pbest i • Step (5): Perform the selection and crossover genetic algorithm operations. • Step (6): Update each particle’s new personal best generated after the crossover c,t ), and compare it with Step (4), then save the best. (Pbest i • Step (7): Update the global best (G tbest ). • Step (8): Perform the mutation genetic algorithm operator. • Step (9): Update the new global best generated after the mutation (G m,t best ), and compare it with Step (7) then save the best. • Step (10): Repeat Steps 3–8 until the ending criterion is met.

5 Parameter Identification System In this section, the process of the parameter identification system is described and presented in Fig. 2, The purpose of the system is to identify the parameters of the combined battery model (K 0 , K 1 , K 2 , K 3 , K 4 , and R) using experimental battery data, where the data that support the findings of this study are openly available in Lithium Polymer battery-data at [21]; this file includes the measured current, measured terminal voltage, and measured state of charge (SOC) in the function of time.

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Fig. 1 Flowchart of embedded PSO-GA

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Fig. 2 System identification of the combined battery model parameters

The process begins by extracting the battery’s experimental terminal voltage. Next, the parameters of the combined battery model are initialized. These parameters are essential for the accurate modeling of battery behavior, and their accurate estimation is critical for the reliable operation of the battery system. After initialization, we calculate the difference between the experimental and optimized terminal voltage using the (CSSV) equation. The goal is to minimize the error between the experimental and optimized terminal voltage. To achieve this, one of the optimization methods, GA, PSO, or PSO-GA, is used to update the parameters based on the calculated error. The system repeats the process of calculating the difference, updating the parameters, and minimizing the error until the maximum iteration is reached. The number of iterations is predetermined. Overall, the parameter identification system presented in Fig. 2 offers an estimate of the parameters of the combined battery model. The use of optimization methods such as GA, PSO, and PSO-GA allows for a reliable estimation of the battery parameters, which is essential for the optimal operation of battery systems.

6 Results and Discussion The experimental data (Time, Current, Terminal voltage, and State of Charge) is extracted from Lithium Polymer with a capacity of 5.4 Ah, and nominal voltage 3.7 V off-the-shelf cell Fig. 3. The battery’s current profile is UDDS which is a laboratory test procedure used to evaluate the emissions and fuel efficiency of light-duty vehicles (such as cars and light trucks) in a simulated urban driving environment. The UDDS cycle was developed by the U.S. Environmental Protection Agency (EPA) and consists of a 10.26 km (6.4 mile) driving schedule with frequent stops and starts, simulating the typical driving conditions of a city. The UDDS cycle is part of the Federal Test Procedure (FTP), which is used to determine a vehicle’s compliance with emission standards

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Fig. 3 Experimental battery framework

Fig. 4 UDDS current profile

in the United States [10]. The current profile and measured Terminal voltages are shown in Figs. 4 and 5. Figure 6 displays the calculated state of charge using the Coulomb counting method. As the battery was discharged from 90% SOC and the current sensor was well-calibrated, the integral error could be ignored. The embedded PSO-GA method is implemented to determine the parameters of the combined battery model. The maximum iteration and population numbers are 150 and 35, respectively; for the embedded algorithm and to show the effectiveness of this algorithm, we choose three different number of populations 10, 18, and 35. The genetic algorithm mutation and crossover probability are set, respectively, as μ = 0.002 and γ = 0.1. The acceleration coefficients C1 and C2 and the inertia coefficient ω of the particle swarm optimization are set as C1 = C2 = 2, ω = 1. And for the improved particle swarm optimization, the parameters are ϕ1 = ϕ2 = 2.05 and K = 1. The parameters of algorithm PSO-GA are summarized in Table 1.

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Fig. 5 UDDS terminal voltage

Fig. 6 Actual state of charge

Table 1 PSO-GA parameters PSO-GA parameters Population size of PSO-GA-10pop Population size of PSO-GA-18pop Population size of PSO-GA-35pop Mutation probability μ Crossover probability γ Acceleration coefficients C1 and C2 Inertia coefficient ω

Values 10 18 35 0.002 0.1 2 1

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Table 2 Lower and Upper searching bound parameters Parameters Lower bound Rcharging Rdischarging K0 K1 K2 K3 K4

0.0001 0.0001 2.001 0.001 0.001 0.001 0.0001

Table 3 Best solution founded by each model Model Rchar Rdischar K0 GA PSO Improved PSO PSO-GA10popa PSO-GA18pb PSO-GA35popc a b c

Upper bound 2.09 2.09 9.4 3.9 4.95 9.50 5.01

K1

K2

K3

K4

0.042 0.03 0.02

0.015 1.10−4 0.04

7.30 4.59 7.30

0.52 0.042 1.92

1.26 1.10−3 0.89

6.17 3.52 2.00

0.33 1.10−4 1.10−4

0.03

0.041

5.96

1.10−3

1.10−3

6.89

0.46

0.031

0.039

8.10

0.97

2.60

4.78

0.002

0.030

0.042

7.33

1.32

1.30

3.61

0.061

Embedded PSO-GA with number of population 10 Embedded PSO-GA with number of population 18 Embedded PSO-GA with number of population 35

The optimization problem is solved and compared using (GA), (PSO), (ImPSO), (PSO-GA-10pop), (PSO-GA-18pop), and (PSO-GA-35pop). To provide a meaningful and fair comparison, the same metaheuristic algorithm initial populations and hyperparameters were conducted; the lower and upper bounds are presented in Tables 2, and 3 presents the optimal parameters identified by each model. The hardware used for this simulation: i7-78500U with 16 Go of memory. The best cost of each iteration by different methods is shown in Fig. 7. It can be seen from this figure that the (GA) is the weakest followed by (PSO); the (ImPSO) and (PSO-GA-10pop) are better compared to the above, and they reach almost the exact final best cost, and after them come the (PSO-GA-18pop) and (PSO-GA35pop), respectively. The best (CSSV) obtained by each algorithm and their root mean square error (RMSE) and simulation time are summarized in Table 4. Figure 8 describes different algorithm competence in finding a better solution in a lower simulation time. This figure shows that (PSO-GA-35pop) records the best cost (RMSE) compared with all other algorithms, but a high simulation time: 0.05%– 281 s. The root mean square error of (ImPSO) and (PSO-GA-18pop) are respectively 0.24 and 0.12%, in almost the same simulation time: 135 s. The (GA) records

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Fig. 7 Best cost in function of iterations of different metaheuristic search methods Table 4 Evaluation of different optimization models Model Num of CSSV Population GA PSO Improved PSO PSO-GA-10popa PSO-GA-18popb PSO-GA-35popc a b c

35 35 35 10 18 35

0.3 0.0980 0.0081 0.2252 0.1204 0.0508

RMSE[%]

Time[s]

1.6159 0.8456 0.2429 0.2252 0.1204 0.0508

134.73 132.33 135.80 89 135.58 281.63

Embedded PSO-GA with number of population 10 Embedded PSO-GA with number of population 18 Embedded PSO-GA with number of population 35

1.61%–134 s and (PSO) 0.84%–132 s. Finally, the (PSO-GA-10pop) reached an RMSE of 0.22% with a simulation time of 89 s. Figure 9 illustrates the comparison between the experimental and the optimized terminal voltage; it is observed that the embedded (PSO-GA) can perform very well compared with (GA) and (PSO) even with a small number of populations. (GA) suffers from a slow convergence speed. Besides, (PSO) has a speed convergence, but it is more easily stuck in the local optimum. By embedding crossover and mutation in the (PSO), the algorithm starts to show fast convergence speed to the optimal solution.

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Fig. 8 RMSE in function of time consumed

Fig. 9 Actual terminal voltage versus optimized terminal voltage

7 Conclusion The accurate parameter identification of the battery model is necessary for (BMS) to protect the electric vehicle (EV) Li-ion batteries from being destroyed. In this paper, the Embedded PSO-GA optimization algorithm is proposed to identify the combined battery model parameters using the parameter identification system based on the cumulative sum of the squared voltage (CSSV) between experimental and optimized terminal voltage. The performance of the proposed method is evaluated

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using the root mean square error (RMSE) and the simulation time consumption. Compared to (GA), (PSO), and (ImPSO) optimization algorithms, the embedded PSO-GA demonstrates quick convergence to the optimal solution.

References 1. Haggi H, Fenton J, Brooker P, Sun W (2022) Renewable hydrogen systems enable deep energy decarbonization of power and transportation sectors. In: Electrochemical society meeting abstracts, vol 241, pp 1785–1785 2. Boulmrharj S, Ouladsine R, NaitMalek Y, Bakhouya M, Zine-dine K, Khaidar M, Siniti M (2020) Online battery state-of-charge estimation methods in micro-grid systems. J Energy Storage 30:101518 3. Zhou J, Xing B, Wang C (2020) A review of lithium ion batteries electrochemical models for electric vehicles. In: E3S web of conferences, p 04001 4. Raszmann E, Baker K, Shi Y, Christensen D (2017) Modeling stationary lithium-ion batteries for optimization and predictive control. In: 2017 IEEE power and energy conference at illinois (PECI), pp 1–7 5. Farag M (2013, Schoolmacsphere) Lithium-ion batteries: modelling and state of charge estimation. (Doctoral dissertation, macsphere) 6. Azam S (2018) Battery identification, prediction and modelling. (Doctoral dissertation, Colorado State University) 7. Vasebi A, Partovibakhsh M, Bathaee S (2007) A novel combined battery model for state-ofcharge estimation in lead-acid batteries based on extended Kalman filter for hybrid electric vehicle applications. J Power Sources 174(1):30–40 8. Ahmed R (2014) Modeling and state of charge estimation of electric vehicle batteries. (Doctoral dissertation, macsphere) 9. Hussein AH, Batarseh I (2011) An overview of generic battery models. In: 2011 IEEE power and energy society general meeting, pp 1–6 10. Lorestani A, Chebeir J, Ahmed R, Cotton J (2020) A new optimization algorithm for parameters identification of electric vehicles’ battery. In: 2020 IEEE power and energy society general meeting (PESGM), pp 1–5 11. Plett G (2004) Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: part 3: state and parameter estimation. J Power Sources 134(2):277–292 12. Kachitvichyanukul V (2012) Comparison of three evolutionary algorithms: GA, PSO, and DE. Ind Eng Manag Syst 11(3):215–223 13. Cuong-Le T, Minh HL, Khatir S, Wahab M, Tran M, Mirjalili S (2021) A novel version of Cuckoo search algorithm for solving optimization problems. Expert Syst Appl 186:115669 14. Kumar V, Kumar D (2021) A systematic review on firefly algorithm: past, present, and future. Arch Comput Methods Eng 28:3269–3291 15. Sharma A, Sharma A, Choudhary S, Pachauri R, Shrivastava A, Kumar D (2020) A review on artificial bee colony and it’s engineering applications. J Critical Rev 7(11):4097–4107 16. Al-Tashi Q, Md Rais H, Abdulkadir S, Mirjalili S, Alhussian H (2020) A review of grey wolf optimizer-based feature selection methods for classification. In: Algorithms and applications, evolutionary machine learning techniques, pp 273–286 17. Ala’a A, Alsewari A, Alamri H, Zamli K (2019) Comprehensive review of the development of the harmony search algorithm and its applications. IEEE Access 7:14233–14245 18. Pant M, Zaheer H, Garcia-Hernandez L, Abraham A et al (2020) Differential evolution: a review of more than two decades of research. Eng Appl Artif Intell 90:103479 19. Katoch S, Chauhan S, Kumar V (2021) A review on genetic algorithm: past, present, and future. Multimed Tools Appl 80(5):8091–8126

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Chapter 13

IoT Applied to Slowing the Effects on Pets Trapped in a Wildfire After a CONAGUA Alert Using an Intelligent Voice-Recognition Assistant Rubén Moreno, Fernanda Romero, Alberto Ochoa-Zezzatti, Luis Vidal, and Elías Carrum

1 Introduction The greatest danger that forests are exposed are wildfires, for many years we have wanted to control this problem, but each time it increases much more as climate change is becoming more dangerous. They also threaten all fauna and flora and seriously disrupt biodiversity and the ecology and environment of a region. Knowing the causes of wildfires is the first step to act for the benefit of these natural CO2 so necessary in the fight against climate change. During summer, when it does not rain for months, forests fill up with dry leaves, which can burn into flames at the slightest spark. In fact, many forests end up burned after the summer period, resulting in large losses of forest mass. Many of the fires end up causing irreparable damage to the fauna and flora. In addition to causing imbalances in nature, wildfires accelerate global warming due to climate change. Effects of wildfires are: – Wildfires destroy habitats of many kinds of animals and vegetation. – The soil in the fire area suffers irreparably. – Extinction of species living in places prone to Wildfires. R. Moreno · F. Romero · A. Ochoa-Zezzatti (B) · L. Vidal Instituto de Ingeniería Y Tecnología (UACJ), Chihuahua, Mexico e-mail: [email protected] E. Carrum Corporación Mexicana de Investigación en Materiales, Saltillo, Mexico A. Ochoa-Zezzatti Facultad de Ingeniería, Universidad Anáhuac México, Naucalpan, Mexico © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 X.-S. Yang (ed.), Benchmarks and Hybrid Algorithms in Optimization and Applications, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-99-3970-1_13

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– Setbacks in the fight against climate change. Trees and plants help produce oxygen in the world. – Excess water used to extinguish fires can cause soil erosion. – Air pollution due to large amounts of smoke released into the atmosphere. – Ash and smoke can cause serious health problems for people suffering from allergies and other medical problems. – Loss of income for farm workers whose crops and animals were destroyed by the wildfire. Our project will oversee improving this problem that we have had for many years in our region, through a system with artificial intelligence and an irrigation system that will alert us and will be activated by means of a virtual assistant with an intelligent speaker that we will have inside a cabin. The virtual assistant will send us an alert of a possible forest fire through a mobile device that will be configured to be linked to the virtual assistant. This project will help us to control that a forest fire can grow more and cannot be stopped because if it grows too fast it can destroy our cabin or habitat of our pets. We can offer a way to protect the population that comes to the forest to spend a day camping with their families in a cabin. The purpose of this project is to take care of a protected natural area of a forest fire and that this is extinguished quickly through a virtual assistant and protect all species and people who can live in it; In order to solve this problem, an irrigation system will be created and installed in the cabins where people live, where via the virtual assistant the people who live in that house will realize that there is a forest fire in that area and the virtual assistant will activate the irrigation system through an order that will be given either through your voice or through a mobile device that is linked to the virtual assistant. With this irrigation system that will be installed in the forest cabins, the people who live in that place will have more time to survive since the whole area of the cabin will be wet and the fire will not spread so fast, the virtual assistant will also be able to call emergencies before the wildfire reaches the area where people live. It should be noted that the space where people live in the forest is made with natural materials, the main natural material is wood. Wood is a material that is flammable and is listed as one of the most flammable materials that exists in nature and can generate large amounts of heat up to 25,000 kcal/m2 . The benefits that this project will have in our region (Chihuahua) and of course in our planet is that climate change does not affect our protected natural areas and that these do not accelerate global warming, since a forest fire is a major source of carbon emissions and increases the absorption of terrestrial heat, It also contaminates the water that may be in that protected natural area, also many species of flora and fauna that live in that area are likely to fail to survive, which is why the irrigation system to be implemented is adequate to protect pets in this type of physical spaces and the emergency call that will make our virtual assistant to detect a possible forest fire.

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2 Purpose The purpose of this project is to take care of pets in country homes located on a protected natural area from a forest fire and that this is extinguished quickly through a virtual assistant and protects all species and people who may live in it; In order to solve this problem, an irrigation system will be created and installed in the cabins where people live. Through the virtual assistant the people who live in that house will realize that there is a forest fire in that area and the virtual assistant will activate the irrigation system through an order that will be given either through your voice or through a mobile device that is linked to the virtual assistant. With this irrigation system that will be installed in the forest cabins, the people living in that place will have more time to survive since the whole area of the cabin will be wet and the fire will not spread so fast, the virtual assistant will also be able to call emergencies before the forest fire reaches the area where people live. It should be noted that the space where people live in the forest is made with natural materials, the main natural material is wood, and wood is a material that is flammable and is listed as one of the most flammable materials that exist in nature and can generate large amounts of heat up to 25,000 kcal/m2 .

3 Theoretical Framework To get more closer with our principal trouble, we need to understand more about wildfire and its specifications to know how they start and can avoid all his risks. The basic way to understand the full trouble is some basic meanings of wildfires like how they are composed of and what are the causes and consequences of this problem, so that we can clearly understand how to prevent these kinds of devastating events.

3.1 IoT Definition Based on [9] is an emerging global Internet-based technical architecture facilitating the exchange of goods and services in global supply chain networks has an impact on the security and privacy of the involved stakeholders. Based on [11], “The Internet of Things (IoT)” aims to take this stride further to seamlessly connect people and various things, To do this system we will use ESP 01S microcontroller that works with Wi-Fi to control the full application to this model will be connected to a web platform”. Transforming the society toward becoming intelligent, convenient, and efficient (ICE) with potentially enormous economic and environmental benefits. In the past decade, the IoT has developed rapidly, spanning diverse application domains from healthcare to home automation, environmental monitoring to smart energy,

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intelligent transportation to smart buildings, smart manufacture to smart agriculture, and smart military to smart ocean.

3.2 Wildfires A fire that spreads uncontrolled through rural or urban vegetation and endangers people, property and the environment. In the world, forest fires are the most important cause of forest destruction. In a forest fire, not only trees and bushes are lost, but also houses, animals, sources of work and even human lives.

3.2.1

Definition

Based on [1] Forest areas are essential for life on the planet. In addition to being a fundamental part of the water production and distribution cycles, they purify the air we breathe by capturing carbon dioxide and releasing oxygen. They also regulate temperature and humidity, thus balancing the climate; they provide food, medicine and shelter to living beings; and they are a source of raw materials for many human activities. These vital processes are threatened by various factors unrelated to forestry activities such as: soil degradation, deforestation, immoderate logging, uncontrolled fires that are related to other activities such as agriculture, livestock, and urban development. Fire can have a positive influence on nature, as it helps to maintain biodiversity. But when it is used irresponsibly or is caused by negligence, it can turn into a forest fire with devastating consequences for the environment, including the health and safety of people and habitats’ animals.

3.3 Principal Causes Based on [1], we estimated that human activities cause 99 percent of these fires and only the rest are caused by natural phenomena such as electrical discharges and eruption of volcanoes. According to the average of recent years, almost half of these fires are caused by agricultural and livestock activities and urbanization, along with intentional actions and carelessness of people who do not put out their cigarettes or campfires properly. Some poachers and illicit crop growers can also cause fires. Kind of Accidental situations associated with wildfire: Breaks in power lines, automobile, railroad and airplane accidents. Negligence: Uncontrolled agricultural burning, campfires by hikers, smokers, garbage burning, road cleaning, and use of fire in other productive activities in forest areas. Intentional burning due to conflicts between individuals or communities, illegal logging or litigation. Natural: Lightning strikes or volcanic eruptions.

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3.4 Consequences and Conditions that Influence the Form and Speed at Which Fire Spreads Based on [1] it is determined that an uncontrolled forest fire can devastate everything in its path, spreading over great distances, overtaking rivers, roads and firebreaks. In hot, dry climates, wildfires are more likely to occur. On average, between 60,000 and 80,000 forest fires occur each year, destroying between 3 and 10 million hectares. In Fig. 1 we can see how wildfires ae more recurrent in the region of Chihuahua, Mexico, where this region is confirmed by deserts, forest and tundra. Considering this research shown on [1] Permanent conditions: Fuel composition (main element that determines fire characteristics). Plant species: Topography Transient conditions (meteorological type) Temperature Relative humidity Wind speed and direction Pluvial precipitation (rainfall). Other elements: Heat source. In the forest there is no spontaneous combustion; an external source of incandescence greater than 200 °C is always required for a fire to occur. Season. Forest fires can occur at any time; however, in Mexico there are two seasons of greater incidence: the first, corresponding to the central, northern, northeastern, southern and southeastern areas of the country, which begins in January and ends in June. The second season begins in May and ends in September in the northwestern part of the country. Both coincide with the dry season (drought) in the country. Human settlements. A forest area that is easily and constantly entered by humans is more susceptible to forest fires.

Fig. 1 Chihuahua region with areas in red, that have more recurrent wildfires

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3.5 Related Research The Internet of Things (IoT) is an emerging technology that has the potential to transform the way we live and work. One of the most important applications of IoT is forest fire prevention. Forest fires are a serious problem in many parts of the world. They can cause significant economic and environmental damage, as well as endanger human life and wildlife. However, with the use of IoT, it is possible to reduce the frequency and severity of these fires. The IoT allows the installation of sensors in critical areas of forests, which can detect changes in environmental conditions that may indicate a risk of fire. These sensors can measure temperature, humidity, wind speed and other factors that may influence fire risk. If the sensors detect a risky situation, they can send an immediate alert to forest fire prevention teams, who can intervene before a fire breaks out. In addition, IoT can also be used to control and monitor human behavior in forest areas. For example, sensors can detect if someone is building a campfire in a prohibited area, or if power tools are being used near dry areas that may be flammable. If a dangerous situation is detected, alerts can be sent to forestry authorities for immediate action. In conclusion, IoT can be a very useful tool to prevent forest fires. By detecting fire hazards early and notifying the relevant authorities, preventive measures can be taken to avoid large fires that can cause damage to nature and human life, as is research in [12–14].

4 How Are We Going to Retard the Fire To retard the fire, we are going to use a specific red chemical that can retard wildfires, this specific chemical is composed by Ammonium Phosphate and has a characteristic red color as we can see in (Fig. 2) the Phosphate Ammonium is thrown from an airplane based on [2]. This red “chemical” is a fire retardant that is used to combat huge wildfires that water alone can’t combat. This chemical has proved multiple times to be a game-changer against fire. As we said before, it is a fire retardant, and it is employed in aggressive wildfires to stop fires from spreading. This fire retardant is made by different companies this means it is very easy to find supplies, taking PhosChek as an example. Phos-Chek is a major brand for that, “red chemical” that is used in combating wildfires, as well as in residences and beneath fireworks displays. The fire retardant is thrown from planes and makes what is called a wall that surrounds the fire, and this give an extra time to fire fighters can suffocate the fire and it doessn’t let the fire keep growing and affect other areas as we can see in (Fig. 3) the function of this red chemical.

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Fig. 2 Airplane throwing Ammonium Phosphate

Fig. 3 Red chemical spread on mountains to reduce consequences of fire forest

5 Methodology Generation Z is characterized by having many diverse kinds of pets that serve as an extension of their family nucleus [3], that is why the present research has a very important relevance, since the danger of their pets in a fire will determine the effects of being able to save them in each eventuality such as a wildfire, normally in case of fire one must wait for the arrival of the rescuers’ teams. In such a situation where the nearest help is more than 30 min away, it is necessary to do everything possible to save our belongings and our lives as well as those of our pets [5]. With the help of artificial intelligence [4], we can develop systems that focus on delaying the fire if possible, incorporating smoke detection by sending a signal to our Amazon Alexa we can realize the possible risks that may arise. About audio-based systems, based on [8] as demonstrated by the recent projects and research studies they are significantly increased by their popularity in the recent years.

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5.1 Research Contribution The motivation of this research resides in their versatility, since audio signals allow capturing people’s activity, monitoring the environment and they enable speechbased user interfaces. In addition to this people perceive microphones as less invasive sensors. In Fig. 4 we use a Diagram to explain the functionality of this IoT system, when MQ2 sensors(smoke and gas sensor) send a signal of fire and smoke to our microcontroller and the last one will send us an alert to our personal email address when we receive this type of advice that means that a wildfire is near and it is the moment to proceed with the next step this is the wildfire system activation using voice commands with Amazon Alexa this activates the fire retardant spreading system this will keep our pets and house safe and give extra minutes to rangers and the fire department, which is decisive to prevent mortality and destruction. Due to the potential effects of a wildfire, it was decided to construct four levels of reaction associated with the proper rescue of pets in cottages, the four levels are described as follows: 1. Identify possible carbon monoxide near to the cabin area and with this signal activated determinse if the risk really exists or is just a false alarm. 2. In case that the signal that we receive is a real emergency we can activate telling Alexa that we need to start with protocol 1(spread water in exterior building wall). 3. If wildfire starts increasing, we start with protocol number 2 this protocol will start when the temperature of the building starts increasing (when this happens, we will start spread water inside the house this will retain the fire for at least (10–15 min).

Fig. 4 Proposal IoT system functionality

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Fig. 5 Methodology of IoT designed system

4. At this moment the spread outside and inside the house will be done and we bring to rescue teams 25–30 min extra that can help us to prevent a huge fire (Fig. 5). It is of utmost importance to describe that the actions to be taken at the different reactive levels that are based on the forest fire alert level, i.e., its intensity and duration.

5.2 Novel Approach IoT systems are becoming more useful for many different tasks that belong to the innovation of their systems and how they are being able to do the task and take roles that make it more efficient and more accurate. This Wildfire detection system focuses on preserving pets’ life in case of a wildfire and is important to have this on mind to understand the basis of this research. The novel approach of this system unlike with other fire detection systems are the IoT used in conjunction with a voice assistant, in

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this particular case is Alexa that is linked to a microcontroller that uses internet of things bring us the opportunity to activate and monitor the system from everywhere in the world by only using a simple internet network.

6 System Assembly and Functionality To do this system we will use ESP 01S microcontroller that works with Wi-Fi to control the full application this system that will be connected to a web platform called smart nest and from there we can control different levels of actions based on telemetry with voice command (as is shown in Fig. 6) and with a cell phone app smartest will be to sync with amazon Alexa and with our cellphone we will use the amazon Alexa skill to control the sequence and our cell phone will ask to turn off or turn on the system/as is shown, and will be organized as different tasks during the process of reactive levels. This propose is shown in Fig. 7. For smoke detection and for fire notification system we will use an ESP 32 microcontroller and a MQ2, based on [10] The MQ-2 smoke sensor test’s goal is to determine the sensor’s ability to detect the presence of smoke.

Fig. 6 Proposed Diagram

Intelligent Voice Assistant

Fig. 7 Wireless connection

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Table 1 Principal components representation ESP-01 s with relay The ESP-01 s is composed system by a ESP-8266 that can be used to communicate by Wi-Fi is usually programmed with Arduino IDE C++ Water pump 12 V DC The water pump will be used to suck in and expel water. In this specific project this will move the Ammonium Phosphate DC DC Converter The DC converter will transform the 12 V AC to DC that can be regulated to DC volts we need 12 V DC cord This will give us 12 V DC that will be reduced voltage with the converter

7 Components Needed to Assemble Our Intelligent Proposal Due to the project’s budget restrictions, we undertook the task of analyzing the components required to adequately develop the project’s activities and arrive at the following project considerations, which are shown in Table 1. Once we had our intelligent system properly built, we were able to establish three levels of reactivity and thus seven decisive actions to try to save the pets in a fire, and as shown in Table 2 this will give us an idea of how we need to react to stop or delay the wildfire in different animal species. By comparing our methodological proposal with different commercial solutions, we have shown that such an IoT project should not exceed 100 USD, while comparable technological solutions exceed up to 1500 USD, and do not consider an intelligent optimization model to specifically plan an escape route associated with the pets in these cottages.

8 Results Based on [7] Internet of Things (IoT) consists of smart devices that communicate with each other. It enables these devices to collect and exchange data. Besides, IoT has now a wide range of life applications such as industry, transportation, logistics, healthcare, smart environment, as well as personal, social gaming robot, and city information. IoT Information Communication Technology (ICT) is expected to be a revolution in transferring the information from human to human, human to things and things to things. Smart devices can connect, transfer information and make decisions on behalf of people. This new technology is called ‘connectivity for anything’. It can connect anywhere, anytime and anything. The IoT environment consists of

4.67

5.49

2.48

Birds

Hamsters

6.13

3.81

2.65

Turtles

Fishes

6.51

5.65

5.38

3.62

5.23

5.71

1.35

6.84

3.75

5.67

5.64

1.95

3.28

3.67

5.36

6.13

5.53

4.16

2.72

3.13

2.94

2.01

4.08

3.53

2.32

6.52

3.84

1.02

6.09 5.37

1.94

4.27

3.72

4.86

4.64

3.98

3.03

2.19

3.25

2.74

2.23

6.99

Effectiveness efficiency

(*These data are represented on the Likert scale to adapt to our Intelligent application).

4.18

5.63

Lizards and Salamanders 1.75

5.58

6.21

4.13

Cats

6.05

2.18

Effectiveness efficiency

Effectiveness efficiency

Effectiveness efficiency

Regulates the temperature by sprinklers

Activates the cooling system

Activates ventilation system

Calms pets with the owner’s voice

Second level of reaction

First level of reaction

Dogs

Kind of pet (animal)

5.24

4.11

5.33

6.14

6.94

6.87

4.97

1.47

6.51

5.38

6.47

2.12

2.55

5.76

Effectiveness efficiency

Sends location loss

5.11

5.02

6.17

3.67

2.68

3.03

6.05

1.98

4.02

3.91

6.08

3.89

5.85

1.89

Effectiveness efficiency

6.94

4.11

6.69

4.75

3.73

2.79

5.16

2.37

6.14

5.78

2.98

6.18

2.37

2.54

Effectiveness efficiency

Generates sound Sends detailed alarm information about each pet to firefighters for special care after rescue

Third Level of reaction

Table 2 Determination of the effectiveness and efficiency of each reactive action of the reactive level to try to help shelter each type of pet depending on their distress due to the fire around their habitat [5]

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Fig. 8 Most common uses for IoT used in a Smart City or Industry 4.0

an enormous number of smart devices, but with many constraints. Processing capability storage volume, short in power life and radio range are among these constraints. Therefore, the IoT implementation requires a communication protocol that can efficiently manage these conditions as we can see in Fig. 8 we can onserve the most common uses for IoT, as is proposed in [15]. Climate change affects our natural protected areas and these do accelerate global warming, also protecting the species that inhabit that area, so that our forests are sources of the best production and distribution of water, purifying the air we breathe by capturing carbon dioxide and releasing oxygen. Without all this flora and fauna we can expect the loss of our habitat and the habitat of most of the animal species that have a very important role to accomplish and bring a stability to our planet. We also want to prevent the loss of many home and recreational places that brings to many people happiness and the total loss of this places represents the loss of many memories, and our goal is to implement the IoT and demonstrate the effectiveness of simple IoT systems like Amazon Alexa and how we can prevent big incidents like wildfires. Using the differential equation of fire propagation and intensity of a fire represented by P Eq. (1) for solving this equation we use the ordinary equations method giving us the following result In Eq. (2), we can determine what trajectory wildfires are and consider the wind velocity represented by y. We will follow this to give us a simply but concrete idea of how wildfires will react in different scenarios giving us an opportunity to understand and react before disasters. P(θ, t) =

∂t (θ, t) = ψ( p(θ, w)θ) ∂p

(1)

where ψ is a function of position that takes into account the factors of soil moisture, orography, biomass and wind. The above equation is nothing more than an ordinary differential equation with an angular parameter ϑ. By using this equation, it is also assumed that the above factors only locally affect the radial velocity of front propagation. In addition, cases where ψ is non-negative are going to be considered. This makes sense in the case where the fire originates at the origin of coordinates, so that the wave front moves away from the origin. The fact that the behaviour of the fire front can thus be simply and satisfactorily represented justifies these assumptions.  y=

√  6 tan 6 · 1.49 + x 4.8

(2)

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For the use and to obtain the proper results we need to use the information of wind direction, speed of the wind type that is moving the wildfire, using CONAGUA data to represent values in Eq. 2, including the multiplication of 6 ∗ 1.4. Once we solve the differential equation, we have the trajectory of the wildfire in a graph (Fig. 9) representing the initial point and the trajectory that the wildfire will follow. To get a full idea of the advance of the wildfires we have to map the zone with points in the area representing coordinates on the map as is shown in Fig. 10. It iss important to know what the next step after the sequence is to finish the next step is to find the best evacuation route to put our family and pets in a safe place to understand what is the most evacuation route. We will use the Dijkstra algorithm to find and search the fastest and safest way to exit from the affected area to apply the Dijkstra algorithm. As we can see in Fig. 11 the location of the cabin is very near to the dunes area wildfire that is coming from the blue point at the North east and by using the Dijkstra algorithm we can appreciate with a Yellow line in Fig. 12 what Fig. 9 Represents the wildfire propagation using Eq. 1

Fig. 10 Represent the mapping area with points representing coordinates

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is the most short and secure way to leave the cabin that is represented with a pink point. In a wildfire, the safe evacuation of people in the affected area is a top priority. However, determining the safest evacuation route can be challenging, especially when there are multiple paths and obstacles that can make egress difficult. In this scenario, Dijkstra’s algorithm can be a very useful tool to help resolve evacuation routes. Dijkstra’s algorithm is a path-finding algorithm used to find the shortest path between two nodes in a weighted network. In the context of wildfire evacuation, nodes can represent entry and exit points, while edges represent the paths between

Fig. 11 Represents the begin of the fire (Blue point) and the cabin location (pink point), including a Diagram to represent better our research

Fig. 12 Represents the Dijkstra algorithm, the yellow line represents the short route

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them. The weights of the edges can be the distance or the time taken to traverse a given path. By applying Dijkstra’s algorithm on a graph representing the network of paths within the fire-affected area, the safest evacuation route for residents can be determined. The algorithm can take into account obstacles, such as downed trees, streams or natural terrain obstacles, to find the quickest and safest route. In addition, Dijkstra’s algorithm can also be used to calculate the estimated time of arrival of people at exit points, which is crucial to ensure that everyone can evacuate in time. This can be particularly useful in situations where time is critical and rapid evacuation is essential to avoid injury and save lives. In conclusion, Dijkstra’s algorithm can be a valuable tool to help resolve evacuation routes in the event of a wildfire. By providing the safest and fastest route for people to evacuate the affected area, the algorithm can help reduce the risk of injury and save lives.

8.1 Discussion of Results The impact of forest fires on wildlife and pets in particular is a serious and growing problem in Mexico. Wildfires are one of the leading causes of animal deaths in forests, jungles, and other ecosystems. Research on the survival times of pet species during a wildfire can be valuable in helping to protect animals and prevent loss of life. To explore this issue, a study was conducted that analysed the survival times of 12 pet species in seven different fire levels using a Likert scale of 1–7. The pet species selected for this study were: dog, cat, ferret, parrot, iguana, tarantula, rabbit, hamster, fish, turtle, hedgehog, and snake. The results of the study revealed that most of the pet species analysed have very low survival times at the highest fire levels. Dogs and cats, for example, had a survival of about 50% at fire level 5 and 6, while at level 7 the survival of these animals was close to zero. The ferret, black rabbit and hamster had lower survival times than dogs and cats at the lowest fire levels (1 and 2), but also had close to zero survival at level 7. On the other hand, pet species that are less dependent on a specific habitat, such as gurami fish and tarantulas, were found to have higher survival times at all fire levels. Species that are able to flee and escape quickly, such as snakes and iguanas, also have relatively high survival times at lower fire levels, although their survival decreases significantly at higher fire levels. It is important to note that the results of this study are only an approximation and may vary depending on the specific circumstances of each fire. However, these results suggest that the most vulnerable pet species during a wildfire are dogs, cats, ferrets, rabbits, and hamsters, while species that are less dependent on a specific habitat, such as fish and tarantulas, have higher survival times. In conclusion, research on survival times of pet species during a wildfire is important to help protect animals and prevent loss of life. The results of this study can be used to inform wildfire management policies and practices that better protect vulnerable pet species. In addition, it is critical to consider that the results of this study indicate that larger pet species may have a greater ability to survive at different levels

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of fire, while smaller pet species may have a lower ability to survive. However, this does not mean that smaller pet species cannot survive in wildfires. It is important to take preventative measures to protect pets in the event of a wildfire, such as keeping them in a safe place and preparing a pet emergency kit. In addition, assessing the survival times of different pet species at different fire levels using a Likert scale from 1 to 7 can provide valuable information on the ability of pets to survive in dangerous situations. However, it is important to keep in mind that the results may be influenced by other factors, and preventive measures should be taken to protect pets in the event of a wildfire, as is shown in Fig. 13.

Fig. 13 In the upper right box, you can see the simulation of a forest fire of 5.87 on a scale of 1–7 and in the graph, you can see the level of survival for a sample of 100 different pets of 12 different species and of different sizes

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9 Conclusion and Future Research Saving a life is a difficult task but not impossible as advanced detection systems that we can have in this new era can bring us the possibility to save lives, pets and our material things. Considering the experience to use a different level of Reactive IoT associated with Voice recognition in this research, we expect to avoid these difficult situations caused by the climate change in the environment. We can prove that IoT systems can be used in this new era as IoT is becoming more relevant. More and more usage of satellite Internet connection ensures that there is no place where the Internet services can’t arrive bringing more opportunity to the forest rangers to activate wildfire protocols by saying just a single word. As shown in Table 2 we can see the effectiveness and efficiency of the three reaction levels in different kind of pets this where reaction levels are shown in lickert scale. Any different pet having different type of action in the different reaction level depending on the pet and the requirements to be alive, this table help us to understand if our reaction levels are being effective and how we can improve it. Wildfire propagates more quickly in dense vegetation and in regions the proximity that have on the tree next to the other ones increases the probability of a wildfire making what is called a Domino effect as we can show in Fig. 11, where we can have a simple but concrete example of what we are explaining about. If wildfires continue attacking habitats it will take a big part of the flora and fauna of the Regions where wildfires are very recurrent and destroy almost all the vegetation in the specific region. We have being losing Chihuahua species due to the wildfire that strikes. In the mountains, an example of the species lost are Mexican wolf, Mexican Bear and recently we are expected to lose a small part of deer of the region caused by wildfires and droughts. For understanding the risk for more endemic species we can see in Table 3 which specifies the optimal temperature for each species. It would be interesting that in future research individualized to each individual in Generation Z be applied to a Cox proportional hazard model that relates environmental factors such as temperature, humidity, light and oxygen associated with the wildfire; and evaluate how they influence the functional life of the polyurethane foam NPs -Si O2 in the walls of a house. Many world research studies believed that by 2050, half of the animal species will have been decimated with the reduction of their habitats, and this will affect not only the environment but will bring long-term side effects for the Z generation, by implementing solutions based on Intelligent IoT that can envision a medium-term solution that can help preserve as a bulwark to the strongholds of species that remain at this time and even mitigate the hostile and dramatic climate change that will affect rich and poor societies alike. This is our last real opportunity to make a paradigm shift in our lives.

Guacamaya de Uruachi

Ardilla Café

Ardilla Roja

Nutria de Urique

2

3

4

Specie

1

Instance

6.96

5.76

3.98

4.87

21.7–27

25.5

24–27

21–31

0.72

74.7 0.59 to the tail

30.9 0.43 to the tail

32.7 0.91 to the tail

19

0.85

0.94

0.92

0.23

0.77

0.33

0.92

0.14

0.68

0.98

0.77

0.72

12.98

11.75

11.75

13.3

12.98

18.27

18.27

11.7

16.05

10.82

10.82

15.69

15.51

18.45

18.45

17.48

Socialization* Temperature Size Habitat Index Growing Fertility Ecological Importance Baluarte Sustainable (°C) (cm) food* Population time* rate* valuation* for the Ecological Ecological Ecology* preservation future** Tourism** of the natural ecosystem**

Table 3 Types of endemic animals on Chihuahuas Northwest’ forest (*Likert scale) and (**Ecological Scale)

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