Applications of Bat Algorithm and its Variants [1st ed.] 9789811550966, 9789811550973

Table of contents :
Front Matter ....Pages i-xii
A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution for Feature Selection and Classification (Abdelmonem M. Ibrahim, Mohamed A. Tawhid)....Pages 1-18
Multi-objective Optimization of Engineering Design Problems Through Pareto-Based Bat Algorithm (Deniz Ustun, Serdar Carbas, Abdurrahim Toktas)....Pages 19-43
A Study on the Bat Algorithm Technique to Evaluate the Skin Melanoma Images (Nilanjan Dey, V. Rajinikanth, Hong Lin, Fuqian Shi)....Pages 45-60
Multi-thresholding with Kapur’s Entropy—A Study Using Bat Algorithm with Different Search Operators (V. Rajinikanth, Nilanjan Dey, S. Kavitha)....Pages 61-78
Application of Bat-Inspired Computing Algorithm and Its Variants in Search of Near-Optimal Golomb Rulers for WDM Systems: A Comparative Study (Shonak Bansal, Neena Gupta, Arun K. Singh)....Pages 79-101
Levy Flight Opposition Embedded BAT Algorithm for Model Order Reduction (Shalini Shekhawat, Akash Saxena, Rajesh Kumar, Vinay Pratap Singh)....Pages 103-118
Application of BAT Algorithm for Detecting Malignant Brain Tumors (Adit Kotwal, Rishika Bharti, Mansi Pandya, Harshil Jhaveri, Ramchandra Mangrulkar)....Pages 119-132
Bat Algorithm with Applications to Signal, Speech, and Image Processing—A Review (K. Prajna, N. Manikanthababu)....Pages 133-153
Bat Algorithm Aided System to Extract Tumor in Flair/T2 Modality Brain MRI Slices (V. Sindhu, M. Singaravelan, J. Ramadevi, S. Vinitha, S. Hemapriyaa)....Pages 155-172

Citation preview

Springer Tracts in Nature-Inspired Computing

Nilanjan Dey V. Rajinikanth   Editors

Applications of Bat Algorithm and its Variants

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.

More information about this series at http://www.springer.com/series/16134

Nilanjan Dey V. Rajinikanth •

Editors

Applications of Bat Algorithm and its Variants

123

Editors Nilanjan Dey Department of Information Technology Techno India College of Technology Kolkata, West Bengal, India

V. Rajinikanth Department of Electronics and Instrumentation Engineering St. Josephs College of Engineering Chennai, Tamil Nadu, India

ISSN 2524-552X ISSN 2524-5538 (electronic) Springer Tracts in Nature-Inspired Computing ISBN 978-981-15-5096-6 ISBN 978-981-15-5097-3 (eBook) https://doi.org/10.1007/978-981-15-5097-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express 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

Swarm intelligence based metaheuristic algorithms are extensively implemented to solve a variety of real-world optimization problems due to their adaptability and robustness. Bat Algorithm (BA) is one of the most successful swarm intelligence procedures developed in 2010 and extensively used in various optimization tasks for a decade. The mathematical model of BA is quite straightforward and easy to understand and enhance, when compared to other swarm approaches. Hence, the BA has attracted the attention of researchers, who are working to find the optimal solutions in a variety of domains, such as N-dimensional numerical optimization, constrained/unconstrained optimization and linear/nonlinear optimization problems. Along with the traditional BA, the enhanced versions of BA are also considered to solve a variety of optimization problems in science, engineering and medical applications. This book highlights the essential concepts of the traditional BA algorithm and its recent variants and also its application to find an optimal solution for a variety of real-world engineering and medical problems. The reason for this book is to help beginners and researchers in understanding the basic concepts and recent advancements in bat algorithms to enhance the results in existing technological trends and design challenges. This book is concerned with supporting and enhancing the utilization of bat algorithms is a variety of real-world optimization problems ranging from numerical optimization to medical data analysis. This work presents a well-standing forum to discuss the characteristics of the traditional and recent versions of the bat algorithm in various fields. The book is proposed for professionals, scientists and engineers, who are concerned about the methods using the bat algorithm. It provides an outstanding foundation for undergraduate and postgraduate students as well. It has several features, including an outstanding basis of the bat algorithm analysis, and it includes different applications and challenges with extensive studies for systems that have used bat algorithms. The book is organized as follows: Chapter 1 proposes a new hybrid binary version of the bat algorithm to solve the dominant feature selection problems, which is a vital procedure to implement a classifier unit. In this work, Bat Algorithm (BA) is integrated with an enhanced v

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Preface

version of the Differential Evolution (DE) algorithm. In this work, the BA with its capacity for echolocation to explore the feature space is combined with DE and its ability to converge to the best global solution in the search space. The general performance of the proposed algorithm is investigated by comparing it with the original optimizers and other optimizers that have been used for feature selection in the literature. The proposed algorithm and its various optimizers are applied over datasets obtained from the UCI repository. The results prove the ability of the proposed algorithm to search the feature space for optimal feature combinations. Key issues and future research directions are also highlighted in this chapter. Chapter 2 discusses the multi-objective optimization of engineering design problems through Pareto based bat algorithm. In multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. In this work, one of the recent metaheuristic optimization methods based on swarm intelligence, that is, the so-called a Pareto based bat algorithm inspired by the behaviour of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions of multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. On obtaining the results (optimal designs), potency, and reliability of the proposed multi-objective Pareto based bat algorithm are reported. Chapter 3 proposes a study on the Bat Algorithm (BA) technique to examine the skin melanoma images. Skin melanoma is one of the major types of cancer in people from Caucasian race. Due to its consequence, a considerable number of research works are being proposed by the researchers to develop the probable computer-based assessment technique for the Skin Melanoma Image (SMI). This work aims to develop and implement a computerized tool for the assessment of the SMI based on the recent machine learning technique. In the proposed work, the Bat Algorithm (BA) assisted examination technique is implemented to process the SMI. In this work, a detailed evaluation of the traditional BA and the recent version of the BA are considered to assess the performance of the proposed technique. This work considers the variants of BA, such as Levy-Flight (LF), Brownian-Walk (BW) and the Ikeda-Map (IM) to pre-process the skin melanoma pictures. The pre-processed SMIs are then processed with the DRLS segmentation approach and the performance of the considered BAs are validated by computing the essential Image Performance Metrics (IPM), and the result of this study confirm that the final outcome attained with the BW-guided BA offered a better result compared to the LF- and IM-based techniques. This technique is tested and validated using the benchmark database existing in the literature. Chapter 4 discusses thresholding of gray/RGB-scale images using Bat Algorithm (BA). The essential task in image thresholding is to enhance the information in raw image by identifying an optimal threshold. The proposed work executes a multi-threshold procedure for a class of benchmark images using

Preface

vii

Kapur’s Entropy (KE). Manual identification of appropriate threshold is a complex task for higher threshold values and hence, this work employed BA to find the finest threshold for the gray/RGB test imagery. In this work, test images with a dimension of 512 x 512 are considered for the experimental evaluation. This work also presents a performance comparison of the traditional and the enhanced BA to identify a suitable methodology to attain better outcomes without compromising the quality. Chapter 5 presents a comparative study on bat-inspired computing algorithm and its variants in search of Near-Optimal Golomb Rulers (OGRs) for WavelengthDivision Multiplexing (WDM) systems. Near-OGR sequences can be used as a channel-allocation scheme to reduce one of the important nonlinear crosstalk generated via Four-Wave Mixing (FWM) signals in optical WDM systems. The OGRs provide unequally spaced channel-allocation, a bandwidth-efficient scheme, and then the uniformly spaced channel-allocation methods to minimize the FWM crosstalk. To explore the search space, the bat-inspired computing algorithm is hybrid in its simple form with Differential Evolution (DE) mutation and random walk characteristics. The algorithms solve the two parameters, namely, the length of the Golomb ruler and total unequally spaced channel bandwidth occupied by OGRs in the optical WDM systems. The results reveal that the presented bat-inspired computing algorithm and its variants are better than other classical computing methods such as Extended Quadratic Congruence (EQC) and Search Algorithm (SA) and nature-inspired computing algorithms, namely, Genetic Algorithms (GAs), and simple Big Bang–Big Crunch (BB-BC) computing algorithm to generate near-OGRs in terms of the length of the ruler, the total occupied channel bandwidth, the Bandwidth Expansion Factor (BEF), the CPU time and the computational complexity. Chapter 6 presents a model order reduction methodology based on the Bat Algorithm (BA). Analytical study of large-scale linear time-invariant systems is a very tedious and complicated task in the category of real-life optimization problems. So, simplification procedures for these complex problems are needed. In the solution tactic of this complex problem, Model Order Reduction (MOR) is a novel concept providing a simpler model than the original one based on mathematical approximation. In the literature, several metaheuristics are employed to solve MOR problem. In the same line of order, this chapter presents a technique to solve MOR problem using modified bat algorithm based on Levy-flight and opposition-based learning. The concept of Levy-flight random walk and Opposition-Based Learning (OBL) is embedded to Bat Algorithm (BA) to avoid local optima trapping and to enhance the exploitation and exploration ability. To evaluate the performance of the proposed methodology, it is tested over three different MOR problems with different transfer functions. The numerical and statistical results verify the supremacy of the proposed variant in terms of stability of reduced-order systems. Chapter 7 proposes a methodology to detect the tumour from brain MRI. Cancer is a disease caused by an abnormal growth of cells. This is a menacing disease that can severely affect the quality of life of individuals. It can also take a toll on the emotional well-being of the patient along with physical repercussions. The cells which form malignant tumours can occur in any part of the body, but the brain is an

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area where the chance of survival is minimal if not treated accurately in time. Radiologists and oncologists make use of MRI scans, which provide images of the brain. These images can have different appearances depending on the setting of pulse sequences of the MRI such as T1-W, T2-W, MPR, DWI and FLAIR. This chapter focuses on the segregation of tumour region based on sequences such as T1-weighted and T2-weighted images of the brain. The segmentation is performed by making use of a fusion of bat and Interval Type-2 Fuzzy C Means Clustering (IT2FCM) algorithms, which is aimed at simplifying the task of a radiologist. Chapter 8 discusses a detailed review of signal, speech and image processing based on Bat Algorithm (BA). BA is a prominent metaheuristic approach based on the hunting mechanism of bats in nature. BA applications are rapidly growing in many engineering research fields since its invention in 2010. This chapter reviews the developments and applications of the bat algorithm in signal, speech and image processing. In particular, this review focuses on five main research areas for BA applications in signal, speech and image processing: speech enhancement, adaptive filtering, image compression, enhancement and thresholding in segmentation. On the other hand, this chapter also reviews the new variants and developments in BA applied for the aforesaid applications. The detailed implementation of the algorithms and their objective functions is also presented in this chapter. Chapter 9 implements the Bat Algorithm (BA) assisted methodology to extract the tumour section from abnormal brain MRI slices. This work implemented a heuristic algorithm based examination procedure. In this, the Bat Algorithm (BA) is used to improve the visibility of the tumour-pixels using Kapur’s Entropy (KE). The improved tumour section is then collected using the Watershed Segmentation Method (WSM). Later, a comparison linking the tumour portion and available Ground-Truth-Image (GTI) is executed and the Quality Measures (QM) are computed individually for FLAIR and T2. During this investigation, the MRI slices with 240  240  1 pixel resolution are considered and this technique is implemented on 400 MRI slices (FLAIR = 200 + T2 = 200). The average result of QM confirmed that, the BA-based technique helped to get superior result (Accuracy >95% for FLAIR/T2 modality slices). In the future, this methodology can be implemented to analyse the MRI slices obtained from the hospitals.

Kolkata, India Chennai, India

Editors Nilanjan Dey V. Rajinikanth

Contents

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution for Feature Selection and Classification . . . . . . . . . . . . . . Abdelmonem M. Ibrahim and Mohamed A. Tawhid

1

2 Multi-objective Optimization of Engineering Design Problems Through Pareto-Based Bat Algorithm . . . . . . . . . . . . . . . . . . . . . . . Deniz Ustun, Serdar Carbas, and Abdurrahim Toktas

19

3 A Study on the Bat Algorithm Technique to Evaluate the Skin Melanoma Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nilanjan Dey, V. Rajinikanth, Hong Lin, and Fuqian Shi

45

4 Multi-thresholding with Kapur’s Entropy—A Study Using Bat Algorithm with Different Search Operators . . . . . . . . . . . . . . . . . . . V. Rajinikanth, Nilanjan Dey, and S. Kavitha

61

5 Application of Bat-Inspired Computing Algorithm and Its Variants in Search of Near-Optimal Golomb Rulers for WDM Systems: A Comparative Study . . . . . . . . . . . . . . . . . . . . Shonak Bansal, Neena Gupta, and Arun K. Singh

79

6 Levy Flight Opposition Embedded BAT Algorithm for Model Order Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Shalini Shekhawat, Akash Saxena, Rajesh Kumar, and Vinay Pratap Singh 7 Application of BAT Algorithm for Detecting Malignant Brain Tumors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Adit Kotwal, Rishika Bharti, Mansi Pandya, Harshil Jhaveri, and Ramchandra Mangrulkar

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8 Bat Algorithm with Applications to Signal, Speech, and Image Processing—A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 K. Prajna and N. Manikanthababu 9 Bat Algorithm Aided System to Extract Tumor in Flair/T2 Modality Brain MRI Slices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 V. Sindhu, M. Singaravelan, J. Ramadevi, S. Vinitha, and S. Hemapriyaa

About the Editors

Nilanjan Dey is an Assistant Professor at the Department of Information Technology, Techno International New Town (formerly Techno India College of Technology), Kolkata, India. He is also a Visiting Fellow of the University of Reading, UK and a Visiting Professor at Duy Tan University, Vietnam. He was an honorary Visiting Scientist at Global Biomedical Technologies Inc., CA, USA (2012–2015). Holding a Ph.D. from Jadavpur University (2015), he is the Editor-in-Chief of the International Journal of Ambient Computing and Intelligence, IGI Global. He is also the Series Co-Editor of Springer Tracts in Nature-Inspired Computing (Springer Nature); Series Co-Editor of Advances in Ubiquitous Sensing Applications for Healthcare (Elsevier); and Series Editor of Computational Intelligence in Engineering Problem Solving and Intelligent Signal Processing and Data Analysis (CRC). He has authored/edited more than 50 books with Springer, Elsevier, Wiley and CRC Press and published more than 300 peer-reviewed research papers. His main research interests include medical imaging, machine learning, computer-aided diagnosis and data mining. He is the Indian Ambassador of the International Federation for Information Processing (IFIP)—Young ICT Group.

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About the Editors

V. Rajinikanth is a Professor at the Department of Electronics and Instrumentation Engineering, St. Joseph’s College of Engineering, Chennai, India. Recently, he edited a book titled Advances in Artificial Intelligence Systems with Nova Science Publisher, USA. He is an Associate Editor for the International Journal of Rough Sets and Data Analysis. Having published more than 75 papers, his main research interests include medical imaging, machine learning and computer-aided diagnosis, as well as data mining.

Chapter 1

A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution for Feature Selection and Classification Abdelmonem M. Ibrahim and Mohamed A. Tawhid

1 Introduction Feature selection (FS) is an approach for figuring out the most essential features and eliminating irrelevant and redundant data [1, 2]. The goals of FS are to reduce the dimensionality of the data, enhance the prediction accuracy, and perceive data for various applications in machine learning [3]. In a variety of applications, data representation often employs many features with some redundant ones, which means selected essential features can be considered while the irrelevant features (superfluous) can be eliminated. Also, the output is affected by the pertinent features because they provide useful information concerning the data, and the outcomes will be unclear if any of them is kept out [4]. The standard optimization methods have some drawbacks in solving the feature selection problems because for N features, 2 N feature subsets have to be generated and computed for a dataset, and it is known to be an NP-hard problem [5]. Thus, metaheuristic algorithms (MAs) are the alternative for overcoming these drawbacks and searching for the optimum solution [4, 6]. MAs may be inspired by biological interaction, group dynamics, nature, and social behavior. The binary version of these algorithms allows many researchers to deal with complex problems like feature selection and attain good results. MAs have been utilized to solve the feature selection problem, for example, binary bat algorithm (BBA) [7], binary crow search algorithm (CSA) [8], binary gray wolf optimization (bGWO) A. M. Ibrahim Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Asyut, Egypt e-mail: [email protected] M. A. Tawhid (B) Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC V2C 0C8, Canada e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 N. Dey and V. Rajinikanth (eds.), Applications of Bat Algorithm and its Variants, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-15-5097-3_1

1

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A. M. Ibrahim and M. A. Tawhid

[9] and binary particle swarm optimization integrating with the gravitational search algorithm (BPSOGSA) [10]. Also, hybridization of these algorithms have attracted many researchers in order to deal with FS problems, for example, [11–14], In this work, improved BA algorithm combined with DE is proposed for feature reduction, and the classification accuracy is calculated. Switching between the two transfer functions gives the proposed algorithm more efficiency as well as using one function. Also, selecting the appropriate parameters to update the features during the search of BA or DE has been carefully selected based on the experiments. Datasets data with high dimensionality have low classification accuracy. Feature selection is a process employed to choose the most informative (providing useful) features from the various types of UCI datasets. It is utilized to enhance the predictive accuracy and reduce the features. The primary aim of the proposed algorithm is to strengthen the efficiency of the feature selection method. The results of the proposed method are compared with the four methods in the literature. The rest of the chapter is structured as Sects. 2–5. Section 3 describes the theoretical background of the hybrid algorithms BA and DE. Section 2 describes the proposed methodology of feature selection. Section 4 explains the proposed algorithm. Section 5 presents the experimental analysis and discussion of the results. In Sect. 6, the chapter concludes with a summary of our contribution and highlights the possibility of some future work.

2 The Proposed Methodology In recent decades, the growth of large datasets in many disciplines has created challenges and difficulties for data mining. Researchers have realized that the feature selection is one of an essential data mining components to achieve a successful handling with datasets [15–18]. Feature selection methods take a lot of time in obtaining a reduct set of the original features. One of the important things that new research has focused on in this area is to find effective and efficient methods for finding the optimal solution at the lowest cost. Thus, this work suggests an effective approach in finding a minimal subset. The methodology adopted in this work for several types of UCI datasets is shown in Fig. 1. The highlight of FS, as a preprocessing step in ML, is viable in diminishing dimensionality, expanding learning exactness, and improving the outcome fathomability [19]. In this chapter, the BBDEA is developed for the feature selection purpose, where the leading including the best subset by choosing the feature selection approaches improves the accuracy of classification. Therefore, classification strategies are applied to assess the implementation of the proposed method of features selection.

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

3

Fig. 1 The proposed framework

Feature Selection method Evaluate Solutions

Classification Techniques

3 Theoretical Background 3.1 The Bat Algorithm The standard Bat algorithm (BA) was suggested by Yang [20] based on the echolocation behavior of the bats. Two of the major steps of BA cover the echolocation process of the bats.

3.1.1

Velocity and Position

BA is one of the most recent and powerful method that deals with various optimization problems. With a random initial population of N bats, BA starts the search process in n-dimensional search space. To update the ith bat/solution in BA, the new bats and velocities xit+1 and vit+1 at the iteration t + 1 respectively, can be updated as follows: αi = αmin + (αmax − αmin )β vit+1 xit+1

= =

vit xit

+ (xit − + vit+1 ,

x

best

)αi

(1) (2) (3)

where β is a uniform random number on [0, 1] and x best is the best solution so far. The pulse frequency released from ith bat for the current iteration is represented by αi , where the smallest and highest values of pulse frequency are set as αmin and αmax , respectively. Initially, αi is selected for each bat in range [αmin , αmax ].

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The other search part of BA selects a random bat between the current best population, and update the new solution based on the following local random step: x  = xr d +  A t ,

(4)

where xr d indicates a random agent (solution) selected from the best agents so far, At is the loudness and  is a vector of random number in range [−1, 1].

3.1.2

Loudness and Pulse Emission

It is worth mentioning that those which are responsible for integrating the mix of local and global movements are loudness (Ai ) and pulse rate (ri ). At the beginning of the search process, the loudness is high and the pulse emission is low. At the stage where the bats get prey, the loudness begins to decrease while the pulse emission gradually increases. Ai and ri are updated according to the following equations. rit+1 = ri0 [1 − exp(−γ t)], Ait+1

=

δ Ait ,

(5) (6)

where δ and γ are constants. The bat temporarily stops making sounds when the bat finds its prey and this happens when Ai is equal to zero. For any δ value between zero and one and γ is greater than zero, then we have Ait → 0, rit → ri0 , as t → ∞.

(7)

3.2 The Differential Evolution Algorithm DE is one of a strong and effective EA developed by Storn and Price (1997), which was designed for solving the variant optimization problems [21]. The DE population of N chromosomes is denoted by X , where X = x1 , x2 , . . . , x N . X is evolved by applying three of the main DE operators, namely, mutation, crossover, and selection. One of the standard mutation techniques for finding the best solution in DE is DE/best/1/bin (to be consistent with the designations adopted to refer the DE variants). The mutation equation is described in the following steps. During the evolutionary process, a new population of solutions is generated based on the old population for each generation/iteration. The basic steps of DE algorithm can be summarized as follows: Step 1: For each i ∈ 1, . . . , N in the gth generation, the target vector xi is the X g−1 population, and it might be used in the mutation operator and also used as one of the basic components to build a trial vector u i in the crossover operator.

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

5

Step 2: To build a new chromosome (update a new solution), the DE mutation operator will apply, by applying a linear combination of many randomly selected chromosomes from the current population (xr 1 , xr 2 ) to construct a mutated vector as follows: (8) vi = x best + F(xr 1 − xr 2 ) where F is known as a scale factor that is used for the status of the differential distinction. Step 3: The crossover operator is applied for building the trial vector u i by selecting the components randomly from either xi or vi . Step 4: The selection from xi or vi is based on a crossover factor (C F), the jth variable of u i is taken from vi in case of a random value in [0, 1] which is j j less than C F, otherwise its value is u i = xi . Step 5: Finally, a one-to-one competition is applied between xi and u i for selecting one of them to be a member of the new generation.

4 The Proposed Algorithm In this section, a new binary hybrid algorithm is introduced that combines the advantages of BA and DE algorithms named BBADE. Every subset of features can be viewed as a solution at any iteration in the algorithm. Each subset includes consideration and non-consideration of n features, where n represents the number of features of the original set. The best solution can be defined by reaching the solution that has a minimum reduct features and a high classification accuracy. Every solution is tested in conjunction with the proposed fitness function. It depends on the error of classification obtained by a classifier, which is necessarily related to the number of consideration features. The algorithm begins with generating a population of random solutions (features subsets). The proposed fitness function is then applied to evaluate each solution. x best is marked as the fittest or best solution in the population. The main loop in BBADE is iterated many times. For every generation, the bat and DE velocities are the main factors in changing the position of solutions based on V-shaped transfer function and S-shaped transfer function, respectively. To hybrid between BA and DE as a binary version, a probability of 60–40% is assumed for each solution to choose between the bat position (Eq. (3)) and DE velocity (Eq. (8)), respectively. The V-shaped transfer function is used for the binary version of bat position as in [10] as follows: t f = arctan(xi,t+1 j ),

(9)

where t f in Eq. (9) represents the V-shaped transfer function of the bat position xi,t+1 j (Eq. (3)). On the other side, for DE velocity is used with S-shaped transfer function as in [8] as follows: (10) t f = 1/(1 − exp(10(vi,t+1 j − 0.5))),

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where t f in Eq. (10) is the S-shaped transfer function for the DE velocity vi,t+1 j (Eq. (8)). In the following step, the positions are converted from continuous to binary search space as follows: 

xi,t+1 j

 =

0, rand() < t f ; 1, otherwise.

(11) 

where rand() is a uniform distribution random number in [0, 1], and xi t+1 indicates the new binary solution in the tth generation. When the updating binary position mechanism is achieved, a combination between exploration and exploitation in binary version is needed. To do that, the bat pulse rate r is used with a generated random vector r v in range [0, 1]. In the case of r v less than r , this means the exploration (searching for other best reduct subset) is used by keeping the updating binary positions in Eq. (11), while the selecting positions from the best subset so far are selected when r v > r for exploitation purpose. Compute the fitness function and update the best population with the best ones. This process will be repeated until the conditions for stopping have been met, which is currently the maximum number of iterations. The flowchart of BBADE is shown in Fig. 2. The initialization parameters at the beginning, BBADE begins with the setting of variable parameters and randomly initializes the binary positions in the search space. The BBADE parameter settings are also shown in the Fig. 2.

Fig. 2 The flowchart of BBADE

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

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5 Experimental Results and Discussions 5.1 Description of Dataset Sixteen UCI [22] benchmark datasets have been used to test the performance of the proposed hybrid algorithm. The “Olive” dataset can be found in “https://rdrr.io/ cran/zenplots/man/olive.html.” It is worth mentioning that in this chapter, the shared datasets do not contain any missing values in any records [22]. Two of the large datasets were used in this study, where their features number over 100 features. A brief overview of each dataset is provided in Table 1.

5.2 Fitness Function Each solution is evaluated with a defined fitness function at each iteration. The data are randomly divided into two separate parts: training and testing datasets. The m-fold cross-validation procedure is used to divide the data randomly into m folds. The first fold is setting for training the classifier while the remaining are

Table 1 Description of dataset ID Dataset D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16

Balance scale Diabetes Olive Breast cancer Heart Vehicle Lymphography Zoo Germen credit Wisconsin diagnosis breast cancer Ionosphere Chess Lung cancer Sonar Hill valley LSVT voice rehabilitation

Number of features

Number of instances

Number of classes

Type

4 6 8 9 13 18 18 18 24 32

625 144 572 683 270 946 148 101 1000 596

3 3 9 2 2 4 4 2 2 2

Social Clinical N/A Clinical Clinical N/A Clinical Life Business Clinical

34 36 56 60 101 309

351 3196 32 20 606 126

2 2 3 2 2 2

Physical Game Clinical Physical N/A Life

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A. M. Ibrahim and M. A. Tawhid

for testing. m are regarded as 10 sets in this study to ensure the reliability of the results achieved. The objective criteria for evaluation are used in this section, namely, loss/error classification for linear classification models. Through dividing the number of correctly categorized instances by the total number of instances, the precision of the classification is determined. In this study, two popular classifiers are employed as a classification method step for fitness function, namely, K-Nearest Neighbor (KNN) and Decision/Classification Trees (CART) [8, 23, 24]. KNN is one of the supervised learning methods that depend on the classification of new instance depending on the distance between the new and the training instances. In this chapter, KNN is used to measure the quality of the considered features for each solution where K equals to 1 with mean absolute distance. The other classifier are the decision trees which are used in data mining and mainly contains two types: Tree classification is one of the two species which depends on where the analysis in the case is when the expected result is the class that belongs to the data. The other type is the regression tree in which the analysis is when the expected result can be considered as a real number. Both the classification and regression trees have things in common as well as differences, such as procedure used to decide where data will be divided. There are several decision trees methods, namely, Iterative Dichotomiser 3 (ID3), Classification and Regression Tree (C4.5, CART), CHi-squared Automatic Interaction Detector (CHAID), and Multivariate Adaptive Regression Splines (MARS). Out of these, we’re going to use the more common ones, which is CART [25]. The first objective for any classifier is to obtain the best accuracy which of course selects the best reduct features, i.e., the best solution is the one which minimizes the classification error, minimizes the number of selected features, and maximizes the classification accuracy. The search process stops when the maximum number of iterations is reached. In all experiments, the maximum number of iterations is set equal to 50.

5.3 Experimental Setup The efficiency of the proposed BBADE algorithm was evaluated using seventeen benchmark datasets. The numeral computation of the proposed algorithm is performed using Matlab. The experiments are tested on an Intel(R) Core(TM) i5 CPU 3.10 GHz and 8 GB RAM and the parameter values of 50 and 20 have been regarded for the maximum number of iterations and population size, respectively. The following criteria are used to compare BBADE with the state-of-the-art selected algorithms: • Fitness values (classification error). They are obtained from each approach as reported (classification error: it is obtained after applying the classifier on the test dataset under the reducted features) The max, mean, and min fitness values are compared. The average gained from 20 runs is computed. • Average selection size. It is the other comparison that has been shown.

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

9

• P value from Wilcoxon’s rank-sum test and the mean rank value R from Friedman test. Friedman test and Wilcoxon’s rank-sum test are non-parametric statistical tests with 5% significance level [26]. The statistical test is necessary to demonstrate that the proposed algorithm is significantly improved comparing to other algorithms [26]. Generally, the best values of P are considered when P value is below 0.05. Therefore, P value < 0.05 can be regarded as an adequate evidence against the null hypothesis. The h values for the Wilcoxon’s test indicate that the null hypothesis is rejected for h = 1, and the proposed algorithm outperforms the other one. h = −1 means the null hypothesis is rejected, and the proposed algorithm is inferior to the other one. h = 0 reveals that the null hypothesis is accepted, and the proposed algorithm ties the other one. The performance of the binary hybrid algorithm BBADE is compared with other optimization algorithms. These algorithms are proposed in the literature for binary optimization or for solving the feature selection problem. These algorithms are binary bat algorithm (BBA) [7], binary crow search algorithm (CSA) [8], binary gray wolf optimization (bGWO) [9], and binary particle swarm optimization integrating with the gravitational search algorithm (BPSOGSA) [10]. The parameter settings are followed from their original papers for all adopted optimization algorithms as the following. In BBA, pulse emission rate r is 0.1, the loudness of emitted sound A is 0.25, and frequency maximum αmax and frequency minimum αmin are 2 and 0, respectively. In CSA, the awareness probability A P is, and the flight length f l is 2, upper bound = size of features, and lower bound = 1. In BPSOGSA, the initial gravitational constant G 0 is 1, the accelerating factors c1 = −2 Tt33 + 2 and c1 = −2 Tt33 + 2, where T is the maximum number of iterations, t indicates the current iteration, and the descending coefficient α is 20. In BBADE, the frequency maximum αmax and frequency minimum αmin are 2 and 0.1, respectively. BDA is a parameter-less algorithm, where version bGWO2 in its original paper has been used in this study as it was proved its efficiency in solving the FS problem.

5.4 Analysis and Experimental Results In this study, various computational experiments on 16 benchmark datasets are shown. Such experiments are aimed at testing the efficiency of the proposed BBADE hybrid algorithm on feature selection problem and contrasting BADE against other metaheuristic methods. All these experiments are conducted with the same specification on the same PC. Table 2 estimates the average score for 50 iterations. As it is shown the BBADE outperforms other algorithms. For KNN experiment, BBADE algorithm obtains the maximum mean fitness value on 9 out of 16 tested datasets (D1, D2, D3, D5, D6, D8, D10, D12, and D16), despite BPSOGSA that obtains better results than BBADE for six benchmark datasets (D4, D7, D9, D11, D14 and D15). For the majority of the datasets, BBA, CSA, and bGWO get the maximum mean fitness (D13, D10, and

10

A. M. Ibrahim and M. A. Tawhid

Table 2 Mean fitness value for metaheuristic algorithms Dataset

KNN

CART

BBA

CSA

bGWO

BPSOGSA BBADE BBA

CSA

bGWO

BPSOGSA BBADE

D1

0.343

0.388

0.348

0.358

0.221

0.268

0.277

0.265

0.281

0.200

D2

0.032

0.040

0.038

0.044

0.030

0.026

0.027

0.027

0.033

0.025

D3

0.087

0.106

0.087

0.097

0.081

0.077

0.091

0.078

0.085

0.074

D4

0.054

0.059

0.053

0.052

0.053

0.042

0.042

0.040

0.040

0.041

D5

0.169

0.198

0.178

0.172

0.163

0.159

0.166

0.157

0.157

0.155

D6

0.270

0.298

0.276

0.267

0.266

0.257

0.262

0.249

0.248

0.252

D7

0.127

0.162

0.128

0.120

0.123

0.139

0.148

0.139

0.133

0.132

D8

0.007

0.022

0.012

0.009

0.000

0.029

0.054

0.044

0.035

0.025

D9

0.277

0.300

0.280

0.271

0.275

0.251

0.260

0.247

0.241

0.238

D10

0.000

0.000

0.000

0.000

0.000

0.015

0.016

0.015

0.016

0.015

D11

0.066

0.085

0.074

0.059

0.062

0.061

0.066

0.062

0.057

0.060

D12

0.026

0.069

0.030

0.027

0.024

0.008

0.038

0.008

0.009

0.008

D13

0.034

0.084

0.066

0.053

0.047

0.123

0.125

0.125

0.125

0.125

D14

0.075

0.098

0.075

0.057

0.063

0.163

0.163

0.175

0.157

0.165

D15

0.375

0.384

0.373

0.363

0.372

0.377

0.376

0.375

0.373

0.372

D16

0.341

0.344

0.348

0.318

0.310

0.138

0.137

0.141

0.133

0.137

p

5.1E−03 6.1E−05 1.2E−04 1.5E−01

h

1

1

1

0

R

2.7

4.8

3.6

2.4

6.8E−03 7.3E−04 3.7E−03 3.0E−01 1.6

1

1

1

0

3.0

4.3

3.1

2.7

1.9

D10) one dataset for each. BPSOGSA is observed to be the second most powerful output on the 16 tested datasets. CSA, for most cases, obtains the worst results. For CART experiment, BBADE algorithm also finds the highest mean fitness value on 9 out of 16 benchmarks datasets, despite BPSOGSA that gets the same or higher results than BBADE for five benchmark datasets. For the majority of the datasets, BBA, CSA, and bGWO achieve the maximum mean fitness. Table 2 reports the p-value and mean ranks R of the average values among five algorithms BBA, CSA, bGWO, BPSOGSA, and BBADE obtained by the Wilcoxon and Friedman tests, respectively, with a confidence level of 0.95 (α = 0.05). As it can be seen, BBADE is statistically significant compared with the other algorithms. This is because all obtained results are less than 0.05 except with BPSOGSA, which is almost similar to BBADE for both KNN and CART. Thus, it can be regarded as sufficient evidence against the null hypothesis. BBADE ranks first with average values obtained over 50 independent runs for each dataset while BPSOGSA in the second rank for both KNN and CART. The best results of BBADE are due to the memory of each subset with initial random positions, as there is no experience with the presumption of the bats. After starting the algorithm with the random initial positions, the selection or non-selection of each feature is applied randomly based on both given transfer functions. Then, the algorithm discovers the best features by utilizing the best solution obtained so far.

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

11

Table 3 Best fitness value for metaheuristic algorithms Dataset

KNN

CART

BBA

CSA

bGWO

BPSOGSA BBADE BBA

CSA

D1

0.341

0.341

0.336

0.338

0.197

0.259

0.259 0.259

bGWO

0.261

BPSOGSA BBADE 0.192

D2

0.021

0.028

0.021

0.035

0.021

0.021

0.021 0.021

0.028

0.021

D3

0.077

0.082

0.077

0.082

0.077

0.070

0.070 0.065

0.068

0.065

D4

0.049

0.049

0.049

0.047

0.047

0.035

0.035 0.033

0.035

0.032

D5

0.156

0.156

0.156

0.156

0.156

0.143

0.146 0.143

0.139

0.139

D6

0.249

0.271

0.267

0.251

0.253

0.243

0.242 0.239

0.236

0.239

D7

0.108

0.122

0.108

0.101

0.115

0.108

0.128 0.101

0.108

0.115

D8

0.000

0.010

0.000

0.000

0.000

0.020

0.040 0.030

0.020

0.020

D9

0.251

0.278

0.259

0.255

0.266

0.237

0.246 0.236

0.229

0.226

D10

0.000

0.000

0.000

0.000

0.000

0.012

0.013 0.012

0.013

0.013

D11

0.046

0.074

0.063

0.046

0.054

0.048

0.060 0.048

0.048

0.051

D12

0.022

0.052

0.022

0.023

0.022

0.007

0.018 0.007

0.007

0.007

D13

0.000

0.063

0.031

0.031

0.031

0.094

0.125 0.125

0.125

0.125

D14

0.048

0.082

0.048

0.034

0.048

0.135

0.135 0.139

0.125

0.120

D15

0.348

0.371

0.350

0.345

0.355

0.356

0.365 0.353

0.351

0.348

D16

0.294

0.317

0.333

0.230

0.222

0.111

0.119 0.127

0.111

0.119

Table 3 presents a comparison for the best results obtained from other metaheuristic algorithms and BBADE. As it can be noticed from this table, BBA obtains the same or highest results for 9 out of 16 datasets for KNN. BBADE, and BPSOGSA are in second place for 8 datasets, and bGWO is in third place. BBA outperforms the other algorithms for D6, D9, and D13, while BBADE outperforms for D1 and D16 and BPSOGSA for D7, D11, D14, and D15. Also, it can be observed that BBADE overcomes the other algorithms using the CART classifier. BBADE obtains the same or highest results for 9 out of 16 datasets, followed by 5 datasets for each BBA and bGWO. BBADE outperforms the other algorithms for D1, D4, D9, D14, and D15. Table 4 gives the worst fitness value for metaheuristic algorithms. As it can be observed, BBADE surpasses other algorithms and gets the highest results for both experiments. BBADE algorithm is in the second place for 13 and 10 out of 16 datasets for KNN and CART, respectively. The results show that the binary pulses rate technique in the BBADE algorithm helped to improve the results from the beginnings of the search and the first iteration. Thus, it finds the highest results for most datasets. Table 5 illustrates the comparison of the competitive algorithm stability. As can be observed that BBADE is superior when it is compared to others in the KNN experiment, while CSA found the best results in the CART experiment. With this strong consistency, however, the CSA produces the worst results in terms of average, worst and best performance. The explanation behind this is the exploitation vulnerability of these algorithms, so the initial solution is slowly improving. BBADE’s main advantage is to have fewer variables to adjust. These parameters can highly impact the performance of any optimization algorithm. However, selecting the opti-

12

A. M. Ibrahim and M. A. Tawhid

Table 4 Worst fitness value for metaheuristic algorithms Dataset

KNN

CART

BBA

CSA

bGWO

BPSOGSA BBADE BBA

CSA

D1

0.347

0.528

0.419

0.422

0.347

0.326

0.328 0.269

bGWO

0.328

BPSOGSA BBADE 0.205

D2

0.049

0.056

0.056

0.076

0.049

0.063

0.035 0.035

0.069

0.028

D3

0.110

0.157

0.103

0.126

0.082

0.094

0.119 0.087

0.136

0.084

D4

0.070

0.069

0.069

0.054

0.072

0.047

0.047 0.047

0.047

0.047

D5

0.190

0.231

0.221

0.224

0.190

0.173

0.187 0.173

0.180

0.170

D6

0.305

0.323

0.305

0.280

0.275

0.273

0.274 0.257

0.265

0.262

D7

0.149

0.196

0.162

0.149

0.135

0.176

0.169 0.155

0.155

0.162

D8

0.010

0.040

0.020

0.040

0.000

0.050

0.069 0.059

0.050

0.040

D9

0.299

0.328

0.299

0.293

0.291

0.268

0.272 0.263

0.266

0.256

D10

0.001

0.000

0.000

0.004

0.000

0.021

0.020 0.018

0.020

0.018

D11

0.080

0.094

0.083

0.074

0.074

0.071

0.071 0.074

0.071

0.071

D12

0.041

0.096

0.043

0.032

0.027

0.014

0.059 0.009

0.014

0.009

D13

0.063

0.125

0.094

0.063

0.063

0.125

0.125 0.125

0.125

0.125

D14

0.101

0.120

0.096

0.091

0.091

0.188

0.188 0.197

0.178

0.202

D15

0.391

0.394

0.389

0.386

0.394

0.398

0.389 0.391

0.388

0.403

D16

0.357

0.365

0.365

0.365

0.365

0.159

0.151 0.159

0.159

0.151

Table 5 Standard deviation for metaheuristic algorithms Dataset

KNN

CART

BBA

CSA

bGWO

BPSOGSA BBADE BBA

CSA

D1

0.002

0.049

0.017

0.027

0.054

0.014

0.021 0.002

bGWO

0.025

BPSOGSA BBADE 0.003

D2

0.008

0.011

0.011

0.011

0.005

0.009

0.005 0.003

0.009

0.003

D3

0.011

0.019

0.007

0.013

0.002

0.006

0.011 0.006

0.016

0.005

D4

0.004

0.007

0.005

0.002

0.005

0.004

0.003 0.004

0.004

0.004

D5

0.010

0.023

0.019

0.019

0.008

0.008

0.011 0.009

0.011

0.008

D6

0.012

0.012

0.009

0.007

0.005

0.008

0.009 0.006

0.008

0.007

D7

0.013

0.017

0.016

0.011

0.007

0.016

0.012 0.014

0.015

0.012

D8

0.005

0.008

0.006

0.009

0.000

0.011

0.009 0.008

0.010

0.008

D9

0.011

0.014

0.010

0.008

0.006

0.010

0.007 0.008

0.010

0.008

D10

0.000

0.000

0.000

0.001

0.000

0.002

0.002 0.001

0.002

0.001

D11

0.011

0.007

0.005

0.007

0.006

0.005

0.004 0.006

0.007

0.005

D12

0.005

0.011

0.005

0.003

0.001

0.001

0.011 0.001

0.002

0.000

D13

0.014

0.023

0.014

0.015

0.016

0.007

0.000 0.000

0.000

0.000

D14

0.014

0.009

0.014

0.014

0.011

0.016

0.012 0.014

0.013

0.019

D15

0.011

0.006

0.009

0.011

0.009

0.011

0.008 0.010

0.010

0.014

D16

0.016

0.012

0.009

0.046

0.050

0.013

0.009 0.007

0.012

0.009

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

13

mum value for each is regarded a difficult task. The experimental results show that the hybrid algorithm with selecting the parameter values can increase the performance and stability of the proposed algorithm. The results also show the BBADE’s stability, repeatability, and ability to find the feature subset are better than the other evolutionary algorithms and other hybrid algorithms in the feature space. This is because the evolutionary algorithms implemented use random parameters to impact their output in their search process. In addition, agents’ random actions can cause high probability stagnation in the optimization process.

5.4.1

Classification Accuracy Versus Feature Selection

The results in Table 2 and Figs. 3, 4, 5, and 6 demonstrate the classification accuracy according to KNN and CART classifiers after running the optimization algorithms. These results show that the proposed algorithm obtained the best mean classification accuracy-KNN and CART and the best attribute reduct for most datasets. Also, for the two large datasets, BBADE obtains the mean best accuracy for ‘LSVT’-KNN and ‘Hill Valley’-CART with 157 and 53 of mean reduct features, respectively. One can see, it does not have to get the highest classification accuracy and the lowest reduct features at the same time because we use one object as a fitness function (classification error). Some algorithms have a low classification accuracy and had lower reduct features. That means we are looking for the best reduct features that have the highest accuracy. Finally, according to classification results, BBADE succeeded in avoiding a significant reduction in classification accuracy for most of the datasets. 1

25

0.95 20 0.9

0.85

15

0.8 10

0.75 0.7

5 0.65 0.6

0

D1

D2

D3

D4

D5

D6

D7

BBA

CSA

bGWO

BPSOGSA

BBADE

BBA

CSA

bGWO

BPSOGSA

BBADE

D8

Fig. 3 The mean classification accuracy-KNN (bars) compared with the mean selected features (lines)

14

A. M. Ibrahim and M. A. Tawhid 1

250

0.95 200

0.9 0.85

150

0.8 100

0.75 0.7

50

0.65 0.6

0

D9

D10

D11

D12

D13

D14

D15

D16

BBA

CSA

bGWO

BPSOGSA

BBADE

BBA

CSA

bGWO

BPSOGSA

BBADE

Fig. 4 The mean classification accuracy-KNN (bars) compared with the mean selected features (lines) 1

20

18 0.95

16 14

0.9

12 10

0.85

8

0.8

6 4

0.75

2 0.7

0

D1

D2

D3

D4

D5

D6

D7

BBA

CSA

bGWO

BPSOGSA

BBADE

BBA

CSA

bGWO

BPSOGSA

BBADE

D8

Fig. 5 The mean classification accuracy-CART (bars) compared with the mean selected features (lines)

5.4.2

Analysis Based on the Convergence History

For more comparison of BBADE with various algorithms, graphical representation of the convergence curve of BBADE is examined, as well. BBADE’s convergence curve on 16 reference datasets of various algorithms is shown in Figs. 7 and 8. In these figures, the number of iterations is taken 50. As it can be seen from these

1 A New Hybrid Binary Algorithm of Bat Algorithm and Differential Evolution …

15 250

1 0.95

200

0.9 0.85

150

0.8 100

0.75 0.7

50

0.65 0.6

0

D9

D10

D11

D12

D13

D14

D15

D16

BBA

CSA

bGWO

BPSOGSA

BBADE

BBA

CSA

bGWO

BPSOGSA

BBADE

Fig. 6 The mean classification accuracy-CART (bars) compared with the mean selected features (lines) 7

BBA BCSA bGWO BPSOGSA BBADE

0.32 0.3

0.05

4 3 2 1

0.24

5

10

15

20

25

30

35

40

45

50

5

10

15

20

30

35

40

45

0.025

50

5

10

15

20

0.1 0.095

Fitness

0.11 0.105 0.1 0.095

25

30

35

40

45

0.09

0.065

15

20

25

30

35

45

50

BBA BCSA bGWO BPSOGSA BBADE

0.05

0.06

40

D4-CART

0.048 0.046 0.044

0.055

5

10

15

20

25

30

35

40

45

0.07

50

0.042

0

5

10

15

20

25

30

35

40

45

0.05

50

0

5

10

15

20

Iterations

D5-KNN

D5-CART

0.195

BBA BCSA bGWO BPSOGSA BBADE

0.21

BBA BCSA bGWO BPSOGSA BBADE

0.19 0.185 0.18

Fitness

0.2 0.19

30

35

40

45

0.04

50

BBA BCSA bGWO BPSOGSA BBADE

0.32 0.31

0.175

10

15

20

25

30

35

40

45

0.155

50

0

5

10

15

20

25

30

35

40

45

0.26

50

BBA BCSA bGWO BPSOGSA BBADE

BBA BCSA bGWO BPSOGSA BBADE

0.19

Fitness

0.18

0.17 0.16 0.15

40

45

50

0.275 0.27 0.265

0.25 0

5

10

15

20

25

30

35

40

45

0.245

50

0

5

10

15

20

BBA BCSA bGWO BPSOGSA BBADE

0.02

0.16

35

40

45

50

BBA BCSA bGWO BPSOGSA BBADE

0.06 0.055 0.05

0.015

0.01

0.15

30

D8-CART

0.065

0.025

0.17

25

Iterations

D8-KNN

0.03

Fitness

0.2

0.18

35

BBA BCSA bGWO BPSOGSA BBADE

Iterations

D7-CART

0.2

0.19

30

0.26

Iterations

D7-KNN

25

D6-CART

0.255

Iterations 0.21

20

0.28

0.3 0.29

Fitness

5

15

0.29

0.27

0.16

0

10

0.285

0.28

0.165

0.17

5

0.295

0.17 0.18

0

Iterations

D6-KNN

0.33

Fitness

0.22

25

Iterations

Fitness

0

0.23

Fitness

10

0.052

0.075

Iterations

0.045 0.04 0.035

0.14

0.03 0.005

0.14

0.13 0.12

5

Iterations

0.08

0.09 0.085

0.16

0

0.054

BBA BCSA bGWO BPSOGSA BBADE

0.07

0.085

0.025 50

D4-KNN

0.075

BBA BCSA bGWO BPSOGSA BBADE

Fitness

0.12

0.08

0.03

0

Iterations

D3-CART

0.105

BBA BCSA bGWO BPSOGSA BBADE

0.115

Fitness

25

Iterations

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figures, BBADE gets the best results. This is due to that its curves are lower than the other competitive algorithms “colored with green.” It can also be noted that in most datasets, the BBADE algorithm converges faster toward the global optima than others. Also, it can be observed that the BPSOGSA curve, in some cases, obtains the highest results. Nevertheless, CSA gets the lowest results. These results are in line with the results obtained in Table 2. Such an improvement of the results arose from embedding both transfer function V-shaped and S-shaped and the improving BA by combining with DE in the searching iterations of the proposed algorithm. It allows the algorithm to avoid local optima and get closer to the global optima faster.

6 Conclusions and Future Work In this chapter, a new hybrid binary version of the bat algorithm (BA) is proposed to solve feature selection problems. In particular, BA is combined with enhanced version of the differential evolution algorithm (DE). In the suggested algorithm, the BA with its capability for echolocation to explore the feature space is integrated with DE and its capacity to converge to the best global solution in the search space. The general performance of the suggested algorithm is examined by comparing it with the original optimizers and other optimizers, namely,binary bat algorithm (BBA) [7],

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binary crow search algorithm (CSA) [8], binary gray wolf optimization (bGWO), [9] and binary particle swarm optimization integrating with the gravitational search algorithm (BPSOGSA) [10]. The proposed algorithm and various optimizers are employed over datasets obtained from the UCI repository. The results prove the ability of the proposed algorithm to search the feature space for optimal feature combinations. Our proposed algorithm motivates us to apply the proposed algorithm to solve traveling salesman problem [27, 28] nonlinear systems [29, 30], integer programming and minimax problems [31, 32], large scale optimization problems [33], and deal with microarray datasets [34].

References 1. Xue B, Zhang M, Browne WN, Yao X (2015) A survey on evolutionary computation approaches to feature selection. IEEE Trans Evol Comput 20(4):606–626 2. Jue W, Qi Z, Hedar A, Ibrahim AM (2014) A rough set approach to feature selection based on scatter search metaheuristic. J Syst Sci Complex 27:157–168 3. Al-Sahaf H, Bi Y, Chen Q, Lensen A, Mei Y, Sun Y, Tran B, Xue B, Zhang M (2019) A survey on evolutionary machine learning. J R Soc N Z 49(2):205–228 4. Nayar N, Ahuja S, Jain S (2019) Swarm intelligence for feature selection: a review of literature and reflection on future challenges. In: Advances in data and information sciences. Springer, pp 211–221 5. Taradeh M, Mafarja M, Heidari AA, Faris H, Aljarah I, Mirjalili S, Fujita H (2019) An evolutionary gravitational search-based feature selection. Inf Sci 497:219–239 6. Hedar A-R, Ibrahim AM, Abdel-Hakim AE, Sewisy AA (2018) K-means cloning: adaptive spherical k-means clustering. Algorithms 11(10) 7. Mirjalili SM, Yang X-S (2014) Binary bat algorithm. Neural Comput Appl 25:663–681 8. Sayed GI, Hassanien AE, Azar AT (2019) Feature selection via a novel chaotic crow search algorithm. Neural Comput Appl 31:171–188 9. Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381 10. Mirjalili S, Wang G-G, Coelho LDS (2014) Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput Appl 25:1423–1435 11. Tawhid MA, Ibrahim AM (2020) Hybrid binary particle swarm optimization and flower pollination algorithm based on rough set approach for feature selection problem. Springer International Publishing, Cham, pp 249–273 12. Tawhid MA, Dsouza KB (2019) Solving feature selection problem by hybrid binary genetic enhanced particle swarm optimization algorithm. Int J Hybrid Intell Syst 1–13 (Pre-press) 13. Tawhid MA, Dsouza KB (2018) Hybrid binary dragonfly enhanced particle swarm optimization algorithm for solving feature selection problems. Math Found Comput 1(2):181–200 14. Tawhid M, Dsouza KB (2018) Hybrid binary bat enhanced particle swarm optimization algorithm for solving feature selection problems. Appl Comput Inform 15. Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182 16. Liu H, Motoda H (2007) Computational methods of feature selection. CRC Press 17. Liu H, Motoda H (2012) Feature selection for knowledge discovery and data mining, vol 454. Springer Science & Business Media 18. Hedar A-R, Ibrahim A-MM, Abdel-Hakim AE, Sewisy AA (2018) Modulated clustering using integrated rough sets and scatter search attribute reduction. In: Proceedings of the genetic and evolutionary computation conference companion, GECCO ’18. ACM, New York, NY, USA, pp 1394–1401

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19. Tawhid MA, Ibrahim AM (2019) Feature selection based on rough set approach, wrapper approach, and binary whale optimization algorithm. Int J Mach Learn Cybern 1–30 20. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. Springer, Berlin, Heidelberg, pp 65–74 21. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359 22. Dua D, Graff C (2017) UCI machine learning repository 23. Stone CJ, Olshen RA, Breiman L, Friedman J (1984) Classification and regression trees. Mathematics & statistics. Chapman and Hall/CRC 24. Witten I, Frank E, Hall M (2011) Data mining: practical machine learning tools and techniques. The Morgan Kaufmann series in data management systems. Elsevier Science 25. Gupta B, Rawat A, Jain A, Arora A, Dhami N (2017) Analysis of various decision tree algorithms for classification in data mining. Int J Comput Appl 163(8):15–19 26. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18 27. Tawhid MA, Savsani P (2019) Discrete sine-cosine algorithm (DSCA) with local search for solving traveling salesman problem. Arab J Sci Eng 44(4):3669–3679 28. Savsani P, Tawhid MA (2018) Discrete heat transfer search for solving travelling salesman problem. Math Found Comput 1(3):265–280 29. Tawhid MA, Ibrahim AM (2020) A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems. Evol Syst 11(1):65–87 30. Ibrahim AM, Tawhid MA (2019) A hybridization of cuckoo search and particle swarm optimization for solving nonlinear systems. Evol Intell 12(4):541–561 31. Tawhid MA, Ali AF (2019) Multidirectional harmony search algorithm for solving integer programming and minimax problems. Int J Bio-Inspired Comput 13(3):141–158 32. Tawhid MA, Ali AF (2016) A simplex social spider algorithm for solving integer programming and minimax problems. Memet Comput 8(3):169–188 33. Tawhid MA, Ali AF (2017) A hybrid social spider optimization and genetic algorithm for minimizing molecular potential energy function. Soft Comput 21(21):6499–6514 34. Maji P, Paul S (2011) Rough set based maximum relevance-maximum significance criterion and gene selection from microarray data. Int J Approx Reason 52(3):408–426

Chapter 2

Multi-objective Optimization of Engineering Design Problems Through Pareto-Based Bat Algorithm Deniz Ustun, Serdar Carbas, and Abdurrahim Toktas

1 Introduction Even though single-objective solution methods have been developed for complex engineering problems since the time of the World War II, multiple objectives need to be optimized simultaneously in order to obtain solutions for real-world engineering problems, which are often used for multipurpose. In such problems, more than one objective, minimization, maximization, or both, must be satisfied. Therefore, solving multi-objective optimization problems is much more difficult than the single-objective ones, as the objectives often have trade-off among each other. In the multi-objective optimization problems, it is not possible to achieve a single optimal set of solutions as in single-objective optimization problems. Furthermore, nowadays, the intertwining systems, the increase in the relations between the disciplines, and the increase of the requirements have revealed the need to consider more objectives instead of a single objective in decision-making problems. But in such cases, the objectives often contradict each other. Generally, when one objective is healed, the other objectives may worsen [1]. D. Ustun Department of Computer Engineering, Faculty of Engineering, Karamanoglu Mehmetbey University, Karaman, Turkey e-mail: [email protected] S. Carbas (B) Department of Civil Engineering, Faculty of Engineering, Karamanoglu Mehmetbey University, Karaman, Turkey e-mail: [email protected] A. Toktas Department of Electrical and Electronics Engineering, Faculty of Engineering, Karamanoglu Mehmetbey University, Karaman, Turkey e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 N. Dey and V. Rajinikanth (eds.), Applications of Bat Algorithm and its Variants, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-15-5097-3_2

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Today, the engineers are constantly faced with various decision-making problems in the solution of engineering design problems. While some of the decisions to be made are quite elementary and straightforward, others have a very complex structure and are of great importance. The classical nature of optimization can be considered as a decision-making process that achieve a specific objective and satisfy certain limitations. However, in reality, most engineering design problems are defined by many objective functions. In this case, it is necessary to choose from a variety of objectives to achieve the best design, which makes some objective functions more or less successful. For this reason, it is unreasonable to define most engineering design problems with a single-objective function; thus, such problems must be specified with multi-objective functions [2]. For example, good design for a bridge construction is expressed by low mass and high durability. An aircraft design requires simultaneous optimization of fuel efficiency, load, and weight. The skylight window design of a car is intended to minimize the noise that the driver would hear and maximize the ventilation. In this regard, there may not be a single solution that is global optimum for all objectives. In this case, the decision-maker (designer and/or engineer) is asked to select a compromised solution from a finite solution set. The appropriate solution should provide an acceptable level of performance for all objectives [3]. Many of the real-world optimization problems are complex and are computationally expensive to solve. The solutions of such problems necessitate longer time. Therefore, in order to reach the solution for these problems, algorithms that give approximate solutions have been used. These algorithms can be divided into heuristic and metaheuristic methods. An algorithm is called as heuristic, if that is specific to the problem encountered in the real world and takes advantage of the inputs of that problem and is expected to give good solutions only to that problem. Metaheuristic algorithms, on the other hand, are approximate algorithms that can produce effective and appropriate solutions in a limited time for combinatorial optimization problems where classical optimization methods cannot produce an acceptable solution. Unlike heuristic algorithms, metaheuristics do not only have problem-specific success, but they are able to achieve effective and appropriate solutions regardless of the problem type. Metaheuristic algorithms are powerful algorithms for the solution of engineering design problems. Their diversity allows them to search solutions at different region of the search space and find effective and appropriate solutions. They are robust algorithms because they can perform local and global search in search space. Although these methods cannot always guarantee the best global solution, they are highly preferred because they can provide effective and appropriate solutions for complex engineering design problems [4–18]. In this study, one of the recent metaheuristics, bat algorithm (BA) [19], is used to obtain optimum solutions for multi-disciplinary multi-objective engineering design problems. BA is a swarm-based heuristic optimization algorithm inspired by the echolocation capabilities discovered by analyzing the behavior of bats such as hunting, moving in dark environments, or determining their position. This algorithm is inspired by the natural behavior of bats, like the direction and distance detection of an object and/or prey using the echo of sound called echolocation. The logic of this algorithm is summarized briefly: (i) All bats determine the location of their prey by

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echolocation. (ii) Each bat has velocity (v), position (x), frequency (f ), pulse rate (r), and loudness (l). (iii) Bats can adjust pulse rate and loudness [19–24]. In this chapter, the multi-objective engineering design optimization problems selected from multi-disciplinary engineering fields are used to verify the effectiveness of Pareto-based BA on optimal design performances of those complex-type problems. The first design example is chosen as a for-bar planar truss, in which the structural weight (mass) and the vertical deflection at single load applied node of the truss are minimized at the same time. The cross-sectional area of each structural element (bars) behaved as design variables. Latter, a real-sized welded steel beam is optimized for simultaneously minimizing the cost of welding and pointing the tip deflection of the beam. In order to do this, optimum design, the shear stress in the group of weld, bending stress in the beam, and buckling capacity of the beam are treated as design constraints. As the last and the most difficult design example, multi-objective design optimization of a multi-layer radar absorbing material used for a radar absorber is preferred. In this design problem, minimizing total thickness in conjunction with total reflection is the objective function. The design variables material type for each layer is chosen from a material database and the thickness of each layer is decided. The achieved optimum designs indicate that the proposed Pareto-based BA approach for multi-objective (pb-MOBA) design of engineering design problems is computationally efficient and performs well in design examples considered from different engineering fields.

2 Concept of Pareto Optimality The concept of Pareto optimality comes from the new theory of economic welfare, originally proposed by Vilfredo Pareto, an Italian economist and sociologist in the early 1900s. Pareto, in researching possible equilibrium states in a nation’s economy, found out the optimal concept of Pareto, which takes its name from itself. When the Pareto optimal condition is achieved, people’s needs for useful goods and services are optimally satisfied. With this concept, the foundations of modern welfare theory were established [25]. The Pareto optimal has three basic elements: (i) optimality in production, (ii) optimality in consumption, and (iii) simultaneous optimality in production and consumption. To do so, in Pareto optimality, the distribution of goods and services among the people in the society and how the factors of production make the distribution of various goods and services are examined [26]. Multi-objective optimization algorithms have been developed by adapting the concept of Pareto optimality to metaheuristic algorithms. Thereby, a solution in the population can be the best, the worst, and the same as the other solutions according to the objective values. Here, the best solution means a solution that is not the worst with respect to any of the objectives and is better than the others in at least one objective. The optimal solution is the best optimal solution among the local optimum solutions in the search space, that is, the global optimum. Such an optimal solution is called

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as a Pareto-optimal solution and the set of all such optimal trade-off solutions is also called as the Pareto-optimal set [27–29]. Generally, the aim of multi-objective metaheuristic algorithms is to determine the set of trade-off surface, that is, non-dominated solution set. This set is particularly referred to as the Pareto-optimal set or other known set of non-dominated or noninferior solutions set as described above. The rest of these solutions are known as dominated solutions. Any of the non-dominated solutions can be considered as solution to the problem. If a solution is selected, problem information and data about some of the factors associated with the problem are needed to be known. If a solution needs to be preferred, knowledge of the problem and a number of factors associated with the problem are required to be known. Therefore, a solution chosen by the decision-maker may not be suitable for another decision-maker or in a different situation. This is why it is important to have knowledge about the problem in order to evaluate Pareto-optimal solutions in multi-objective optimization problems [30]. Taking into account the entire objective functions, the set of all dominated solutions is called the Pareto-optimal set. In this context, Pareto-optimal set is a solution of the problems arising in the field of trade-off in a problem with multi-objective functions. In a multi-objective optimization problem handled, Pareto-optimal set (P) and Pareto-front (PF) are defined as PF = {u = F(x) | x ∈ P}. Figure 1 presents the Pareto-front curve of an exemplary minimization problem for two objectives (f 1 and f 2 ). This Pareto-front defines the limit of solutions that can be achieved in a multi-objective optimization problem. The X E and X F solutions shown in this figure are on the Pareto-front curve and the other X A , X B , X C , X D , and X G solutions are located in the region of the dominated (feasible) solutions. For a multi-objective solution to be better, it means that no objective value of this solution is lower than the objective values of any other solutions. For example, solution X C is a better solution than solution X B . However, solution X F dominates both solutions X C and X B . The X E and X F solutions are equivalent because one of the objective values is optimal in one solution and the other is optimal in the other solution. Since there are no other dominant solutions on X E and X F within the design space, these solutions Fig. 1 Physical meaning of Pareto-front curve

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are included in the Pareto-optimal set. By navigating on the Pareto-front curve, it is possible to find solutions for different tolerance levels for different objectives.

3 Bat Algorithm 3.1 Bats Bats are very impressive animals that constitute about 1000 of the approximately 4500 mammal species living on earth. Even if they are in the dark by means of the very high-frequency sound waves they emit, which hit and return from the objects around them, they find their direction, escape from obstacles, hunt, and move. These properties of bats that resemble sonar systems are called echolocation [19, 20, 31]. Sounds that can be heard by bats cannot be heard by humans many times. Bats use these sonic characteristics, similar to the sonar system, to determine their orientation, hunting, and movement, even though they see. Thanks to these features, bats can move and hunt without hitting any obstacles. Bats make sounds with their nose and mouth, and the echo of sounds is perceived by ears that look like a dish. When bats fly to hunt, they scream about 200 per second [32]. Bats use the physical relationship between wavelength and velocity to perceive the reflected sounds from the objects (Eq. (1)). λ=

v f

(1)

3.2 Echolocation Features of Bats Most, if not all, species of bats use a kind of sonar called echolocation to determine the location of their prey, to communicate each other, to act in a manner that does not strike very thin objects by detecting its around them even in completely dark environments, and to distinguish different species of insects moving in dark environments [33, 34]. Echolocation using all living things (dolphins, whales, country mice, and some bird species), including bats, emit pulses at a certain frequency, often beyond the upper limits that the human ear can detect (about 20 kHz) and are called ultrasonic. Bats emit pulses with a wide range of frequencies from very high pitch (>200 kHz) to low pitch (~10 kHz), which are not included in the ultrasonic group because the human ear can easily detect these sounds [33]. Bats identify, categorize, and localize objects around them by analyzing the echoes caused by the pulses they emit, and hitting the objects around them [35] as described in the following.

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(1) Identification: Bats can use the echolocation pulse or the sniffing, hearing, and visual senses to determine the presence of the target or prey. (2) Categorizing: Bats can categorize their target prey through echoes generated by the echolocation pulse. The size, shape, texture, and so on of the targets are housed in echoes in a complexly coded state. Echo amplitude and frequency modulation provide information about the movement of the prey. (3) Localization: The echolocation reports not only the vertical and horizontal position but also the distance of a target to the bat. The time difference between the moment the pulse starts to be emitted by the bat and the moment when the echo first reaches to the bat reports the distance of the target prey to the bat.

3.3 Structure of Bat Algorithm Bat algorithm (BA) was developed by Yang in 2010 [19] based on the features of bat echolocation mentioned in the previous section and have been used for different optimization problems [36]. The brief pseudocode of the BA is depicted in Fig. 2. According to Fig. 2, the main structural rules of the BA can be summarized as follows [19–24, 36, 37]: (i)

All bats use echolocation to detect distance and to recognize food, prey, and obstacles. (ii) Bats randomly fly at vi speed, x i position, f min constant frequency, with wavelength λ, and loudness A0 to find their food or prey. They can both automatically f(x) (objective function), x = (x , ..., x ) (design variables) bat population x (i = 1, 2, ..., n) and v are initialized pulse frequency f at x are defined pulse rates r and the loudness A are initialized while ( iter < maxiter ) new solutions are generated by adjusting frequency, velocities and locations/solutions are updated if (rand > r ) solution among the best solutions is selected a local solution around the selected best solution is generated end if a new solution is generated by flying randomly if (rand < A & f(x ) < f(x )) the new solutions are accepted the r and A are increased end if the bats are ranked and the current best x is found end while T

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adjust the frequency of the pulses they emit, and adjust the pulse emission rate (r ∈ [0, 1]) relying on the proximity of their targets. (iii) The loudness varies from a large value A0 to a minimum value Amin .

3.3.1

Formation of Bat Population

The search space in the algorithm is considered to be a region with prey/food resources. The BA aims to find the best quality or optimum of these food sources by the bats. Since it is not known in which region the targeted food sources are located in search space, the bat population randomly distributes into the search space by N population number and d size. The bats scattered in search space calculate the fitness value of the prey/food sources of their location and the fitness value of each bat is kept in memory. xi, j = xmin j + ϕ(xmax j − xmin j )

(2)

In Eq. (2), when i = 1, 2, …, N and j = 1, 2, …, d, x i,j describes the jth size of the ith bat. xmin j and xmax j define the minimum and maximum values of jth size. ϕ represents a randomly distributed value in the range [0, 1].

3.3.2

Movements of Bats in the Search Space

After the random distribution of bats into the search space, their fitness values affect the next direction of movement and intensity of the entire population. The bats determine the velocity (vi ) they produce and their position in the next step, depending on the frequency (f i ) and the solution value (x * ) of the best individual in the population. f i = f min + β( f max − f min )

(3)

vit = vit−1 + f i (xit − x∗ )

(4)

xit = xit−1 + vit

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In Eqs. (3)–(5), f i denotes the frequency value of ith bat, f min and f max stand for minimum and maximum frequency values, respectively, β represents a number randomly distributed in [0, 1], x * indicates the solution values of the best individual within the population up to time t, vit specify the velocity of ith individual at time t.

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Local Search Capability of the BA

It is ensured that the bats in the population turn to higher quality resources in the vicinity of the existing prey/food resources. Thus, each bat chooses another solution from the population, depending on the quality of its fitness value, and revolves to the new resource around the solution it chooses. This increases the local search capability of the algorithm. Equation (6) is used for position update. xnew = xold + ε At

(6)

In Eq. (6), ε represents a randomly generated number in the range [−1, 1], x old presents the solution values of the individual selected based on the quality of the fitness value within the population through certain mechanisms (roulette wheel, rank selection, elitism, etc.). At denotes the average loudness value of all bats at time t.

3.3.4

Loudness and Pulse Emission Rate

The intensity of the loudness produced by the echolocation and the pulse emission rate of the bats need to be updated as iteration progresses and approaches the desired objective. As the bat approaches the prey, the loudness (A) decreases and the pulse emission rate (r) increases. The loudness can be selected as any value between Amin and Amax . Assuming Amin = 0, it means that a bat has found its prey and temporarily ceased to emit any sound. So, the loudness updating process takes place as in Eqs. (7) and (8). Ait+1 = α Ait

(7)

rit+1 = ri0 (1 − e−γ t )

(8)

The α and γ values in Eqs. (7) and (8) are the constant values. If 0 < α < 1 and γ > 0 the below-mentioned Eq. (9) is obtained. while t → ∞, Ait → 0 and rit → ri0

(9)

Here, the initial loudness (A) and pulse emission rate (r) values are determined randomly and are generally in the range of A ∈ [1, 2], r ∈ [0, 1].

4 Multi-objective Pareto-Based Bat Algorithm As stated above, the multi-objective design optimization problems are so complex than single-objective ones. Moreover, as it is explained in the previous sections, it is

2 Multi-objective Optimization of Engineering Design Problems …

27

more difficult to obtain solutions for multi-objective optimization problems as they carry the trade-off phenomenon in their essence. In addition, bat algorithm (BA) is modified to accommodate the multi-objectives by applying Pareto-front concept properly as stated in Fig. 3. The optimal designs of multi-disciplinary engineering problems considered in this chapter are resolved by using the multi-objective Pareto-based bat algorithm (pb-MOBA). Its corresponding steps are summarized as follows; • Step 1: First, the inputs about the problem data are read (the selected operative parameters for the pb-MOBA algorithm are read). • Step 2: The lower and upper limits of the parameters are chosen. Also, the algorithm settings such as pulse frequency, pulse rates, loudness, and the maximum number of iterations are determined. • Step 3: The initial bat population is generated randomly in the feasible range. Each bat indicates a promising optimal location. • Step 4: The fitness function is evaluated. In this step, the expected value of the objective functions can be calculated for each solution or bat. • Step 5: The better bat in the population is selected. • Step 6: Considering the Pareto-front multi-objective solution concept, the frequency, velocity, and locations of the bats are updated using Eqs. (3)–(5) • Step 7: The population is updated by adding new solutions. • Step 8: The stopping criterion is checked. That is, the stopping criterion is the maximum number of iterations to update the BA population. If it is satisfied then proceed to next step, otherwise return to Step 3. f(x) (objective function), x = (x , ..., x ) (design variables) the bat population x (i = 1, 2, ..., n) and initialized velocity v , pulse rate r and the loudness A are initialized while ( iter < maxiter ) new solutions x* are generated by adjusting frequency, velocities and locations/solutions are updated if (rand > r ) a solution among the best solutions is selected a local solution around the selected best solution is generated end if if (rand < A & f(x ) dominated f(xi)) the new solutions are accepted and x* is added to the population r and reduce A are increased else if (rand < A & f(x ) dominated f(x*)) nothing is done else if (rand < A & f(x ) & f(x*) are non-dominated solutions) new solutions are accepted and x* is added to the population the r and A are increased end if the bats are ranked and the current best x is found end while T

1

d

i

i

i

i

i

i

i

*

i

i

i

i

i

i

i

*

Fig. 3 Pseudocode of multi-objective Pareto-based BA

28

D. Ustun et al.

• Step 9: The best trade-off solutions are chosen, finally.

5 Design Examples In this chapter, three engineering design problems taken from multi-disciplinary engineering fields are resolved to demonstrate the effectiveness and practicability of the proposed pb-MOBA for the multi-objective design optimization problems. Namely, these problems are a four-bar truss design problem, a welded beam design problem, and a multi-layer radar absorber design problem. Throughout the multiobjective optimization procedure, the operative parameters of pb-MOBA are selected the same for all design examples as follows: population size N = 150, minimum and maximum frequencies f min = 0.0 and f max = 2.0, initial loudness Amax = 0.5, initial pulse emission rate r 0 = 0.5, and maximum number of iterations max iter = 10,000. Also, the Pareto population number identifies the amount of non-dominated solution values on Pareto-front curve, which is taken as 150. The above-mentioned values for parameters of proposed multi-objective Pareto-based bat algorithm (pb-MOBA) are considered in accordance with afore pronounced studies on the bat algorithm [19–24, 36, 37]. Virtually owing to the nature of the constitutions, the engineering design problems are constrained in real applications. In order to handle with these constraints, the simplest way is to convert those types of problems into the unconstrained ones by using the penalty function strategy. Here, Eq. (10) is implemented in the pb-MOBA to do the conversion when constraint handling is needed (e.g. in second design example) [38]. F p = F(1 + C)ξ

(10)

Here, F p denotes the penalized objective function. F represents the objective function of the design problem. C represents the sum up of the violations of the constraints. ζ is the coefficient of penalty, taken as 2.0 [39, 40] as computed in Eqs. (11) and (12). C=

ci =

⎧ ⎨ 0 if gk ≤ 0 ⎩

gk if gk > 0

cn 

ci

(11)

i=1

k = 1, 2, 3, . . . , cn

(12)

Here, gk is the kth constraint function and cn is the amount of constraints in the design optimization problem. It is worth mentioning that before using the design

2 Multi-objective Optimization of Engineering Design Problems …

29

algorithm whole of the constraints should be normalized and has to be less than or equal to zero.

5.1 Four-Bar Planar Truss Design Problem The first design example is selected as four-bar planar truss design problem in which it has four nodes and four structural members, as shown in Fig. 4 [41–43]. The objectives of this structural design problem are that minimizing the volume of the planar truss f 1 (x) and the vertical displacement (δ) of the node 2 f 2 (x), synchronously. The cross-sectional areas of the structural members are managed as design variables in this engineering optimization problem. The mathematical formation of the problem is submitted through Eqs. (13) and (14). f 1 (x) = (L)(2x1 +



2x2 +

√

x3 + x4 )

   √ √ f 2 (x) = F L E (2/x1 ) + (2 2/x2 ) − (2 2/x3 ) + (2/x4 )

(13) (14)

Here, the external nodal force F = 10 kN, the length of the fourth structural member L = 200 cm, normal stress of a structural element σ = 10 kN/cm2 , and the elasticity modulus E = 2 × 105 kN/cm2 . The lower and the upper bounds of the design variables x 1 to x 4 are introduced in Eqs. (15) and (16).     F 3F σ ≤ x1 , x4 ≤ σ

Fig. 4 Four-bar planar truss

(15)

30

D. Ustun et al.

Fig. 5 Pareto-front curve obtained via multi-objective bat algorithm for four-bar planar truss design problem

 √   F 2 3F ≤ x , x ≤ 2 3 σ σ

(16)

The Pareto-front curve of four-bar planar truss problem obtained via the pbMOBA is presented in Fig. 5. From this figure, it can be easily seen that for this multi-objective structural engineering design optimization problem, the Pareto-based bat algorithm generates evenly spread-out non-dominated solutions which constitute a smoothly converged Pareto-front curve. The pb-MOBA results in a Pareto-front curve between (0.04 (maxf 2 ), 1174.1972 (minf 1 )) and (0.0028 (minf 2 ), 2127.7382 (maxf 1 )). These edge values were obtained as (0.035, 1400) and (0.0035, 3000) using a swarm metaphor-based multi-objective design algorithm [44]. If these edge values of objective functions are compared, it is obvious that the proposed pb-MOBA finds out more optimal edge designs. Moreover, from Fig. 5, a selection shown with a star point among non-dominated optimal designs is carried out through points on Pareto-front curve obtained by the proposed pb-MOBA to specify the optimal trade-off objective function values. According to main aim of this problem which is defined as minimizing both objective function values, the optimal trade-off point within non-dominated design set which has to be the nearest one to utopic objective values point (0, 0) is obtained as (1555.6870, 0.0149), namely, f 2 = 0.0149 and f 1 = 1555.6870. In Table 1, the design variables belonging to the optimal trade-off objective functions are exhibited. Also, in the same table, design variable values are tabulated by which the afore-named edge objective function values are attained.

2 Multi-objective Optimization of Engineering Design Problems …

31

Table 1 Optimal designs for four-bar planar truss design problem obtained by pb-MOBA Design variable values Edge points objective function values

maxf 2 = 0.04

x1

x2

x3

x4

1.0

1.4142

1.4142

1.0

3.0

3.0

1.4142

1.0

1.5699

3.0

1.4142

1.0

minf 1 = 1174.1972 minf 2 = 0.0028 maxf 1 = 2127.7382

Optimal trade-off point objective function values

optimal f 2 = 0.0149 optimal f 1 = 1555.6870

5.2 Welded Steel Beam Design Problem A real-sized welded steel beam is preferred as second multi-objective engineering design optimization problem. The 3-D view and the structural dimensions of the beam are demonstrated on Fig. 6. The multi-objective design optimization of this beam is conducted to carry a certain concentrated load by concurrently satisfying minimum overall cost of fabrication and the least deflection under the tip (load applied) point. This multi-objective structural engineering design optimization problem has four design variables which are weld thickness h = x 1 , weld length l = x 2 , beam width t = x 3 , beam thickness b = x 4 [44–46]. The mathematical model of the problem including two objective functions and five design constraints (the shear and bending stresses in the beam, the end deflection of the beam, the buckling load on the bar, and a side constraint) are presented from Eq. (17) to Eq. (22). Minimize: f 1 (x) = 1.10471 x12 x2 + 0.04811 x3 x4 (14.0 + x2 ) f 2 (x) = δ(x) =

Fig. 6 Welded steel beam

4 P L3 2.1952 = E x33 x4 x4 x33

(17) (18)

32

D. Ustun et al.

subjected to g1 (x) = τ (x) − τmax ≤ 0

(19)

g2 (x) = σ (x) − σmax ≤ 0

(20)

g3 (x) = P − Pc (x) ≤ 0

(21)

g4 (x) = x1 − x4 ≤ 0

(22)

Also, the design variable ranges of the multi-objective welded steel beam problem are limited as in Eq. (23). 0.125 ≤ x1 ≤ 5.0, 0.1 ≤ x2 ≤ 10, 0.1 ≤ x3 ≤ 10, 0.125 ≤ x4 ≤ 5.0

(23)

where  τ (x) =

(τ  )2 +

2τ  τ  x2 6PL + (τ  )2 , σ (x) = , 2R x4 x32

 x2 MR , M=P L+ ,R = ,τ = τ = √ J 2 2 x1 x2 

P





x22 + 4 

 x1 + x3 2 , 2

  ( x32 x46 )  

  4.013 E √ x22 E x1 + x3 2 x3 36 + , Pc (x) = 1 − J = 2 x1 x2 2 12 2 2L 4 G L2 

in which, P = 6000 lb, L = 14 in, E = 30 × 106 psi, G = 12 × 106 psi τmax = 13600 psi, σmax = 30000 psi. Figure 7 depicts the Pareto-front curve constituted by non-dominated solutions via pb-MOBA improved within the scope of this chapter. From this figure, the extremum designs attained by pb-MOBA are (0.008945 (maxf 2 ), 2.562379 (minf 1 )) and (0.000675 (minf 2 ), 37.722234 (maxf 1 )). The edge values for minimum fabrication cost and related deflection (minf 1 , maxf 2 ) are pronounced as (0.0115, 2.5325) obtained using multi-objective water cycle algorithm (MOWCA), as (0.0131, 2.8959) yielded using Pareto -dominance-based orthogonal differential evolution for multiobjective optimization (pa-ODEMO), and as (0.0088, 3.0294) attained using nondominated sorting genetic algorithm the second (NSGA-II) [46]. It can be concluded from these extreme values that the proposed pb-MOBA obviously produces better designs for minf 1 than pa-ODEMO and NSGA-II. If related objective function value attained by pb-MOBA is compared with those obtained from MOWCA, it is obvious that pb-MOBA generates very slightly heavy objective function value for minf 1 than

2 Multi-objective Optimization of Engineering Design Problems …

33

Fig. 7 Pareto-front curve obtained via multi-objective bat algorithm for welded steel beam design problem

MOWCA. Similarly, the minimized deflection (minf 2 ) associated to cost of fabrication (maxf 1 ) obtained from MOWCA, pa-ODEMO, and NSGA-II are (0.000439, 37.9686), (0.00044, 36.6172), (0.000439, 37.4018). These results, also, ensure that the proposed pb-MOBA is a thriving method in determination of a great variety of Pareto-optimal non-dominated solutions. Likewise, as in the first design example, among the non-dominated optimal solutions located on the Pareto-front curve attained by the proposed pb-MOBA, an optimal solution set is chosen to identify the global optimum trade-off multi-objective design. This point is presented as a star point in Fig. 7. To do so, the solution point (0.002842, 9.074429) indicating f 1 and f 2 on the Pareto-front curve is decided as the nearest point to utopia point which is (0, 0). The design variables values, by which the so-called global optimum trade-off multi-objective design is attained, are h = x 1 = 0.125, l = x 2 = 9.9529, t = x 3 = 10.0, b = x 4 = 0.7725. Table 2 not only involves the extremum designs on Pareto-front curve but also includes the global optimum trade-off multi-objective design of the real-sized welded steel beam. Table 2 Optimal designs for welded steel beam design problem obtained by pb-MOBA Design variable values Edge points objective function values

maxf 2 = 0.008945

x1

x2

0.1250

6.6964

x3 9.9935

0.2459

x4

0.1264

9.9954

9.9989

3.2527

0.1250

9.9529

minf 1 = 2.562379 minf 2 = 0.000675 maxf 1 = 37.722234

Optimal trade-off point objective function values

optimal f 2 = 0.002842 optimal f 1 = 9.074429

10.0

0.7725

34

D. Ustun et al.

5.3 Multi-layer Radar Absorbing Material Design Low-observable technology has been the highly demanded property for aerospace platforms in recent years. By this technology, it is aimed at minimizing the electromagnetic (EM) waves reflected from the aerospace platforms for ensuring minimized EM wave reaches back to the radar systems [47]. The radar systems hence could not recognize the platform. It is possible to minimize EM reflection from the platforms by shielding the platform with radar absorbing material (RAM). The traditional singlelayer RAM could be designed by simple approximating and fitting approaches [48]. However, the design of RAM with as thin and low reflection as possible looks like unreasonable by using the traditional single-layer RAMs for today’s advanced systems. Nevertheless, it might be possible with multi-layer RAM (MRAM) having design variables such as layers’ thicknesses and dielectric materials used in each layer. The MRAM designs have received growing interest owing to having capability of thin, low reflection under broadband, and broad-angle waves with polarizations of both transverse electric (TE) and transverse magnetic (TM) [49–51]. The MRAM is composed of superimposed multi-layer material placed on the perfect electric conductor (PEC), each of which has different thicknesses and material types. Note that recursive reflections at inner interface herewith occur up to the PEC layer, giving rise to total reflection (TR) at the top interface. For global optimizing of an MRAM, two objectives of the TR coefficient and total thickness (TT) should be synchronously minimized to determine the design variables like the thickness and material of each layer together under broadband and broad-angle waves. EM modeling of an MRAM would have been straightforward for the normal incidence in which the angle and the polarizations of the incident wave had not been considered. In order to design highly realistic MRAMs, all possibilities of broadband and broad-angle waves have to be considered in the optimization scheme. It is worth noting that there is a trade-off between the two objectives while synchronously minimizing the TR and TT. This is obviously a computational expensive multi-objective engineering problem requiring a robust and versatile algorithm to overcome. The structure of the considered n-layer MRAM with interface reflections is shown in Fig. 8. Each layer’s thickness is di, complex permittivity/permeability is εi = εi  − jεi  /μi = μi  − jμi  , i indexes the recursive layers by starting from i = 0 layer which indicates the air medium. The propagating wave in the air with TE or TM polarizations arrives on Interface 1 with the incident angle of θ . The relationship between the incidence angle θ i−1 and transmitted waves incident angle θ i at each interface could be determined by the Snell’s law. An EM model, which recursively calculating the TR at each interface by taking into consideration the sub-reflections and the incident angle with the polarizations is constituted [52, 53]. In the EM model, the reflection coefficients at each interface are given as

2 Multi-objective Optimization of Engineering Design Problems …

35

Fig. 8 The MRAM structure

eΓi =

μi kz i−1 − μi−1 kz i μi kz i−1 + μi−1 kz i

(24a)

mΓi =

εi kz i−1 − εi−1 kz i εi kz i−1 + εi−1 kz i

(24b)

where e i and m i are, respectively, the interface reflection coefficients for TE and √ TM polarizations. kz i = cosθi ω μi εi is the complex wave number along the zdirection and ω = 2π f is the angular frequency, and f is the frequency of the incident wave. Therefore, the TR coefficient at any interface comprises its TR coefficients at sub-interfaces together with interface reflection (Eqs. (24a) and (24b)) and can be defined as follows eΓtot i = mΓtot i =

eΓi + (eΓtot i+1 )e−2 jkzi di 1 + eΓi (eΓtot i+1 )e−2 jkzi di

(25a)

mΓi + (mΓtot i+1 )e−2 jkzi di 1 + mΓi (mΓtot i+1 )e−2 jkzi di

(25b)

Here, eΓtot i and mΓtot i are, respectively, the TR for TE and TM polarizations. (Γtot i ) is the TR coefficient involving its interface reflection coefficient ( i ) and the TR (Γtot i+1 ) at sub-interfaces. This is continued recursively up to the TR

36

D. Ustun et al.

(eΓtot 1 or mΓtot 1 ) at interface 1 (air-Layer 1 interface), which is the TR of an n-layer MRAM based on incident wave frequency and angle and TE and TM polarizations. The TR coefficient which comprises the arithmetic mean of the polarizations of TE and TM at Interface 1 can be calculated as Γtot ( f, θ ) =

|eΓtot 1 ( f, θ )| + |mΓtot 1 ( f, θ )| 2

(26)

The mean oblique incident (MOI)-TR which is also the arithmetic mean of the TRs for the incident angle range θ l and θ u (the lower and upper bounds) at a frequency point can be calculated as  θu [Γtot ( f )]MOI =

θl

Γtot ( f, θ ) Nap

(27)

where [Γtot ( f )]MOI is the MOI-TR and N ap is number of angle points in the range of θl◦ and θu◦ at a particular angle step. Therefore, frequency-average MOI-TR (MOI-TRavg ) to be used as the first objective function (of 1 ) arises as in the following  fu [Γtot ( f )]MOI avg =

fl

[Γtot ( f )]MOI Nfp

(28)

Finally, the two objective functions (of 1 and of 2 ) concerning the MOI-TRavg and TT, respectively, constituted as minimize o f 1 = MOI − TRavg minimize o f 2 = TT =

n 

di

(29a) (29b)

1

N fp is the number of frequency points at the range of f l and f u which refer to the lower and upper bounds, respectively. The material database, thickness range of the layers, the incident wave’s frequency and incident angle range should be first appointed for a global optimization design of MRAM. The MOI-TRavg and TT are the two minimizing objective functions (Eqs. (29a) and (29b)). The design variables of MRAM are optimally determined in the ranges of lower and upper bounds: Frequency range f l –f u , incident wave angle range θ l –θ u , thickness range d l –d u . In this chapter, a broadband and broad-angle MRAM operating at 6–18 GHz is optimally designed by considering the incident wave angle range, which is taken as θl◦ –θu◦ = 0°–40° at 1° steps with the mean of TE and TM polarizations. In the design, d l – d u = 0.08 – 2 mm and the MOI-TRavg is computed at 0.2 GHz steps between the frequency bounds. N fp related to the frequency band of the MRAM is 61 and Nap is 41 for the designed MRAM. The material types are optimally selected from an artificially defined material database [54] via multi-objective Pareto-based

2 Multi-objective Optimization of Engineering Design Problems …

37

bat algorithm (pb-MOBA), including 16 pairs of relative complex permittivity and permeability. The database is mostly preferred material list in the literature, since they are frequency-depended and most realistic materials (Table 3). Figure 9 illustrates the Pareto-curve, which contains the non-dominated solutions, constituted by the pb-MOBA. The global optimum design shown by a red star is selected from the non-dominated solutions in the sub-figure. While it is being selected, it is considered to be closed to the origin, as well as the MOI-TR versus frequency plots are observed. In order to examine the globally optimized MRAM, Table 4 contains the TR and TT in terms of the normal incidence and MOI together with their maximum, Table 3 Predefined dispersive material database used in the design of the MRAM [54] Lossless dielectric materials (μ = 1, μ = 0) Mat. #

ε

1

10

2

50

Lossy magnetic materials (ε = 15, ε = 0) μ ( f ) =

μ (1 GHz) fα

· · · μ ( f ) =

μ (1 GHz) fβ

Mat. #

μ (1 GHz)

α

μ (1 GHz)

β

3

5

0.974

10

0.961

4

3

1.000

15

0.957

5

7

1.000

12

1.000

Lossy dielectric materials (μ = 1, μ = 0) ε ( f ) =

ε (1 GHz) fα

· · · ε ( f ) =

ε (1 GHz) fα

Mat. #

ε (1 GHz)

α

ε (1 GHz)

β

6

5

0.861

8

0.569

7

8

0.778

10

0.682

8

10

0.778

6

0.861

Relaxation-type magnetic materials (ε = 15, ε = 0) μ ( f ) = Mat. #

μm f m2 f 2 + f m2

· · · μ ( f ) = μm

μm f m f f 2 + f m2

f and f m in GHz fm

9

35

0.8

10

35

0.5

11

30

1.0

12

18

0.5

13

20

1.5

14

30

2.5

15

30

2.0

16

25

3.5

38

D. Ustun et al.

Fig. 9 Pareto-front curve obtained via pb-MOBA for the MRAM design problem (The MOI-TR plots for the global optimal design at the angle range between 0° and 40°)

Table 4 An elaborate view on the optimally designed MRAM at 6–18 GHz

Layer #

Material number

Thickness

1

14

0.08

2

16

0.08

3

16

0.08

4

16

0.1596

5

8

0.7657

Total thickness (mm)

1.1653

Total reflection (dB)

Maximum level

Minimum level

Average# Incidence

Normal (0°)

−11.29

−47.00

−20.92 Mean oblique incidence (2.28)

−11.22

−32.78

−19.36

minimum, and average values. MOI-TR is computed TR by averaging for (0°:1°:40°) steps by 1° with mean of |TE|&|TM| (Eq. (27)). The average reflection (Eq. (28)) is computed by averaging MOI-TR for (f l :0.2: f u ) GHz. The MRAM has very thin thickness of 1.1653 mm, though it has five layers. The frequency-average TR for normal incidence and MOI are −20.92 dB and −19.36 dB, respectively. The reason of such a better result is averaging objective functions (Eqs. (29a) and (29b)) regarding the TR and TT employed in the multi-objective of the MRAM.

2 Multi-objective Optimization of Engineering Design Problems …

39

The TR variations at various incident angles such as normal (0°), 20°, and 40° with TE and TM polarizations are revealed in Fig. 10. Note that the TR at normal incidence for TE and TM polarizations is the same as is expected. It is clearly seen that the globally optimized MRAM has outstanding absorbing performance. The TRs at normal incidence are the lowest among all variations. It can be hence inferred that the absorption decreases as the incident angle is increased, and an optimization scheme considering only normal incidence is not sufficient for a global optimization design. A broad incident angle range should be considered in the multi-objective scheme for global optimization of the MRAM designs with ensuring the trade-off for as close to real applications as possible. Eventually, the results imply that not only the TR but also the TT of an MRAM should be optimized for achieving globally optimized designs. Fig. 10 The TR plots at normal (0°), 20° and 40° incident angles for the globally optimized design. a TE polarization, b TM polarization

40

D. Ustun et al.

Table 5 An expatiated scheme for the optimal trade-off points of whole engineering design problems Design problem

Four-bar truss

Welded beam

Multi-layer radar absorber

Optimal trade-off points

optimal f 1 = 1555.6870 (volume)

optimal f 1 = 9.074429 (overall fabrication cost)

optimal f 1 = −19.36 (total reflection)

optimal f 2 = 0.0149 (vertical displacement)

optimal f 2 = 0.002842 (deflection at the tip)

optimal f 2 = 1.1653 (total thickness)

In order to demonstrate the improvements achieved by the pb-MOBA through obtained final optimal designs for engineering problems selected from multidisciplinary engineering fields as design examples of this chapter, namely a four-bar truss design problem, a welded beam design problem, and a multi-layer radar absorber design problem. The objective function values of the optimal trade-off points among non-dominated optimal designs are totally tabulated in Table 5. These solutions are chosen as close as to the utopia points of the Pareto-front curves from Pareto-optimal solution sets to identify the optimal trade-off objective function values as shown in Figs. 5, 7, and 9, for each design example, respectively.

6 Conclusions In this chapter, for solving complex and difficult multi-objective engineering design optimization problems, a Pareto-based bat algorithm (pb-MOBA) is presented. The fundamental conception of the proposed pb-MOBA stimulates the echolocation characteristics of bats to be used for preying, flying in the dark, and determining the positions of objects. For testing the capability of the proposed pb-MOBA, three complex multi-disciplinary multi-objective engineering design optimization problems are employed. These problems are a four-bar planar truss design, a real-sized welded steel beam design, and a multi-layer radar absorbing material design problem. The algorithm contains a constraint handling strategy for multi-objective problems with discrete design variables without any limitations on the amount of design variables, constraints, and objectives functions. Furthermore, the proposed pb-MOBA does not need any extra gradient information and/or data. Even though the supremacy of the bat algorithm to obtain single-objective optimization problems was ensured previously, the algorithmic performance capability of which is validated through obtained optimal designs for the selected engineering design problems in terms of Pareto-front curves yielded by the proposed pb-MOBA. The algorithm uses a Paretooptimal strategy to procure the trade-off designs through non-dominated solutions. This strategy is efficient to find edge (extremum) points of the Pareto-front curve

2 Multi-objective Optimization of Engineering Design Problems …

41

while retaining a logical scatter throughout the curve. The obtained Pareto-front curves with respect to convergence and coverage in non-dominated Pareto-optimal solutions demonstrate that the pb-MOBA has enough quality and quantity for solving real multi-objective engineering design optimization problems. Also, the obtained optimal designs are compared with the previously reported ones to prove the effectiveness and productivity of pb-MOBA. Besides, global optimal trade-off solution selections are offered for whole design examples to specify the convergence capability of proposed pb-MOBA to the utopia point. The optimum designs attained in this chapter expose that the proposed pb-MOBA has a skillful approach to produce an optimal Pareto-front curve and supply distinguished non-dominated multi-objective designs for complicated multi-disciplinary engineering optimization problems.

References 1. Rao SS, Sundararaju K, Prakash BG, Balakrishna C (1992) Multiobjective fuzzy optimization techniques for engineering design. Comput Struct 42(1):37–44 2. Deb K (2011) Multi-objective optimization using evolutionary algorithms. Wiley Ltd., England 3. Deb K (2001) Genetic algorithms for optimization. KanGAL report: 2001002 4. Kochenberger GA, Glover F (2003) Handbook of metaheuristics. Kluwer Academic Publishers 5. Yang XS (2010) Engineering optimization; an introduction with metaheuristic applications. Wiley Inc, Hoboken, New Jersey 6. Dreo J, Petrowski A, Siarry P, Taillard E (2006) Metaheuristics for hard optimization. Springer, Berlin, Heidelberg 7. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceedings of the world congress on nature and biologically inspired computing, Coimbatore, India 8. Carbas S, Saka MP (2012) Optimum topology design of various geometrically nonlinear latticed domes using improved harmony search method. Struct Multidiscip Optim 45(3):377–399 9. Carbas S (2017) Optimum structural design of spatial steel frames via biogeography-based optimization. Neural Comput Appl 28(6):1525–1539 10. Carbas S, Dogan E, Erdal F, Saka MP (2011) Comparison of metaheuristic search techniques in finding solution of optimization problems. In: Proceedings of the second international symposium on computing in science & engineering, Izmir, Turkey, pp 712–719 11. Hasancebi O, Carbas S (2011) Ant colony search method in practical structural optimization. Int J Optim Civ Eng 1(1):73–90 12. Carbas S, Saka MP (2013) Efficiency of improved harmony search algorithm for solving engineering optimization problems. Int J Optim Civ Eng 3(1):99–114 13. Carbas S (2015) Artificial bee colony based optimum design of reticulated domes to LRFDAISC. In: Proceedings of twenty seventh the IIER international conference, St. Petersburg, Russia 14. Aydogdu I, Carbas S, Paksoy A (2018) Investigation the effect of greedy selection strategies on the performance of the tree seed algorithm. In: Akgul M, Yilmaz I, Ipek A (eds) International conference on mathematical studies and applications, Karaman, Turkey, pp 67–75 15. Uray E, Carbas S, Erkan IH, Tan O (2019) Parametric investigation for discrete optimal design of a cantilever retaining wall. Chall J Struct Mech 5(3):108–120 16. Dey N, Ashour AS, Bhattacharyya S (eds) (2020) Applied nature-inspired computing: algorithms and case studies. Springer tracts in nature-inspired computing. Springer, Singapore 17. Dey N (ed) (2017) Advancements in applied metaheuristic computing. IGI Global 18. Dey N (ed) (2020) Applications of firefly algorithm and its variants. Springer tracts in natureinspired computing. Springer, Singapore

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19. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010), vol 284, pp 65–74 20. Yang X-S (2011) Bat algorithm for multi-objective optimisation. Int J Bio-Inspir Comput 3:267–274 21. Hasancebi O, Carbas S (2014) Bat inspired algorithm for discrete size optimization of steel frames. Adv Eng Soft 67:173–185 22. Hasancebi O, Teke T, Pekcan O (2013) A bat-inspired algorithm for structural optimization. Comput Struct 128:77–90 23. Satapathy SC, Raja NSM, Rajinikanth V, Ashour AS, Dey N (2018) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29(12):1285–1307 24. Rajinikanth V, Satapathy SC, Dey N, Fernandes SL, Manic KS (2019) Skin melanoma assessment using Kapur’s entropy and level set—a study with bat algorithm. In: Satapathy S, Bhateja V, Das S (eds) Smart intelligent computing and applications. Smart innovation, systems and technologies, vol 104. Springer, Singapore 25. Mock WBT (2011) Pareto Optimality. In: Chatterjee DK (ed) Encyclopedia of global justice. Springer, Dordrecht 26. Mas-Colell A, Whinston MD, Green JR (1995) Equilibrium and its basic welfare properties, Chapter 16. In: Microeconomic theory, Oxford University Press 27. Dias AHF, de Vasconcelos JA (2002) Multiobjective genetic algorithms applied to solved optimization problems, II. IEEE Trans Magn 38(2):1133–1136 28. Osyczka A (2002) Evolutionary algorithms for single and multicriteria design optimization. Physica Verlag, New York 29. Deb K (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197 30. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley-interscience series in systems and optimization. Chichester 31. Yang X-S, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483 32. Alp H (2009) Properties of bats and controlling methods for bats. J Veter Fac Dicle Univ 2(4):57–63 33. Fenton MB (2004) Bat natural history and echolocation. In: Brigham RM, Elisabeth KVK, Gareth J, Stuart P, Herman AL (eds) Bat echolocation research tools, techniques and analysis (2-6). Bat Conservation International, Austin, TX, USA, p 167 34. Hagen E (2009) ASU-Ask a biologist. http://askabiologist.asu.edu/echolocation. Accessed 09 Mar 2020 35. Schnitzler HU, Kalko EKV (2001) Echolocation by insect-eating bats. Bio Sci 51(7):557–569 36. Yang X-S (2013) Bat algorithm: literature review and applications. Int J Bio-Inspir Comput 5(3):141–149 37. Hasancebi O, Carbas S (2013) Optimum design of steel space frames via bat inspired algorithm. In: Proceedings of tenth world congress on structural and multidisciplinary optimization. Orlando, Florida, USA 38. Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech 191:1245–1287 39. Hasancebi O, Carbas S, Dogan E, Erdal F, Saka MP (2009) Performance evaluation of metaheuristic techniques in the optimum design of real size pin jointed structures. Comput Struct 87(5–6):284–302 40. Hasancebi O, Carbas S, Dogan E, Erdal F, Saka MP (2010) Comparison of non-deterministic search techniques in the optimum design of real size steel frames. Comput Struct 88(17– 18):1033–1048 41. Stadler W, Dauer J (1992) Multicriteria optimization in engineering: a tutorial and survey. American Institute of Aeronautics and Astronautics, pp 209–249 42. Cheng FY, Li XS (1999) Generalized method for multiobjective engineering optimization. Eng Optim 31:641–661

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43. Coello CAC, Pulido GT (2005) Multiobjective structural optimization using a microgenetic algorithm. Struct Multidiscip Optim 30(5):388–390 44. Ray T, Liew KM (2002) A swarm metaphor for multiobjective design optimization. Eng Optim 34(2):141–153 45. Gong W, Cai Z, Zhu L (2009) An efficient multiobjective differential evolution algorithm for engineering design. Struct Multidisc Optim 38:137–157 46. Sadollah A, Eskandar H, Kim JH (2015) Water cycle algorithm for solving constrained multiobjective optimization problems. Appl Soft Comput 27:279–298 47. Vinoy KJ, Jha RM (1996) Radar absorbing materials: from theory to design and characterization. Kluwer Academic Publishers, Springer 48. Fante RL, McCormack MT (1988) Reflection properties of the Salis-bury screen. IEEE Trans Antennas Propag 36(10):1443–1454 49. Goudos SK, Sahalos JN (2006) Microwave absorber optimal design using multi-objective particle swarm optimization. Microw Opt Technol Lett 48(8):1553–1558 50. Roy S et al (2015) Particle swarm optimization for optimal design of broad-band multilayer microwave absorber for wide angle of incidence. Prog Electromagn Res 62:121–135 51. Ranjan P, Arvind Choubey A, Mahto SM (2018) A novel approach for optimal design of multilayer wideband microwave absorber using wind driven optimization technique. AEU-Int J Electron C 83:81–87 52. Toktas A, Ustun D, Tekbas M (2019) Multi-objective design of multi-layer radar absorber using surrogate-based optimization. IEEE Trans Microw Theory Tech 67(8):3318–3329 53. Chew WC (1995) Waves and fields in inhomogeneous media. IEEE Press 54. Michielssen E et al (1993) Design of lightweight, broad-band microwave absorbers using genetic algorithms. IEEE Trans Microw Theory Tech 41(6):1024–1031

Chapter 3

A Study on the Bat Algorithm Technique to Evaluate the Skin Melanoma Images Nilanjan Dey, V. Rajinikanth, Hong Lin, and Fuqian Shi

1 Introduction The recent statement of World Health Organization (WHO) confirmed that the skin melanoma (SM) is one of the threatening syndromes in humans and approximately 132,000 SM incidences are documented worldwide each year [1]. Further, its happening pace is more in humans, whose skin is habitually exposed to the ultraviolet rays. The recent report also confirms that the SM occurs more in a particular ethnic group compared to the ethnic group with brown/dark skin [2–4]. Recently, a considerable number of safety measures have been suggested to reduce the rate of SM [5–10]. Even though the safety measures are followed, the occurrence of SM gradually raised. Premature screening and the management is the solitary technique to decrease the casualty pace [11]. If the SM is detected in its premature stage, then a probable N. Dey Department of Information Technology, Techno India College of Technology, Kolkata 700156, West Bengal, India e-mail: [email protected] V. Rajinikanth (B) Department of Electronics and Instrumentation Engineering, St. Josephs College of Engineering, Chennai 600119, Tamil Nadu, India e-mail: [email protected] H. Lin Department of Computer Science and Engineering Technology, University of Houston-Downtown, Houston, TX 77002-1001, USA e-mail: [email protected] F. Shi College of Information and Engineering, Wenzhou Medical University, Wenzhou 325035, China e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 N. Dey and V. Rajinikanth (eds.), Applications of Bat Algorithm and its Variants, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-15-5097-3_3

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treatment can be executed to manage the syndrome evolution. The analysis of SM engages in: (i) a visual verification by a dermatologist and (ii) assessment of the apprehensive fragment with a dermoscopy. The untreated SM may increase the threat and also allow the spreading of cancerous cells to other organs through the blood flow and therefore, it should be identified in its early phase. Owing to its significance, a number of SM inspection practices are proposed and executed to investigate the SM sections from the clinical grade and the benchmark skin melanoma image (SMI) [12–20]. Earlier works confirmed that computerized estimation is commonly executed because of its easiness and improved accuracy. The most common computerized techniques are: (i) semi-automated practice and (ii) automated practice. Implementation of the above techniques can be selected based on the visibility of the skin infection and availabilities of artifacts. Usually, SMIs are linked with the artifacts, such as hair fragment, medical-gel used during capturing SMI and other related issues. When the artifact level is high, it is advisable to utilize the semi-automated approach than automated evaluation. The clinical level diagnosis of the SMI is performed with a visual check along with the ABCD or ABCDE rule [12, 21, 22]. Implementation of these rules with a dermatologist is quite time-consuming and hence, the recent approaches developed a possible computerized method for these rules [11, 23]. Recently, a number of methods are proposed and executed to examine a class of signals and images [24–28]. The earlier methods confirm that image-based techniques coupled with recent algorithms offered better results [29, 30]. The proposed study aims to implement a semi-automated SM evaluation procedure by integrating the prominent imaging procedures like multi-threshold and segmentation. In the multi-thresholding task, the optimal threshold level, which enhances the infected region of SMI, is identified with the assistance of bat algorithm (BA) [31, 32]. Earlier studies confirmed that the Kapur’s entropy threshold (KET) offers better enhancement compared to other techniques [33]. Hence, this work implemented BA + KET to enhance the SMI and the enhanced region is then extracted with the distance-regularized level-set (DRLS) segmentation [34, 35]. The proposed technique is tested on the PH2 SMI [36] database and the performance of the proposed technique is then verified with a comparative study on the existing ground-truth (GT) picture. The performance of the proposed practice is verified by computing the essential image performance metrics (IPM) and the outcome of this work verifies that the implemented work offers well on SMI images, with and without the artifacts. This technique is primarily implemented on the gray-scale and the RGB-scale pictures and in both cases, the attained IPM are better. In the literature, a considerable number of heuristic methods exist; among them, BA emerged as one of the thriving techniques to resolve a class of engineering optimization tasks. Further, earlier works also confirm the accessibility of various BA techniques [37–39]. The proposed work aims to evaluate the performance of the BA, used in image thresholding tasks. Hence, this work considers the BA with varied operators, such as Levy-Flight (LF), Brownian-Walk (BW) and Ikeda-Map (IM). The BA is then used to pre-process the SMI using KET.

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In this study, the initial execution is carried with the LF-driven BA and the results attained are better. Further, the performance of the LF is then compared against the existing search operators, like BW and IM. The overall result of the proposed research confirms that the results attained with all the search operators are approximately similar and the LF operator takes very less CPU runtime compared to BW and IM. The other part of the study is organized as follows: Section 2 outlines the related methods, Sections 3 and 4 discuss about the formulation of the research problem and its solutions correspondingly. Section 5 elaborates the argument on attained results and the future direction, and the conclusion of this work is presented in Sect. 6.

2 Related Methods SM emerged as one of the major causes of death in humans and the happening rate is progressively increasing due to various causes [1]. Early identification is one of the proven procedures to cure SM with a possible treatment procedure. According to its harshness, the SM is classified as nevus and lentigo [16]. In the existing works, various research works are implemented to examine the lentigo class images, due to its availability. The existing datasets, such as PH2 [36], DermIS, DermQuest [40] and ISIC [41] are widely used in the literature to test the performance of the automated and semi-automated evaluation tools. All these images are associated with a less amount of the nevus class and large number of lentigo class pictures. Hence, in most of the earlier works, lentigo SMI is considered for evaluation. In the literature, segmentation approaches, machine-learning technique (MLT) and deep-learning technique (DLT) are already implemented to examine the SM attained from the datasets and clinics. The earlier machine learning and deep learning techniques implemented using ISIC dataset can be accessed from [41]. The segmentation approaches implemented on the DermIS, DermQuest and PH2 datasets can be accessed from [36, 40]. From the above works, it can be noted that, a considerable number of assessment procedures are existing to evaluate the SM with a class of methods. Further, the segmentation and evaluation of the SM section from the SMI is also discussed by most of the researchers. This research aims to assess the RGB scale image from its gray-scale version. Further, the essential need is to attain better evaluation outcome in the grayscale version with a reduced complexity. These works confirm that the SM evaluation further requires an approach which works well on the SM images with or without the artifacts.

3 Problem Formulation In clinics, the harshness of SM is generally evaluated by examining the SMI by an experienced dermatologist, who may analyze the abnormal section with or without

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ABCD rule. The examination of SM section also needs various preliminary preparation works and some time it may need the assistance of computerized technique to speed up the diagnosis process. The outcome of the computerized technique will help the dermatologist to speed up the diagnosis. In the literature, notable SMI examination procedures are available to forecast the skin infection rate. Every method has its own merits and demerits. The proposed work aims to develop and implement a semi-automated computerized tool to examine the SMI with better accuracy. This work implements BA + KET followed by DRLS segmentation to extract and evaluate the SM section. The implementation of the proposed technique is depicted in Fig. 1. The handling of SMI is discussed in this division, which involves: (i) threshold with bat algorithm and Kapur’s entropy and (ii) segmentation with DRLS, and (iii) verification and validation. Fig. 1 Implemented evaluation technique

Pre-processing of SMI with BA+KET

DRLS segmentation to mine SM section

Mined SM section

Ground-Truth

Computation of IPM and development of confusion matrix

Validation and Recommendation of proposed system

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3.1 SMI Dataset In the literature, the availability of SMI database is very limited and the proposed work considered the PH2 database for examination [36]. The PH2 database includes 200 numbers of RGB-scale SM images with dimensions 765 × 572 pixels. Every image is associated with a ground-truth (GT) picture offered by an expert. The existing SMI are of clinical grade available with and without the artifact. During the assessment task, the essential melanoma segment is to be extracted with a suitable technique for further evaluation. After extracting this section, the ABCD rule can be implemented to compute the metrics, such as asymmetry, border, color and diameter. Based on these values, the severity of the SM section is confirmed.

3.2 Processing The initial processing is achieved with a multi-threshold, which segregates the SMI into background, normal skin and melanoma. This work is achieved with bat algorithm and Kapur’s entropy (BA + KE). The earlier similar work on BA + KE can be found in [5]. The role of BA is to randomly adjust the threshold till the image is enhanced to a considerable level.

3.2.1

Bat Algorithm

Bat algorithm (BA) is one of the successful swarm techniques proposed by Yang [31, 32]. This algorithm works based on the mathematical expression of bat’s hunting and flying strategy. BA has three different arithmetical equations for (i) velocity, (ii) position and (iii) frequency updating, and it is depicted in the following equations:   Vi(t+1) = Vi(t) + Pi(t) − G B · Fi

(1)

Pi(t+1) = Pi(t) + Vi(t+1)

(2)

Fi = FM + (FX − FM ) · ψ

(3)

where V = velocity, P = position, (t) and (t + 1) presents the initial and final values, GB = global best, F = frequency function, F M = minimal frequency, F X = maximal frequency and ψ = random number of value [0, 1]. In BA, every bat is allowed to identify the optimal solution based on the given problem as depicted in Fig. 2. Initially, all the bats are randomly initiated inside the search space and the bat position will be continuously adjusted based on optimal solutions. This process will help to attain the best result during the search operation.

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Fig. 2 Optimization search in BA with chosen agents

This algorithm will modify the position of each bat based on the outcome attained after every iteration, and this process will be stopped only when the cost function of the optimization search is maximized [8]. The search speed and the optimization accuracy of the BA depend mainly on the search operator implemented to enhance its performance. In the proposed work, the BA with various search operators, such as Levy-Flight (LF), Brownian-Walk (BW) and Ikeda-Map (IM) were considered and the outcome of this study confirmed that BA with IM proposed by Satapathy et al. [42] offered better result on the gray-scale edition of the SMI. Hence, this work considered BA with IM to recognize the most favorable threshold.

3.2.2

Kapur’s Entropy

Entropy-assisted image evaluation technique is considered to examine the biomedical images because of its superiority [13, 14]. Kapur’s entropy (KE) is one of the widely implemented image enhancement techniques due to its proven results [33]. The considered BA is to discover the finest thresholds for the picture by maximizing the Kapur’s entropy (KE). The maximized KE can be represented as: Jmax = Z kapur (T h) =

n  j=1

T jC

(4)

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IM-BA driven with IM

Kapur’s entropy

Maximized entropy

SMI for postprocessing

Fig. 3 IM-BA based KE search to find optimal threshold

3.2.3

BA + KE Implementation

In this work, the Ikeda Map-based BA (IM-BA) discussed by Satapathy et al. (2018) is adopted to find the thresholds [42]. Various phases involved in BA_KE are depicted in Fig. 3. The main role of BA is to vary the threshold value of the test image to find the maximized J max . When the KE is maximized, then the BA search stops and the threshold image is then transferred to the next section called the segmentation. The need for this procedure is to improve the visibility of the infected skin region my dilating other normal skin sections and the artifact. Similar skin enhancement procedures are already implemented on a class of SM cases and the thresholding helped to achieve a better outcome during the disease examination. In the proposed work, BA + KE technique is implemented on smooth as well as SM image with the artifact such as the hair. The need for this research work is to prove that the thresholding will help to dilate/partially remove the artifact to reduce the complexity during the SM evaluation task. Further, this research aims to confirm that the thresholding and segmentation works together will help to achieve better accuracy during the SM evaluation. The proposed work is experimentally investigated on the benchmark PH2 database existing in [36]. This dataset is available along with the ground-truth (GT), which helps to compute the accuracy based on a relative analysis with the extracted melanoma section with a chosen segmentation method.

3.3 DRLS Segmentation The chief use of segmentation is to extort the asymmetrical section from the threshold image. This work implemented the distance-regularized level-set (DRLS) proposed by Li et al. (2010) [43].

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This work is based on the energy minimization procedure and it is expressed as: 

e (φ) =

 ε(|∇φ|)d X

Ω

(5)

where ε = energy density value with ε = [0, α] → . In DRLS, an adoptable arc is endorsed to distinguish all the feasible pixels connected to the uneven division existing in SMI. After identifying all the probable pixel groups, it will extract the piece which is within the converged curvature for the assessment exercise.

3.4 Evaluation and Validation The performance appraisal and justification process is a necessary step to substantiate the working of image assessment process. In this, an evaluation is executed among the tumor and the GTI and the essential performance values are then computed. Based on these values, the eminence of the proposed tool is confirmed. In this work, the following performance values are used [44–48]: TPR = Sensitivity = SE =

TP TP + FN

TNrate = Specificity = SP =

TN TN + FP

(6) (7)

FNrate =

FN FN + TP

(8)

FPrate =

FP FP + TN

(9)

 Jaccard Index = JI = IGT ∩ IT IGT ∪ IT

(10)

 Dice = DC = 2(IGT ∩ IT ) |IGT | ∪ |IT |

(11)

Accuracy = AC =

TP + TN TP + TN + FP + FN

(12)

TP TP + FP

(13)

2TP 2TP + FN + FP

(14)

Precision = PR = F1Score = F1S =

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where I GT = GT, I T = threshold, ∪ is the union procedure and ∩ is the intersection function. TP, TN, FP and FN indicate the true-positive, true-negative, false-positive and false-negative, correspondingly.

4 Problem Solution In this work, the SMIs of the PH2 database are considered for the evaluation. This dataset consists of the standard and artifact-associated lentigo images (Fig. 4a, c) along with the associated GT images (Fig. 4b, c). All the images are in RGB form and it can be assessed in its original case or in gray-scale version. The RGB version

Fig. 4 Sample test images of PH2 database. a Image without artifact, c image with artifact, b and d ground-truth

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of the picture is quite complex and requires more computational time. Hence, in the proposed work, the gray-scale version is considered for examination. The sample test images of standard and artifact class along with its GT are depicted in Fig. 4. These images are in RGB form and evaluation will be a tedious task due to its complex histogram pattern. Hence, in this work, the gray-scale version of the test image is considered to minimize the evaluation complexity. The converted grayscale version of the SMI pictures is then considered to test the performance of the proposed technique. Initially, the SMI evaluation is implemented on the smooth image with an assigned threshold of three, and the related outcomes are recorded as in Fig. 5. Figure 5a, b depicts the trial picture and the GT, Fig. 5c, d shows the thresholded and inverted images, Fig. 5e depicts the initial box of DRLS, Fig. 5f, g depicts the converged DRLS and extracted skin-melanoma segment. In order to evaluate the performance of the proposed technique, Fig. 5g is compared against Fig. 5b and the essential IPMs are computed. Based on these values, a confusion matrix is then constructed as in Fig. 6 and from this table, it is confirmed that the developed disease examination system works well on the SMI considered in this work. Other related measures are depicted in Table 1. This table shows the values of IPM attained for a single image and the smooth SMI class database (mean value). This verifies the superiority of the proposed SMI assessment system by offering an overall accuracy of >96%. Similar technique is then implemented on the SMI with the hair-section. In literature, a complex evaluation technique is already used to reduce the impact of hair in the SMI. Earlier work also confirmed that thresholding will help to reduce the effect of hair. Hence, in this work, the proposed threshold is used to reduce the hair impact, which improves the diagnosis accuracy [49–51]. Initially, this system is tested on the image depicted in Fig. 7a. Figure 7b shows the GT and Fig. 7c, d presents the thresholded and its complemented versions. Figure 7e, f and g shows the initial DRLS, final DRLS and extracted melanoma, respectively. Later, Fig. 7b, g is compared and based on the attained parameters, the confusion matrix shown in Fig. 8 is constructed. The values in figure also confirm the performance of this tool on the SMI with artifact. Further, other IPMs for the single and the whole-image case are then computed and these values are presented in Table 2. This table confirms that the IPMs attained with the individual image (Fig. 7a) and the average value attained for SMI with artifact is better and the attained accuracy is >94%. This confirms that this tool works on the SMI with and without artifact.

5 Discussion and Future Scope The proposed experimental work confirmed that the BA + KE thresholding and DRLS segmentation approach worked well on the considered SMI. The outcome of these two image cases confirmed that this work offered an average accuracy >94%. Hence, this procedure can be considered to evaluate the SMI available from other benchmark datasets.

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Fig. 5 Results attained for the trial artifact less image. a Chosen test image, b GT, c outcome of BA + KET, d complement of threshold image, e initial DRLS, f converged DRLS, g mined SM section

Actual Class

Fig. 6 Confusion matrix for the chosen test picture

Extracted Class

TP=115148 FN=7827 P=TP+FN=12 2975

FP=5128

TPR=0.9364

TN= 309357

FNR=0.0636

N=FP+TN=314 485

TNR=0.9837

Total pixels=437460

FPR=0.0163

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Table 1 Performance values attained for smooth SM images Image

JI

DC

SE

SP

AC

PR

F1S

Single image

0.8989

0.9467

0.9364

0.9837

0.9704

0.9574

0.9467

Database (average)

0.9017

0.9362

0.9317

0.9784

0.9624

0.9372

0.9311

Fig. 7 Results attained for the trial image with artifact. a Chosen test image, b GT, c outcome of BA + KET, d complement of threshold image, e initial DRLS, f converged DRLS, g mined SM section

The future scope of this research work are as follows: (i) The thresholding performance of BA can be confirmed with a study by considering other heuristic methods. (ii) Similar procedure can be tested with other threshold approaches, like Otsu, Tsallis and Shannon. (iii) The robustness of the proposed tool can be evaluated on the

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Fig. 8 Confusion matrix for the chosen test picture Extracted Class

Actual Class TP=46398

FP=3478

TPR=0.8471

FN=8373

TN= 380815

FNR=0.1529

P=TP+FN=54771

N=FP+TN=384293

TNR=0.9909 FPR=0.0091

Total pixels=439064

Table 2 Performance values attained for SM images with artifact Image

JI

DC

SE

SP

AC

PR

F1S

Single image

0.7965

0.8868

0.8471

0.9909

0.9730

0.9303

0.8868

Database (average)

0.8466

0.8948

0.9012

0.9652

0.9447

0.9018

0.9141

SMI corrupted with the noise. (iv) A classifier is then implemented to classify these images into benign/acute disease class based on the ABCD rule evaluation and chosen image features.

6 Conclusion The proposed work aims to develop a system to examine SMI with and without artifact with better accuracy. The chosen SMIs are in RGB scale and to reduce the evaluation complexity, a gray-scale version of SMI is considered. Initially, the BA + KE is executed to pre-process the test picture for an assigned threshold of three. Later, the melanoma part of the thresholded image is mined using the DRLS. Finally, an assessment between the mined melanoma and the GT is executed and the essential IPMs are then computed and a confusion matrix is constructed to examine the performance. The results of the proposed method confirm that this work achieved an accuracy >94% on both the SMI cases.

References 1. https://www.who.int/uv/faq/skincancer/en/index1.html 2. Glaister J, Wong A, Clausi DA (2014) Segmentation of skin lesions from digital images using joint statistical texture distinctiveness. IEEE Trans Biomed Eng 61(4):1220–1230 3. Amelard R, Glaister J Wong A, Clausi DA (2015) High-level intuitive features (HLIFs) for intuitive skin lesion description. IEEE Trans Biomed Eng 62(3):820–831 4. Rajinikanth V, Raja NSM, Arunmozhi S (2019) ABCD rule implementation for the skin melanoma assessment—a study. In: IEEE international conference on system, computation,

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N. Dey et al. automation and networking (ICSCAN). IEEE, pp 1–4. https://doi.org/10.1109/icscan.2019. 8878860 Rajinikanth V, Satapathy SC, Dey N, Fernandes SL, Manic KS (2019) Skin melanoma assessment using Kapur’s entropy and level set—a study with bat algorithm. Smart Innov Syst Technol 104:193–202. https://doi.org/10.1007/978-981-13-1921-1_19 Dey N, Rajinikanth V, Ashour AS, Tavares JMRS (2018) Social group optimization supported segmentation and evaluation of skin melanoma images. Symmetry 10(2):51. https://doi.org/ 10.3390/sym10020051 Amelard R, Glaister J, Wong A, Clausi DA (2013) Melanoma decision support using lightingcorrected intuitive feature models. In: Computer vision techniques for the diagnosis of skin cancer. Series in bioengineering, pp 193–219 Kowsalya N et al (2018) Skin-melanoma evaluation with Tsallis’s thresholding and ChanVese approach. In: IEEE international conference on system, computation, automation and networking (ICSCA), pp 1–5. https://doi.org/10.1109/icscan.2018.8541178 Kuwahara H, Furukawa H, Kitamura K et al (2011) Sentinel lymph node detection in melanoma using real-time fluorescence navigation with indocyanine green. Skin Cancer 26:55–58 Niakosari F, Kahn HJ, McCready D et al (2008) Lymphatic invasion identified by monoclonal antibody D2-40, younger age, and ulceration: predictors of sentinel lymph node involvement in primary cutaneous melanoma. Arch Dermatol 144:462–467 Fernandes SL et al (2019) A reliable framework for accurate brain image examination and treatment planning based on early diagnosis support for clinicians. Neural Comput Appl 1–12. https://doi.org/10.1007/s00521-019-04369-5 Hueston JT (1970) lntegumentectomy for malignant melanoma of the limbs. Aust N Z J Surg 40:114–118 Jones RF, Dickinson WE (1972) Total integumentectomy of the leg for multiple in-transit metastases of melanoma. Am J Surg 123:588–590 Mali B, Miklavcic D, Campana LG et al (2013) Tumor size and effectiveness of electrochemotherapy. Radiol Oncol 47:32–41 Spratt DE, Gordon-Spratt EA, Wu S et al (2014) Efficacy of skin-directed therapy for cutaneous metastases from advanced cancer: a meta-analysis. J Clin Oncol: Off J Am Soc Clin Oncol 32:3144–3155 Rubin AI, Chen EH, Ratner DT (2005) Basal-cell carcinoma. N Engl J Med 353:226269 Hayashi T, Furukawa H, Oyama A et al (2012) Dominant lymph drainage in the facial region: evaluation of lymph nodes of facial melanoma patients. Int J Clin Oncol 17:330–335 Nguyen CL, McClay EF, Cole DJ et al (2001) Melanoma thickness and histology predict sentinel lymph node status. Am J Surg 181:8–11 Paek SC, Griffith KA, Johnson TM et al (2007) The impact of factors beyond Breslow depth on predicting sentinel lymph node positivity in melanoma. Cancer 109:100–108 Burmeister BH, Mark Smithers B, Burmeister E et al (2006) A prospective phase II study of adjuvant postoperative radiation therapy following nodal surgery in malignant melanoma— Trans Tasman Radiation Oncology Group (TROG) Study 96.06. Radiother Oncol 81:136–142 Kunz MW, Stolz W (2018) ABCD rule, Dermoscopedia Organization. https://dermoscopedia. org/ABCD_rule. Accessed 17 Jan 2018 Ma Z, Tavares JMRS (2014) Segmentation of skin lesions using level set method. In: Computational modeling of objects presented in images. Fundamentals, methods, and applications. Lecture notes in computer science, vol 8641. Springer, pp 228–233 Dey N et al (2019) Social-Group-Optimization based tumor evaluation tool for clinical brain MRI of Flair/diffusion-weighted modality. Biocybern Biomed Eng 39(3):843–856. https://doi. org/10.1016/j.bbe.2019.07.005 Pugalenthi R et al (2019) Evaluation and classification of the brain tumor MRI using machine learning technique. Control Eng Appl Inf 21(4):12–21 Satapathy SC, Rajinikanth V (2018) Jaya algorithm guided procedure to segment tumor from brain MRI. J Optim 2018:12. https://doi.org/10.1155/2018/3738049

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26. He T, Pamela MB, Shi F (2016) Curvature manipulation of the spectrum of a Valence–Arousalrelated fMRI dataset using a Gaussian-shaped fast fourier transform and its application to fuzzy KANSEI adjective modeling. Neurocomputing 174:1049–1059 27. Hore S, Chakroborty S, Ashour AS, Dey N, Ashour AS, Sifakipistolla D, Bhattacharya T, Bhadra Chaudhuri SR (2015) Finding contours of hippocampus brain cell using microscopic image analysis. J Adv Microsc Res 10(2):93–103 28. Rajinikanth V, Dey N, Kumar R, Panneerselvam J, Raja NSM (2019) Fetal head periphery extraction from ultrasound image using Jaya algorithm and Chan-Vese segmentation. Procedia Comput Sci 152:66–73. https://doi.org/10.1016/j.procs.2019.05.028 29. Acharya UR et al (2019) Automated detection of Alzheimer’s disease using brain MRI images—a study with various feature extraction techniques. J Med Syst 43(9):302. https:// doi.org/10.1007/s10916-019-1428-9 30. Jahmunah V et al (2019) Automated detection of schizophrenia using nonlinear signal processing methods. Artif Intell Med 100:101698. https://doi.org/10.1016/j.artmed.2019. 07.006 31. Yang XS (2011) Bat algorithm for multi-objective optimization. Int. J. Bio-Inspired Comput 3:267–274 32. Yang XS (2010) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press, United Kingdom 33. Raja NSM, Rajinikanth V, Fernandes SL, Satapathy SC (2017) Segmentation of breast thermal images using Kapur’s entropy and hidden Markov random field. J Med Imaging Health Inform 7(8):1825–1829 34. Roopini TI, Vasanthi M, Rajinikanth V, Rekha M, Sangeetha M (2018) Segmentation of tumor from brain MRI using fuzzy entropy and distance regularised level set. Lect Notes Electr Eng 490:297–304. https://doi.org/10.1007/978-981-10-8354-9_27 35. Rajinikanth V, Fernandes SL, Bhushan B, Sunder NR (2018) Segmentation and analysis of brain tumor using Tsallis entropy and regularised level set. Lect Notes Electr Eng 434:313–321 36. https://www.fc.up.pt/addi/ph2%20database.html 37. Jayabarathi T, Raghunathan T, Gandomi AH (2018) The bat algorithm, variants and some practical engineering applications: a review. In: Yang X-S (ed) Nature-inspired algorithms and applied optimization. SCI, vol 744. Springer, Cham, pp 313–330. https://doi.org/10.1007/9783-319-67669-2_14 38. Gandomi AH, Yang XS, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255 39. Gandomi AH, Yang XS (2014) Chaotic bat algorithm. J Comput Sci 5(2):224–232 40. http://vip.uwaterloo.ca/demos/skin-cancer-detection 41. https://challenge.kitware.com/#challenge/5aab46f156357d5e82b00fe5 42. Satapathy SC et al (2018) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29(12):1285–1307. https://doi.org/10.1007/s00521-016-2645-5 43. Li C, Xu C, Gui C, Fox MD (2010) Distance regularized level set evolution and its application to image segmentation. IEEE Trans Image Process 19(12):3243–3254 44. Rajinikanth V, Dey N, Satapathy SC, Ashour AS (2018) An approach to examine magnetic resonance angiography based on Tsallis entropy and deformable snake model. Future Gener Comput Syst 85:160–172 45. Revanth K et al (2018) Computational investigation of stroke lesion segmentation from Flair/DW modality MRI. In: Fourth international conference on biosignals, images and instrumentation (ICBSII). IEEE, pp 206–212. https://doi.org/10.1109/icbsii.2018.8524617 46. Rajinikanth V, Raja NSM, Kamalanand K (2017) Firefly algorithm assisted segmentation of tumor from brain MRI using Tsallis function and Markov random field. J Control Eng Appl Inform 19(3):97–106 47. Amin J, Sharif M, Yasmin M et al (2018) Big data analysis for brain tumor detection: deep convolutional neural networks. Future Gener Comput Syst 87:290–297 48. Fernandes SL, Rajinikanth V, Kadry S (2019) A hybrid framework to evaluate breast abnormality. IEEE Consum Electron Mag 8(5):31–36. https://doi.org/10.1109/MCE.2019. 2905488

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49. Dey N, Ashour AS, Bhattacharyya S (2019) Applied nature-inspired computing: algorithms and case studies. Springer tracts in nature-inspired computing 50. Dey N (ed) (2017) Advancements in applied metaheuristic computing. IGI Global 51. Dey N (2020) Applications of Firefly algorithm and its variants. Springer tracts in natureinspired computing

Chapter 4

Multi-thresholding with Kapur’s Entropy—A Study Using Bat Algorithm with Different Search Operators V. Rajinikanth, Nilanjan Dey, and S. Kavitha

1 Introduction Image processing technique (IPT) is extensively used in various domains to convert the raw and pixel-level data into useful information. Based on the requirement, the raw images are recorded using various methods and dimensions. In general, every digital image can be categorized into two classes, such as the gray and the RGB class. Based on the application, the image can be recorded in the form of gray/RGB with a varied pixel dimensions. Even though various IPTs are available, the thresholding and the segmentation procedures are widely implemented to extort the information from the raw picture [1–3]. The thresholding procedures are the pre-processing methods and it can be used to process the test images at initial stage. The segmentation is normally used as the post-processing method used to extort the section of notice from the raw or pre-processed image. The overall quality of the IPT depends mostly on the pre-processing approach and a wrongly chosen pre-processing methodology can degrade the overall quality V. Rajinikanth (B) Department of Electronics and Instrumentation Engineering, St. Josephs College of Engineering, Chennai 600119, Tamil Nadu, India e-mail: [email protected] N. Dey Department of Information Technology, Techno India College of Technology, Kolkata 700156, West Bengal, India e-mail: [email protected] S. Kavitha Department of Electronics and Instrumentation Engineering, Annamalai University, Annamalai Nagar, Chidambaram 608002, Tamil Nadu, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 N. Dey and V. Rajinikanth (eds.), Applications of Bat Algorithm and its Variants, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-15-5097-3_4

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of the IPT considered for a particular task [4–6]. To attain better result, it is essential to choose an appropriate thresholding methodology to enhance the raw image at the beginning. In the literature, there exist a number of threshold techniques, such as arbitrary technique, between-class variance and entropy-based procedure. Entropy-based technique already proved its competence in a variety of imagethresholded tasks, ranging from conventional image examination to the medical image assessment [5, 7–9]. From the literature, it can be noted that the real-time image processing procedures offered enhanced outcome when the entropy-based thresholds are implemented. The entropies, like Kapur, Tsallis, Renyi, Fuzzy and Shannon are widely considered to process the images available in gray/RGB form [10–19]. The proposed work considered the Kapur’s entropy (KE) for the study and the processing performance of KE is analyzed using a class of images ranging from the gray to RGB. During this evaluation, the threshold value is chosen from two to five (Th = 2, 3, 4 and 5) for each image and the outcome of this procedure is then compared against the raw test image. Manually identifying the bi-level threshold for a picture is easy for a gray-scale picture and the complexity will augment based on the increase in the threshold value. For higher thresholds, manual identification of finest threshold is quite difficult. Further, this difficulty will increase for the RGB class picture, due to its multiple histograms of R, G and B color bands [4, 20]. Hence, in recent years, heuristic techniques are widely implemented to identify finest threshold for the gray/RGBscale images irrespective of its dimensions [21–26]. This work aims to implement the bat algorithm (BA) and the KE thresholding procedure for a class of chosen gray/RGB-scale pictures. Further, this work is also aimed at in presenting a detailed relative assessment between five numbers of the BA available in the literature [27–33]. To maintain a fair evaluation, all the algorithms are assigned with similar algorithm constraints and a five-fold cross-validation is then implemented. Finally, the average of the quality parameters is considered to assess the performance of the chosen BA. In this work, the performance of the BA is separately evaluated on the gray/RGB-scale images. This work helps to identify the right BA for the thresholding process with the KE. Other sectors of this study are arranged as follows: Sect. 2 discuss about the former correlated works, Sects. 3 and 4 present the implementation of thresholding operation and its solutions likewise. Section 5 presents the argument on the result and the future investigation direction, and the conclusion of this work is presented in Sect. 6.

2 Related Earlier Works In the literature, a number of threshold methods are obtainable for gray/RGB-scale images of various dimensions. The normal procedure implemented in thresholding is processing the test picture with a chosen threshold and selected methodology. Owing

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to its practical importance, the threshold approaches are implemented in a class of medical image assessment procedures [34]. In most of the applications, entropybased procedures are normally considered. The entropy technique will enhance the abnormal section in the test picture. Kapur’s function is one of the entropy techniques normally considered by the researchers to pre-process the medical images. The earlier image-thresholding work for a class of images can be found in [13]. The task in this procedure is to enhance the considered test picture using a finest threshold. In the literature a plethora of research works exists, to learn and practice the thresholding operation, and this operation is recently adopted in various real-world applications [3–7].

3 Problem Formulation The main task considered in this study is to enhance the trial picture based on the given threshold. In the multi-thresholding task, the BA is allowed to arbitrarily alter the thresholds in the image, till the KE reaches a maximum value (Fig. 1).

Initial algorithm parameters

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3.1 Benchmark Image Database The conventional benchmark dataset available in the literature is very limited, and in this work the image databases [35–37] used in earlier research are considered for analysis. These images are available in various dimensions, and in the proposed work, the images with dimensions 512 × 512 × 1 and 512 × 512 × 3 are used for experimental evaluation. The computer algorithm, which works well on these images, will offer better performance on the real-time images of a chosen modality.

3.2 Multi-thresholding Image thresholding is normally used to enhance the chosen image (gray/RGB) by clustering the similar pixels based on the assigned threshold value. Earlier works on image processing provided the insight on the image processing task, and these works confirmed that Kapur’s thresholding is one of the proven procedures for realworld image evaluation [38]. Hence, the proposed research implemented the KE thresholding to enhance gray/RGB-scale pictures. Further, to reduce the complexity in the threshold selection operation, a bat algorithm (BA) is employed. The bat algorithm was proposed in 2010 by Yang to find optimal solution for numerical optimization problem and because of its merit, recently it was considered in various domains [30]. The operation of traditional BA was related with echolocation/bio-sonar personality of microbats and its mathematical representation is used as BA. The BA has the following representations: Velocity update = Vin+1 = Vit + [Pit − G best ]Fi

(1)

Location update = Pin+1 = Pin + Vnn+1

(2)

Frequency alteration = Fi = Fmin + (Fmax − Fmin )β

(3)

where β is a random value of range [0, 1]. Equation (3) controls Eqs. (1) and (2) and hence, the choice of the frequency value should be appropriate. The updated value for every bat is produced based on Pnew = Pold + ε An

(4)

where ε is a random value in the range [−1, 1] and A is the loudness constraint during the exploration.

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Optimal solution

Fig. 2 Conventional BA with three bats

The expression of the loudness variation can be represented as Ain+1 = α Ai (n)

(5)

where α is a variable with a value 0 < α < 1. The other values based on BA can be found in the literature [31, 32]. The conventional working of the BA is shown in Fig. 2. The objective of the BA is to identify the optimal solution for a given problem by exploring the search area. If a single bat identifies the optimal solution, then it will invite the other bats toward the solution. The probability of getting the global maxima in BA is better compared with other algorithms and hence it is one of the successful approaches and used in various optimization tasks [33]. In this work, the performance evaluation of BAs, such as traditional BA (BA1) [30], BA with Brownian operator (BA2) [39], BA with Ikeda Map search (BA3) [40], Binary BA (BA4) [41] and Chaotic BA (BA5) [33] are presented for image multi-thresholding problem. In order to implement the chosen problem, this work considered the Kapur’s entropy (KE) and the maximized KE is chosen as the objective value for the BA search. The essential information on KE is already presented in detail in [38] and the objective value considered in this work is depicted in Eq. (6). Maximization of KE can be represented as follows: Jmax = f kapur (T ) =

k 

H jC

(6)

j=1

For a chosen image, the entropy is independently computed according to the assigned threshold. In this work, BA is permitted to subjectively alter the threshold values, till J max is achieved. If J max for the chosen image is reached, the exploration task is terminated and the pre-processed image is displayed. In this work, the BA

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parameters are assigned as follows: number of agents = 30, search length = 3, iteration = 3000 and the stopping utility = J max .

3.3 Evaluation and Validation Normally, the performance of the implemented threshold task is confirmed by calculating the essential image quality parameters (IQPs) using a relative assessment between the original and threshold image. The IQP considered in the proposed work is depicted below for an image of dimension A × B for original (O) and threshold (T ) image: Mean Squared Error (MSE) =

A B  1  O j,k − T j,k AB j=1 k=1

Root MSE (RMSE) =

√ MSE

(8)

Picture Signal-to-Noise Ratio (PSNR) = 10 log Normalized Cross Correlation (NCC) =

(255)2 MSE

Correlation Length of image patch × Length of template

 A B Average Difference (AD) =

j=1

k=1

A

(O j,k − T j,k )

AB B

j=1

k=1

O j,k

j=1

k=1

T j,k

Structural Content (SC) =  A  B Normalized Absolute Error (NAE) =

A  B 

(7)

(O j,k − T j,k )

(9) (10)

(11)

(12)

(13)

j=1 k=1

The other related values of these IQPs can be found in the literature [21, 42–46].

4 Problem Solution This work implements a multi-threshold method for a class of images of dimension 512 × 512 pixels. The examination is implemented by the Matlab software and the proposed method is individually tested on all the considered images with a threshold value ranging from 2 to 5. This procedure is initially implemented with the traditional BA (BA1) and then similar task is extended with other BAs (BA2, BA3, BA4 and BA5) considered in this research.

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Later a comparison of threshold image and the original picture is executed to find the IQPs, and based on these values, the performance of this system is validated. Initially, the proposed method is tested on the benchmark gray-scale pictures shown in Fig. 3. This table presents the preferred trial images (Fig. 3a) along with its gray histogram (Fig. 3b). The histogram of this image is very complex and hence, identification of the finest thresholds is quite complex with manual techniques and hence this work implemented the BA + KE thresholding. Initially, the multi-thresholding is applied on Barbara image and similar procedure with BA1–BA5 is then executed for the other test images available in Fig. 3 and its outcomes are recorded for further assessment. Initially, traditional BA-based search helped to find the optimal thresholds for all the test images and its search convergence for Th = 2 is presented in Fig. 4. Figure 4e presents the convergence of BA1–BA5 and from this, it can be confirmed that the entire BAs helped to attain similar thresholds irrespective of the search process. Figure 4a depicts that J max = 13.27 for Barbara, while other figures gives J max for the test images, like 18.274, 22.7, 26.755 and 26.78, respectively, when the chosen threshold = 2. After completing the thresholding with BA + KE, its performance is then validated by computing the IQPs using a study between the original and threshold picture and the attained values of RMSE, PSNR, NCC, AD, SC and NAE are presented in Table 1. This table value confirms that the IQPs vary based on the value of Th and these values improve with increase in the thresholds (Fig. 5). Figure 6 depicts the RGB-scale test pictures considered in this work. Figure 6a presents the image and Fig. 6b presents the RGB thresholds. Identification of optimal threshold is quite complex in RGB-scale images due to its complex pixel distribution. Further, it is essential to identify optimal thresholds for every color spaces, like R, G and B. This work implemented the BA + KE to find the thresholds for a chosen value of 2–5 and the corresponding results are assessed. Initially, BA1 is implemented on these test images and then the other chosen BA is employed. The outcome of the threshing with BA1 + KE for various thresholds is presented in Fig. 7. Similar to the gray images, a comparison of original and threshold image is then executed and the attained values of IQPs are then computed as depicted in Table 2. The results attained with the BA1 are approximately equal to the results obtained with other BA considered in this research. In order to assess the performance of used BA, the average time computed using Matlab’s tic-toc command is used and these values are individually computed for gray and RGB images. The mean time for gray is depicted in Fig. 8 and for RGB it is shown in Fig. 9. These two figures confirm that the time required by BA1 (BA with Levy search) is superior compared to other enhanced versions of the BA variants. This research results confirms that all the BA variants presented similar outcome with varied algorithm convergence. These results also verify that BA1 is sufficient to identify the better threshold when the function is chosen as KE. Levy-flight (LF) is used in BA1 to enhance its search performance for the optimization process. Figure 10 depicts the sample Levy’s pattern and the BA1 uses this

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Fig. 3 Benchmark test images of dimension 512 × 512. a Image, b gray thresholds

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13.24 13.22 13.2 13.18 13.16 13.14

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(e) Hunter Fig. 4 Convergence of BA + Kapur’s search on the test images for Th = 2

pattern while searching the threshold. Along with the above-discussed images, five more images of Berkeley [37] dataset are also assessed and its sample result is shown in Fig. 11. The future scope of the proposed technique is as follows: (i) The performance of BA1 can be validated with other heuristic methods available in the literature to confirm its eminence and (ii) implementing the BA1 to find the optimal threshold using other functions, like Otsu, Tsallis, Fuzzy-entropy, Renyi and Shannon’s.

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Table 1 Image quality values attained for BA1 threshold image Image

Th

RMSE

PSNR

NCC

AD

SC

NAE

Barbara

2

69.7702

11.2574

0.5688

60.9040

2.3366

0.5188

3

48.0993

14.4880

0.7191

41.6451

1.7353

0.3548

4

35.2962

17.1763

0.7986

30.8752

1.4889

0.2630

5

28.0199

19.1815

0.8441

24.0935

1.3605

0.2052

2

53.2685

13.6014

0.7006

46.6003

1.8706

0.3423

3

38.5446

16.4115

0.7697

34.8885

1.6415

0.2563

4

35.5272

17.1196

0.7955

32.1908

1.5378

0.2365

Boat

Jet

Mandrill

Hunter

5

29.8426

18.6341

0.8251

27.0072

1.4449

0.1984

2

67.7400

11.5139

0.7201

58.0823

1.7404

0.3241

3

39.5171

16.1951

0.8171

35.1128

1.4709

0.1959

4

29.6215

18.6987

0.8604

26.7479

1.3396

0.1493

5

28.7349

18.9626

0.8662

25.7918

1.3219

0.1439

2

60.7329

12.4623

0.6228

52.9883

2.2454

0.4103

3

40.3401

16.0161

0.7557

35.4515

1.6679

0.2745

4

28.9741

18.8906

0.8199

25.2894

1.4592

0.1958

5

24.0536

20.5072

0.8498

20.7387

1.3680

0.1606

2

46.3087

14.8176

0.6011

36.8594

2.3302

0.4736

3

44.2835

15.2060

0.6170

35.6446

2.2650

0.4580

4

30.3059

18.5003

0.7482

24.5041

1.6847

0.3149

5

22.5553

21.0658

0.8200

18.3661

1.4412

0.2360

5 Conclusion This work aims to propose a methodology to solve a multi-thresholding problem applicable for gray/RGB-scale images using the KE. This work considered the threshold values from 2 to 5, and to discover the finest threshold, BA is considered. The role of BA is to randomly adjust the thresholds till the KE value (J max ) is maximized. This work separately implements this technique for both the gray and RGB-scale pictures. After finding the essential threshold for the selected picture, in order to validate the performance of BA + KE, a comparison is performed among the original and the threshold image to find the IQPs. Based on these values, the performance is confirmed. In this work, five different BA techniques are considered and the result confirmed that the average IQPs attained with all these BA methods are identical. Further, the Levy-based BA offered better convergence speed compared to other BA techniques considered in this work. From these results, it is established that the proposed system works well on a class of image cases and in future, it can be used to process the real-world images.

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Jet

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(b) Th=3

Fig. 5 Thresholding outcome with BA1

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Lena

Pixel level

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G

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Jet

Pixel level

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Threshold 3000

Mandrill

Pixel level

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Threshold 16000

Peppers

Pixel level

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Threshold

(a) Fig. 6 Sample trial pictures and RGB histogram

(b)

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Lena

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(b) Th=3

Fig. 7 Outcome of BA1 + KE for various thresholds

(c) Th=4

(d) Th=5

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Table 2 Results attained for BA1 approach Image

Th

RMSE

Lena

2

80.7215

Jet

Mandrill

Peppers

PSNR 9.9910

NCC

AD

SC

NAE

0.4177

76.3483

4.8997

0.6155

3

45.9351

14.8879

0.6817

43.0906

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0.7914

30.3219

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24.6249

20.3033

0.8397

22.7423

1.4013

0.1833

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46.3226

14.8150

0.7900

42.2882

1.5559

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Fig. 10 Conventional Levy-flight strategy

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Fig. 11 Segmented image, thresholds and search convergence with BA1 + KE

Appendix See Figs. 10 and 11.

References 1. Dey N et al (2019) Social-Group-Optimization based tumor evaluation tool for clinical brain MRI of Flair/diffusion-weighted modality. Biocybern Biomed Eng 39(3):843–856. https://doi. org/10.1016/j.bbe.2019.07.005 2. Hore S, Chakroborty S, Ashour AS, Dey N, Ashour AS, Sifakipistolla D, Bhattacharya T, Bhadra Chaudhuri SR (2015) Finding contours of hippocampus brain cell using microscopic image analysis. J Adv Microsc Res 10(2):93–103 3. Dey N, Rajinikanth V, Ashour AS, Tavares JMRS (2018) Social group optimization supported segmentation and evaluation of skin melanoma images. Symmetry 10(2):51. https://doi.org/ 10.3390/sym10020051 4. Dey N, Shi F, Rajinikanth V (2019) Leukocyte nuclei segmentation using entropy function and Chan-Vese approach. Inf Technol Intell Transp Syst 314:255–264. https://doi.org/10.3233/9781-61499-939-3-255 5. Raja NSM et al (2019) A study on segmentation of leukocyte image with Shannon’s entropy. Histopathol Image Anal Med Decis Mak 1–27. https://doi.org/10.4018/978-1-5225-6316-7. ch001 6. Rajinikanth V, Dey N, Kumar R, Panneerselvam J, Raja NSM (2019) Fetal head periphery extraction from ultrasound image using Jaya algorithm and Chan-Vese segmentation. Procedia Comput Sci 152:66–73. https://doi.org/10.1016/j.procs.2019.05.028 7. Rajinikanth V, Dey N, Kavallieratou E, Lin H (2020) Firefly algorithm-based Kapur’s thresholding and Hough transform to extract leukocyte section from hematological images. In: Applications of Firefly algorithm and its variants: case studies and new developments, pp 221–235. https://doi.org/10.1007/978-981-15-0306-1_10

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8. Raja NSM, Rajinikanth V, Fernandes SL, Satapathy SC (2017) Segmentation of breast thermal images using Kapur’s entropy and hidden Markov random field. J Med Imaging Health Inform 7(8):1825–1829. https://doi.org/10.1166/jmihi.2017.2267 9. Rajinikanth V, Dey N, Satapathy SC, Kamalanand K (2020) Inspection of crop-weed image database using Kapur’s entropy and spider monkey optimization. Adv Intell Syst Comput 1048:405–414. https://doi.org/10.1007/978-981-15-0035-0_32 10. Shriranjani D et al (2018) Kapur’s entropy and active contour-based segmentation and analysis of retinal optic disc. Lect Notes Electr Eng 490:287–295. https://doi.org/10.1007/978-981-108354-9_26 11. Roopini TI, Vasanthi M, Rajinikanth V, Rekha M, Sangeetha M (2018) Segmentation of tumor from brain MRI using fuzzy entropy and distance regularised level set. Lect Notes Electr Eng 490:297–304. https://doi.org/10.1007/978-981-10-8354-9_27 12. El Aziz MA, Ewees AA, Hassanien AE (2017) Whale optimization algorithm and moth-flame optimization for multilevel thresholding image segmentation. Expert Syst Appl 83:242–256 13. Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13:146–168. https://doi.org/10.1117/1.1631316 14. Dirami A, Hammouche K, Diaf M, Siarry P (2013) Fast multilevel thresholding for image segmentation through a multiphase level set method. Signal Process 93:139–153 15. Marciniak A, Kowal M, Filipczuk Pawełand Korbicz J (2014) Swarm intelligence algorithms for multi-level image thresholding. In: Intelligent systems in technical and medical diagnostics. Springer, pp 301–311 16. Elaziz MEA, Ewees AA, Oliva D et al (2017) A hybrid method of sine cosine algorithm and differential evolution for feature selection. In: International conference on neural information processing, pp 145–155 17. Ibrahim RA, Elaziz MA, Ewees AA et al (2018) Galaxy images classification using hybrid brain storm optimization with moth flame optimization. J Astron Telesc Instrum Syst 4:38001 18. Bhandari AK, Kumar A, Singh GK (2015) Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions. Expert Syst Appl 42:1573–1601 19. Brajevic I, Milan T (2014) Cuckoo search and Firefly algorithm applied to multilevel image thresholding. In: Cuckoo search and Firefly algorithm, pp 115–139 20. Rajinikanth V, Raja NSM, Satapathy SC, Dey N, Devadhas GG (2018) Thermogram assisted detection and analysis of ductal carcinoma in situ (DCIS). In: International conference on intelligent computing, instrumentation and control technologies (ICICICT). IEEE, pp 1641– 1646. https://doi.org/10.1109/icicict1.2017.8342817 21. Rajinikanth V, Couceiro MS (2015) Optimal multilevel image threshold selection using a novel objective function. Adv Intell Syst Comput 340:177–186 22. Rajinikanth V, Raja NSM, Satapathy SC, Fernandes SL (2017) Otsu’s multi-thresholding and active contour snake model to segment dermoscopy images. J Med Imaging Health Inform 7(8):1837–1840 23. Anitha P, Bindhiya S, Abinaya A, Satapathy SC, Dey N, Rajinikanth V (2017) RGB image multi-thresholding based on Kapur’s entropy—a study with heuristic algorithms. In: Second international conference on electrical, computer and communication technologies (ICECCT). IEEE, pp 1–6. https://doi.org/10.1109/icecct.2017.8117823 24. Ashour AS et al (2015) Computed tomography image enhancement using cuckoo search: a log transform based approach. J Signal Inf Process 6(3):244–257 25. Wang Y et al (2019) Morphological segmentation analysis and texture-based support vector machines classification on mice liver fibrosis microscopic images. Curr Bioinform 14(4):282– 294. https://doi.org/10.2174/1574893614666190304125221 26. Moraru L, Obreja CD, Dey, N, Ashour AS (2018) Dempster-Shafer fusion for effective retinal vessels’ diameter measurement. Soft Comput Based Med Image Anal 149–160 27. Rajinikanth V, Satapathy SC, Dey N, Fernandes SL, Manic KS (2019) Skin melanoma assessment using Kapur’s entropy and level set—a study with bat algorithm. Smart Innov Syst Technol 104:193–202. https://doi.org/10.1007/978-981-13-1921-1_19

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28. Rajinikanth V, Aashiha JP, Atchaya A (2014) Gray-level histogram based multilevel threshold selection with bat algorithm. Int J Comput Appl 93(16):1–8 29. Jayabarathi T, Raghunathan T, Gandomi AH (2018) The bat algorithm, variants and some practical engineering applications: a review. In: Yang X-S (ed) Nature-inspired algorithms and applied optimization. SCI, vol 744. Springer, Cham, pp 313–330. https://doi.org/10.1007/9783-319-67669-2_14 30. Yang XS (2010) A new metaheuristic bat-inspired algorithm. Nat Inspired Coop Strateg Optim (NICSO) 284:65–74 31. Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483 32. Gandomi AH, Yang XS, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255 33. Gandomi AH, Yang XS (2014) Chaotic bat algorithm. J Comput Sci 5(2):224–232 34. Fernandes SL et al (2019) A reliable framework for accurate brain image examination and treatment planning based on early diagnosis support for clinicians. Neural Comput Appl 1–12. https://doi.org/10.1007/s00521-019-04369-5 35. http://sipi.usc.edu/database/database.php?volume=misc 36. http://decsai.ugr.es/cvg/CG/base.htm 37. http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/BSDS300/html/dataset/ images.html 38. Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vis Graph Image Process 29:273–285 39. Preethi BJ, Sujitha RA, Rajinikanth V (2015) Otsu based multi-level image segmentation using Brownian bat algorithm. Int J Comput Appl 3:10–16 40. Satapathy SC et al (2018) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29(12):1285–1307. https://doi.org/10.1007/s00521-016-2645-5 41. Nakamura RYM et al (2012) BBA: a binary bat algorithm for feature selection. In: 25th SIBGRAPI conference on graphics, patterns and images. IEEE. https://doi.org/10.1109/sibgrapi. 2012.47 42. Abhinaya B, Raja NSM (2015) Solving multi-level image thresholding problem—an analysis with cuckoo search algorithm. Inf Syst Design Intell Appl Adv Intell Syst Comput 339:177–186 43. Rajinikanth V, Raja NSM, Latha K (2014) Optimal multilevel image thresholding: an analysis with PSO and BFO algorithms. Aust J Basic Appl Sci 8(9):443–454 44. Dey N, Ashour AS, Bhattacharyya S (2019) Applied nature-inspired computing: algorithms and case studies. Springer tracts in nature-inspired computing 45. Dey N (ed) (2017) Advancements in applied metaheuristic computing. IGI Global 46. Dey N (2020) Applications of Firefly algorithm and its variant. Springer tracts in nature-inspired computing

Chapter 5

Application of Bat-Inspired Computing Algorithm and Its Variants in Search of Near-Optimal Golomb Rulers for WDM Systems: A Comparative Study Shonak Bansal, Neena Gupta, and Arun K. Singh

1 Introduction Numerous nonlinear optical effects [1–8] occur in an optical wavelength division multiplexing (WDM) systems. The nonlinear effect exhibits itself in a distinctive way so as to degrade the performance of the system. Among the various optical effects, the crosstalk generated via the four-wave mixing (FWM) signals is the main nonlinear effect in optical WDM systems utilizing the uniformly spaced channel allocation schemes. FWM is a third-order noise effect where the different mixing products are produced by mixing signals of two or more frequencies (or wavelengths). For equally/uniformly spaced optical WDM channels, the produced FWM crosstalk signal products fall on other active channels of the band, resulting in an inter-channel crossover effect. If FWM crosstalk signals generation is prohibited at the channel frequencies, performance can be massively improved. The effectiveness of FWM signals depends on the spacing among different channels. By keeping the frequency separation different among the channel pair in an optical WDM system, the crosstalk produced due to FWM signals can be prohibited [1–8]. To overcome the FWM crosstalk signals in optical WDM systems, several unequal spaced channel allocation schemes have been suggested in Refs. [4, 9–14]. But these

S. Bansal (B) · N. Gupta · A. K. Singh Department of Electronics and Communication Engineering, Punjab Engineering College (Deemed to be University), Sector-12, Chandigarh, India e-mail: [email protected] N. Gupta e-mail: [email protected] A. K. Singh e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 N. Dey and V. Rajinikanth (eds.), Applications of Bat Algorithm and its Variants, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-15-5097-3_5

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schemes suffer from the shortcoming of large channel bandwidth requirement as compared with the uniformly spaced channel allocation schemes. This chapter presents an unequally spaced bandwidth-efficient channel allocation scheme, considering the idea of near-optimal Golomb ruler (OGR) sequences [1, 15–17] to minimize the FWM crosstalk signals in optical WDM systems. It has been shown that the generation of Golomb ruler sequences is a class of NPcomplete [18] problems. For large mark values, searching for Golomb rulers through exhaustive computer search [19, 20] is a difficult task. To deal with Golomb ruler problem, numerous approaches have been proposed in Refs. [19–23]. To date, no efficient approach to finding a ruler of minimum length is known. Nature-inspired optimization computing approaches such as Memetic approach [23], Tabu search (TS) [23], genetic algorithms (GAs) [24–27], biogeography-based optimization (BBO) [27, 28], hybrid evolutionary algorithms [29], big bang–big crunch (BB–BC) [30– 33], Firefly algorithms [31, 34], bat-inspired algorithm [35], Cuckoo search algorithms [36–38] and Flower pollination algorithms [38] are a good start for a nearOGR generating algorithm. Therefore, nature-inspired computing algorithms are the best way to deal with such a NP-complete problem. This chapter presents a comparative study of the bat-inspired computing algorithm and its hybrid variants in the search of either optimal or near-to-optimal Golomb rulers in a reasonable time. The performance of bat-inspired computing algorithms has been compared with the classical computing methods, namely, extended quadratic congruence (EQC) and search algorithm (SA) and nature-inspired computing algorithms, named, GAs and BB–BC computing algorithm to generate near-OGRs.

2 Optimal Golomb Rulers (OGRs) The perception behind Golomb rulers was first developed by Babcock [1], which was further described in detail by Golomb et al. [15]. The rulers offered by Babcock up to 8-marks are optimal rulers, while 9 and 10-marks are the near-optimal rulers [39, 40]. Golomb rulers are an ordered sequence of unequal numbers at positive integer locations such that the individual pairs of numbers from the sequence do not show the similar difference [41–43]. The numbers in the sequence are stated to as marks. The total number of marks on a Golomb ruler sequence is regarded as ruler size. The difference between the largest and smallest number represents the length of the ruler, that is, ruler length [15, 27]. A Golomb ruler sequence having the minimum length is termed to be as an optimal Golomb ruler. There can be many different OGRs for a given number of marks. On the other hand, a Golomb ruler sequence which estimates all integer distances from 0 to ruler length (RL) is considered as a perfect Golomb ruler sequence [18, 24, 27]. The RL for an n-mark/order perfect Golomb ruler sequence is approximated by [22]:

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n(n − 1)  i = 2 i=1 n−1

RL =

(1)

Figure 1a, b demonstrates an example of 4-mark OGR and a 6-mark non-OGR sequence with their respective differences. It is clear that Fig. 1a represents the unique 4-mark ruler that estimates all the integer distances from 0 to the ruler length 6 and hence designated as a perfect Golomb ruler. The sequence shown in Fig. 1b has the ruler length of 20. Furthermore, it is clear from the differences that the numbers 10, 14, 15, 16, 18 are missing, hence cannot be considered as a perfect Golomb ruler sequence. Golomb rulers find their possible role in many real-world applications such as radio frequency channel allocation, radio telescope, computer communication network, sensor placement in X-ray crystallography, pulse phase modulation, circuit layout, self-orthogonal codes, very large-scale integration (VLSI) architecture, geographical mapping, linear arrays, fitness landscape analysis, coding theory, antenna design in radar missions, planetary and earth sciences, NASA missions in astrophysics and sonar applications [1, 15, 22, 24, 39, 40, 44–50].

Fig. 1 Golomb ruler sequences with their respective differences from 0 to RL. a A 4-mark optimal Golomb ruler sequence. This is only the unique perfect ruler with RL = 6; b a 6-mark non–OGR and non-perfect sequence with RL = 20

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By implementing OGRs as a channel allocation scheme in optical WDM systems, it is possible to obtain the smallest number used for the optical WDM channel allocation problem. As the difference among any two numbers is different, the new FWM crosstalk frequency signals generated will not mix up with the one already assigned for the carrier channels.

3 Bat-Inspired Computing Algorithm and Its Variants Optimization of highly complex and nonlinear engineering design problems is very challenging. As conventional classical computing approaches are local search approaches that often miss the global optimality and cannot be used significantly for global optimization thereafter. Additionally, design solutions have to be low cost, robust, subject to uncertainty in parameters and tolerance for imprecision of available components and materials. Nature-inspired computing algorithms are now the better tool for optimizing complex problems. The guiding principle is to design an algorithm of computation that results into an adequate solution at the lowest cost by obtaining an approximate solution to an impossible or exact problem [32, 33, 38, 51, 52].

3.1 Bat-Inspired Computing Optimization Algorithm Yang [51–54] presented an optimization computing algorithm named bat-inspired metaheuristic optimization algorithm, which was based on the echolocation characteristics of microbats. In formulating the algorithm, Yang defines the following three ideal rules: • Bats use the echolocation characteristic to find the prey, any obstacle in their path and distance and also they know about the surroundings; • Bats fly at position x i with velocity vi , with a varying frequency range [f min , f max ] or a varying wavelength range [λmin , λmax ] and loudness A0 to search the prey. Bats automatically adjust the frequencies/wavelengths of their emitted pulses; • The loudness changes from a maximum stable (positive) value A0 to a minimum stable (positive) value Amin . For a bat i, its frequency f i , position x i , loudness Ai , velocity vi , and the emission pulse rate r i ∈ [0, 1] in a search space must be defined. The velocities vit and positions xit must be updated sequentially during the iteration t. The rules for updating the velocities and positions are approximated by Eqs. (2)–(4) [51, 53, 54]:   f i = f min + f max − f min rand

(2)

  vit = vit−1 + xit−1 −x∗ f i

(3)

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xit = xit−1 + vit−1

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(4)

where rand ∈ [0, 1] corresponds to a uniformly distributed random vector. x * denotes the current global best solution that is located after comparing all the solutions among all the bats. For each bat, a new solution is found locally by using random walk to modify the current best solution as given by Eq. (5) [55]: xnew = xbest + ε At

(5)

where xbest = x∗ , ε ∈ [−1, 1] corresponds to a random scaling factor and At represents the loudness. The loudness Ai and pulse emission rate r i are updated accordingly as iterations proceed as given by Eq. (6) and Eq. (7), respectively. t−1 Ait = α Ai

(6)

  rit = ri0 1 − e−γ t

(7)

where 0 < α < 1 and γ > 0 are constants. For easiness, in most of the simulations α = γ = 0.9 is preferred [53, 54].

3.2 Variants of Bat-Inspired Computing Optimization Algorithm The success of any nature-inspired computing algorithm lies in how quickly the algorithm explores new solutions and how efficiently exploits solutions to improve them. Though optimization algorithms in their simple form perform better in exploitation, there are still some difficulties in global exploration of the search space. If all solutions in the primary phase of computing algorithm are collected in a small part of the search space, then the algorithm cannot find the optimal solution and with high probability, it can get trapped in that sub-domain. To avoid such an issue, a large number of solutions can be considered for one problem. But it also leads to an increase in function calculations, computational time and cost. Hence there is a need by which exploration and exploitation can be enriched and computing algorithms can perform efficiently. To achieve this, fitness (i.e. cost)-based mutation scheme and Lévy-flight distribution (i.e. random walk) have been introduced in the simple bat-inspired computing algorithm. In variants of the bat algorithm, the mutation rate is estimated by means of a fitness value. For each solution x i , the mutation rate probability M R it at iteration t is estimated by Eq. 8 [38, 56]: M R it =

f it   Max f t

(8)

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  where f it corresponds to the fitness value of each solution, and Max f t represents the maximum fitness value in the population at iteration index t. The mutation equation [57, 58] is approximated as:  t−1    − xit−1 + pm xrt−1 − xrt−1 xit = xit−1 + pm xbest 1 2

(9)

where xit represents the population at iteration t, pm is mutation operator and lies t−1 = x∗t−1 represents the current global best solution at between 0.001 and 0.05. xbest iteration one less than current iteration index t, r 1 and r 2 are the two uniformly distributed random integer numbers between 1 and problem size. The values of r 1 and r 2 are kept separate from running index. The mutation scheme increases the probability of a better solution, but the higher mutation rate results in much higher exploration and causes problems with the improvement of the solutions. As the mutation operator pm decreases from 1.0 to 0.01, the optimization ability greatly increases, but as pm continues decreasing to 0.001, the optimization capacity decreases rapidly. A small value of pm is not able to sufficiently increase the diversity of solutions [27]. The distribution of Lévy-flight [38] is given by the Eq. 10:   λΓ (λ) sin πλ   2 (s  s0 > 0) L(λ) = π s 1+λ

(10)

where (λ) corresponds to the standard gamma for s > 0. In this work, λ = 1.5 is used. In practice, s0 must be positive and as small as 0.1 [38, 56]. By introducing these two schemes in the bat-inspired computing algorithm (BA), the perception of search space is modified. As a result, algorithm can detect new search locations by the mutation and random walk schemes. A fundamental advantage of using these two characteristics with the bat-inspired computing algorithm in this chapter is its capability to improve the solutions over time, which does not seem in the earlier-stated algorithms [23–29] to generate the near-OGR sequences. With the mutation (see Eqs. (8) and (9)) and Lévy-flights distribution (see Eq. (11)) schemes, along with the standard bat-computing algorithm, three other hybrid algorithms, namely, bat-inspired algorithm with mutation (BAM), Lévy-flight bat-inspired algorithm (LBA) and Lévy flight bat-inspired algorithm with mutation (LBAM) are discussed in this chapter. For LBA, the modified version of Eq. (5) is as follows: xnew = xbest + ε At ⊕ L(λ)

(11)

Based on the above discussions, the basic steps of bat-inspired computing algorithm and its hybrid variants are briefly presented as a general pseudo-code, as shown in Fig. 2. In Fig. 2, if the principle of Lévy-flights (lines 9 and 10) and mutation (lines 15–20) is not used, Fig. 2 represents the general pseudo-code for simple bat-inspired computing algorithm. If only the idea of mutation is not used in Fig. 2, it represents

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Fig. 2 The general pseudo-code for bat-inspired computing optimization algorithms

the pseudo-code for LBA, otherwise Fig. 2 shows the general pseudo-code for LBAM computing algorithm.

4 Problem Formulation To find a bandwidth-efficient scheme for an optical WDM system, two issues, generation and optimization, are studied. First, there is a need to generate Golomb ruler sequences desired as an unequally spaced channel allocation scheme in optical WDM systems. Secondly, these generated sequences are optimized via the bat-inspired computing algorithms, by minimizing both the R L and total occupied unequally spaced optical channel bandwidth T BWun . Thus the application of Golomb rulers as the

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unequally spaced channel allocation scheme is a two-objective optimization problem. If each individual element (IE) in non-negative integer location is a Golomb ruler, then the sum of all individual elements of the sequence forms T BWun . If n corresponds to the total number of channels and C S denotes the spacing among the channels in a Golomb ruler sequence, then the R L and T BWun are approximated by Eqs. 12 and 13, respectively. f1 = R L =

n−1 

(C S)i = I E(n) − I E(1) subject to

i=1

(C S)i = (C S) j and (I E)i = (I E) j f 2 = T BWun =

n 

(I E)i subject to (I E)i = (I E) j

(12) (13)

i=1

where i = j with i, j = 1, 2, . . . , n in Eqs. 12 and 13. The functions f 1 and f 2 are merged into a single objective function f to estimate the Pareto front as computed by Eq. 14. f = w1 f 1 + w2 f 2 with w1 + w2 = 1

(14)

1 2 , with w1 > 0 and w2 = u 1u+u , with w2 > 0. where w1 = u 1u+u 2 2 The lower bound on T BWun is given by Eq. 15 [9, 13]

 T BWun ≥ 1 +

n 2

 −1 (n − 1)C S S

(15)

where S corresponds to the smallest channel separation. The optimization of TBW un results in the optimized bandwidth expansion factor (BEF) as given by Eq. 16 [9, 13] BEF =

T BWun T BWeq

(16)

where T BWeq = (n − 1)C S represents the equally spaced total occupied channel bandwidth of an optical WDM system. The pseudo-code for generating near-OGRs via bat-inspired computing algorithms is summarized in Fig. 3. The core of the proposed bat-inspired computing algorithms is given in lines 17–29 that look for Golomb ruler sequences until an optimal or nearly-optimal solution is found for a number of iterations. In addition, the size of the generated population should be equal to the initial population size (Popsize) at the end of the iteration. Since there are many solutions, a substitution approach should be illustrated in Fig. 3 to extract the worst individuals. This means that the proposed bat-inspired computing algorithm preserves a fixed Popsize of

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Fig. 3 The pseudo–code for bat-inspired computing optimization algorithms to generate nearOGRs

rulers and performs a fixed number of iterations until an optimal or near-to-optimal solution is found.

5 Results and Discussion This section presents the performance of bat-inspired computing algorithms and their comparative studies to generate optimal Golomb ruler sequences with the best solutions, that is, known OGRs [15, 20, 22, 40, 59–62], two classical computing methods, namely EQC and SA [4, 13] and two nature-inspired computing algorithms, namely, GAs [27] and simple BB–BC [31, 32] computing algorithm, of generating

88 Table 1 Optimized simulated parameter values for all bat-inspired computing algorithms

S. Bansal et al. Parameter

Value

A0

0.8

r0

0.5

pm

0.01

unequal channel allocation scheme. All algorithms have been coded and verified utilizing the Matlab software to generate near-OGR sequences. To generate near-OGR sequences, the selected optimized simulation parameter values for all the bat-inspired computing algorithms are given in Table 1. As there are no concrete rules, choosing a reasonable parameter value of a nature-inspired computing algorithm is problem dependent. All the proposed algorithms generate 100 Pareto fronts points N. With these parameter values, each algorithm was executed 20 times until near-to-optimal solution was found. Although the algorithms generate the same Golomb ruler sequences, the difference lies in the maximum number of iterations, CPU time and bandwidth expansion factor that are discussed in the subsequent subsections. The increase in Popsize increases the diversity of possible solutions, thus exploring the search space. But this increase in Popsize will increase the computation time required to obtain the optimal (or near-optimal) solutions. The TS approach [23] generates 10- to 16-marks Golomb rulers with a Popsize of 190. The hybrid scheme described in [26] creates 11- to 23-marks Golomb rulers within the Popsize range of 20–2000. The hybrid evolutionary approaches [29] produce near-OGR sequences with a maximum Popsize of about 50. Near-OGRs generated via GAs and BBO [27] produce the maximum Popsize set to 30, whereas the BB–BC algorithm [31, 32] produces OGR sequences with a maximum Popsize of 10. For all the proposed batinspired computing algorithms for finding OGRs, the Popsize parameter has little effect. So here a Popsize of 10 was found suitable for all algorithms for generating OGRs. The selection of the best maximum iteration (Maxiter) value for any natureinspired optimization algorithm is always critical for a particular problem. Increasing the Maxiter parameter will increase the possibility of reaching optimal solutions and exploitation of the search space. This means, the chance of finding the correct search increases significantly. As the iterations increase, the ruler length and total occupied optical channel bandwidth tend to decrease. This means that the generated Golomb rulers reach their optimal (or near-optimal) values after a few iterations. This is the point where no further improvement is seen. The iterations have little effect for loworder marks. But for large-order marks value, the iterations have a significant effect on the total occupied optical channel bandwidth, that is, the channel bandwidth is optimized after a certain number of iterations. The TS approach described in Refs. [23, 26], generates Golomb rulers with maximum iterations of 10,000 and 30,000. The hybrid approach [26] generates Golomb rulers within maximum iterations of 100,000. The hybrid evolutionary approaches [29] find Golomb rulers within iterations of 10,000. The GAs and BBO approaches [27] generate near-to-optimal Golomb

5 Application of Bat Inspired Computing Algorithm …

89

rulers, the Maxiter parameter was set to 5000, whereas the BB–BC algorithm [32] had maximum iterations of 1000. In this chapter, all the proposed computing algorithms to generate either the optimal or near-to-optimal Golomb rulers get stabilized in about 1000 iterations. To generate the n-marks near-OGRs, the Maxiter value was set to number of mark n times 100 [32]. Maxiter = n × 100

(17)

5.1 Comparative Study of Bat-Inspired Computing Algorithms in Terms of the Length of the Ruler and Total Occupied Unequally Spaced Optical Channel Bandwidth Table 2 shows the ruler length and total occupied unequally spaced optical channel bandwidth by individual Golomb ruler sequences from the bat-inspired computing algorithms after 20 trials and their comparison with best solutions, EQC, SA, GAs and BB–BC. The EQC and SA approaches are restricted to prime powers only [4], so the ruler length and total occupied optical channel bandwidth are presented by a dashed line in Table 2. From Table 2, it is concluded that the results are impressive. It is first noted that all the bat-inspired computing algorithms generate the best ruler up to 17-marks. This means that the ruler length and the total occupied unequally spaced optical channel bandwidth up to 17-marks are similar to the best-known OGRs. The bat-inspired computing algorithm (BA) and its hybrid variants, that is, BAM and LBA, generate near-to-optimal rulers for the 18- to 20-marks. The hybrid computing algorithm LBAM generates the best rulers of up to 20-marks very well and efficiently in a reasonable time. This proves that LBAM has 100% success rate. Secondly, observe that for marks 5–9 the total occupied unequally spaced optical channel bandwidth is smaller than the best-known OGRs. The results in Table 2 conclude that bat-inspired computing algorithms to generate near-OGRs outperform other existing classical computing and nature-inspired computing algorithms in terms of the length of the ruler and the total occupied unequally spaced optical channel bandwidth.

5.2 Comparative Study of Bat-Inspired Computing Algorithms in Terms of Bandwidth Expansion Factor The bandwidth expansion factor (BEF) considers the expanded bandwidth with the usage of unequally spaced optical channel allocation for a given channel to that of equally/uniformly spaced channel allocation for the same channel. The BEF calculated for the various channels by the bat-inspired computing algorithms is listed in

3

6

11

17

25

34

4

5

6

7

8

RL

117

77 81 87 90 95

44 47 50 52

25 28

11

4

TBW un (Hz)

Known OGRs [15, 20, 22, 40, 59–62]

3

n

91

–

45

–

15

6

RL

378

–

140

–

28

10

TBW un (Hz)

49

–

20

–

15

6

RL

189

–

60

–

28

4

TBW un (Hz)

35 41 42 45 46

27 28 29 30 31 32

17 18 21

12 13

6 7

3

RL

121 126 128 129 131 133

73 78 79 80 83 86 95

42 44 45

23 25 29

11

4

TBW un (Hz)

GAs [27]

39 41 42

25 26 28 30

17 18

11 12

6 7

3

RL

113 118 119

73 74 77 81

42 44

23 25

11

4

(continued)

TBW un (Hz)

BB–BC [31, 32]

Other nature-inspired computing algorithms

EQC [4, 13]

SA [4, 13]

Classical computing methods

Table 2 Comparison of bat-inspired computing algorithms to channel allocation in optical WDM systems in terms of RL and TBW un for various channels n

90 S. Bansal et al.

44

55

72

85

106

127

10

11

12

13

14

RL

924

660

503

386 391

249

206

TBW un (Hz)

Known OGRs [15, 20, 22, 40, 59–62]

9

n

Table 2 (continued)

325

–

231

–

–

–

RL

2340

–

1441

–

–

–

TBW un (Hz)

286

–

132

–

–

–

RL

1820

–

682

–

–

–

TBW un (Hz)

206 228 230

203 241

123 128 137

94 96

75 76

52 56 59 61 63 65

RL

1172 1177 1285

1015 1048

532 581 660

395 456

283 287 301

192 193 196 203 225

TBW un (Hz)

GAs [27]

221

110 113

85 91

72 105

77

44 45 46 61

RL

1166

768 753

550 580 613

377 490 456

258

179 248 253 262

(continued)

TBW un (Hz)

BB–BC [31, 32]

Other nature-inspired computing algorithms

EQC [4, 13]

SA [4, 13]

Classical computing methods

5 Application of Bat Inspired Computing Algorithm … 91

199

216

246

283

17

18

19

20

TBW un (Hz)

2794

2225

1894

1661

1298

1047

703

–

561

–

–

–

RL

3

6 7

4

11

4 6 7

3

RL

3

BAM

RL

TBW un (Hz)

BA

7163

–

5203

–

–

–

TBW un (Hz)

11

4

TBW un (Hz)

703

–

493

–

–

–

RL

6460

–

5100

–

–

–

6 7

3

RL

LBA

TBW un (Hz)

4660 4826 4905 4941

3432 5067

2599 3079

2205

1985

1634 1653

11

4

691

584

427

369

316

267

RL

6

3

RL

LBAM

TBW un (Hz)

TBW un (Hz)

615 673 680 691

567 597

427 463

355

316

275 298

RL

GAs [27]

11

4

(continued)

TBW un (Hz)

4941

4101

3079

2201

1985

1322

TBW un (Hz)

BB–BC [31, 32]

Other nature-inspired computing algorithms

EQC [4, 13]

SA [4, 13]

Classical computing methods

Bat-inspired computing algorithms

177

16

n

151

RL

Known OGRs [15, 20, 22, 40, 59–62]

15

n

Table 2 (continued)

92 S. Bansal et al.

17 18

25 28

34 39

44

55

72

85

6

7

8

9

10

11

12

503

386

249

206

113 117

74 77 81 90

42 44

85

72

55

44 57

34 39

25 26 27

17 18

11 12 13

RL

23 25

TBW un (Hz)

RL

11 12 13

BAM

BA

Bat-inspired computing algorithms

5

n

Table 2 (continued)

503

386

249

183 206

113 117

73 77

42 44

23 24

TBW un (Hz)

85

72

55

44 58

34 39

25 27

17 18

11 12 13

RL

LBA

503

391

249

177 206

113 117

73 77

42 44 47 50

23 24 28

TBW un (Hz)

85

72

55

44 47

34 39

25 26 27

17 18

11 12 13

RL

LBAM

503

386 391

249

185 206

113 117

73 77

42 44 47 50

23 24 25

(continued)

TBW un (Hz)

5 Application of Bat Inspired Computing Algorithm … 93

127

151

177

199

427

467

578 615

14

15

16

17

18

19

20

4306 4660

3337

3079

1661

1298

1047

924

578

467

445

199

177

151

127

106

RL

TBW un (Hz)

660

RL

106

BAM

BA

Bat-inspired computing algorithms

13

n

Table 2 (continued)

TBW un (Hz)

4306

3337

2566

1661

1298

1047

924

660

578 593

475

362

199

177

151

127

106

RL

LBA TBW un (Hz)

4306 4859

3408

2912

1661

1298

1047

924

660

283

246

216

199

177

151

127

106

RL

LBAM TBW un (Hz)

2794

2225

1894

1661

1298

1047

924

660

94 S. Bansal et al.

5 Application of Bat Inspired Computing Algorithm …

95

Table 3. From Table 3 it is noted that the BEF gets increased with the number of channels for bat-inspired computing algorithms and is smaller than the other classical and nature-inspired computing algorithms. The estimated BEF value suggests that the hybrid algorithm LBAM requires a smaller bandwidth than other computing algorithms.

5.3 Comparative Study of Bat-Inspired Computing Algorithms in Terms of Computational CPU Time The Golomb ruler sequence generation and its optimization is a challenging problem. The generation of OGRs by exhaustive parallel search approach for higher order marks is computationally time-consuming, which can take many hours, months, even years to compute over a network of several thousand computers [20, 22, 40, 61–63]. The distributed OGR project [63] calculated years on multiple computers to prove optimality for 20- to 26-marks. This subsection is dedicated to reporting the average CPU time taken by the batinspired computing algorithm and its hybrid variants to generate optimal or nearOGRs and their comparative study with the computation time taken by existing approaches [20, 22, 24, 26, 27, 32, 40, 63]. Table 4 lists the average CPU time taken by the proposed algorithms to generate near-OGRs of up to 20-marks. Golomb ruler sequences generation for 5- to 13-marks via heuristic-based exhaustive search approach [24], the computation time ranged from 0.035 s to 6 weeks. OGRs generated with the exhaustive search approaches [20] for 14- and 16-marks took approximately one and hundred hours, respectively, whereas 17, 18 and 19marks OGRs reported in [22, 40], took about 1440, 8600 and 36200 CPU hours (~7 months), respectively, on Sun Sparc Classic workstation. On the other hand, the non-heuristic exhaustive search approach took around 12.57 min, 2.28 years, 2.07 × 104 years, 3.92 × 109 years, 1.61 × 1015 years and 9.36 × 1020 years for 10-, 12-, 14-, 16-, 18- and 20-marks, respectively [24]. In Ref. [26], it is mentioned that the CPU time in seconds taken by TS approach to search OGRs is about 0.1, 720, 960, 1913, 2516 for 5-, 10-, 11-, 12- and 13-marks, respectively. The 11- to 12-marks OGRs generated through hybrid GAs [26] took around 5–11 h. In near-OGR generated up to 20-marks by GAs and BBO [27], the maximum computation time was around 31 h (~1.3 days), while for BB-BC [32] it was about 28 h (~1.1 days). From Table 3, it is clear that for bat-inspired computing algorithms, the average CPU time varies from 0.0 s to 21 h for 3- and 20-mark rulers, respectively. By using the mutation and Lévy-flight schemes with the bat-inspired computing algorithm, the execution time for 20-mark ruler is reduced to ~19.5 h (i.e. ri then Optimize the given solutions Select from the given set of optimized solution, a locally acceptable solution One random solution to be generated end if if random < Ai and f (xi ) < f (x) then Where, x is the current best solution Accept this newly generated solution Increment ri and Decrement loudness Ai end if Rank bats in order of ri and rank the current best solution end while

4 Interval Type-2 Fuzzy C-Means Algorithm (IT2FCM) After the introduction of the Fuzzy Logic System, the modeling of uncertainty has become less ambiguous in the last decade. Fuzzy logic is an approach to computing based on degrees of truth rather than the usual true or false (1 or 0) Boolean logic on which the modern computer is based. Interval Type-2 Fuzzy Logic System (IT2FLS) [9] and Interval Type-1 Fuzzy Logic System (IT1FLS) work on the principles of the Fuzzy Logic System. IT2FSL is used over IT1FLS because it makes a superior forecast and assessment of unpredictability, which is a very important faction in the analysis of medical images. Let A be a fuzzy set for IT1FLTS with membership function A(x) which is closely related with universe of discourse X and gives a value between 0 and 1. X is an input image of m × n with x as each pixel on this input image. This fuzzy set A can be calculated by the equation: A = (x, A(x))|x X

(1)

The relationship between Fuzzy logic is framed using two significant responses: acceptable universe identification and membership function expose. There are infinite number of membership functions that can be used like trapezoidal, triangular,

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Gaussian, etc. This chapter makes use of the Type-1 Gaussian description as the membership function (Fig. 1). Let A¯ be a fuzzy set for IT2FLS having a membership function A¯ (x, u) where x X and u Jx ⊆ [0, 1]. A¯ can be derived from the equation: A¯ = (x, u) A¯ (x, u)|∀u ∈ Jx ⊆ [0, . . . , 1]

(2)

¯ The scope of A(x,u) is between 0 and 1 which can also be expressed as the equation given below which is an amalgam function of all admissible values of input x and u: 



x∈X u∈Jx

¯ A(x, u) Jx ⊆ [0, 1] (x, u)

(3)

¯ u) Here ‘x’ is the primary membership function defined by Jx ⊆ [0, 1] and A(x, is the secondary fuzzy set which makes use of x. So, the grade of type-2 membership function can range from values between 0 and 1. This can also result in the secondary membership function being associated with each of the primary membership functions. The secondary membership also helps in the phrasing of the primary membership function that lies between 0 and 1. We also use the concept of Footprint of Uncertainty (FOU) which is used to create a graph of type-2 fuzzy set more easily. It is the region bounded by the Upper Membership function (UMF) and Lower Membership Function (LMF). A larger FOU means the problem has a higher amount of uncertainty. The values of UHF(μA(x)) and LMF(μA(x)) can be calculated by the equations: μ A = μik = c j=1

= c j=1

μ A = μik = c j=1

= c j=1

1 (dik /d jk )

, 2/(m 1 −1)

1 (dik /d jk )2/(m 2 −1) 1 (dik /d jk )

(dik /d jk )2/(m 2 −1)

(4)

, otherwise

, 2/(m 1 −1)

1

c  di k 0, then Ait → 0

(7)

rit → 0 as, t → ∞

(8)

and

The flow chart for BA is shown in Fig. 1. Pseudocode of BA Set the bat population ( psi = 1, 2, . . . , n b ) and velocity Set frequency f qi at psi Set pulse rates ri and the loudness Ai While (t < maximum runs) Create new positions of bats by changing frequency, and Update velocities and positions using Eqs. (2) and (3) If (rand > r i ) Choose a new position from available best positions Build a neighbor position for the chosen new position End Create a new position for bat by random flight

8 Bat Algorithm with Applications to Signal, Speech …

Fig. 1 Simplified performance model of a critical access module

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If(rand < Ai & f ( psi ) < f ( ps∗ )) Take the new solutions Increment of ri and decrement of Ai End Rate the bats to know current best End

2 BA Applications to Signal Processing 2.1 FIR Filter Coefficients Optimization One of the common applications of meta-heuristic optimization algorithms [4–6] in the research area of signal processing is that the optimization of filter coefficients of the digital filters. Bat algorithm has been applied for the optimization of FIR filter coefficients [7]. In this work, authors utilized BA for the design of Generalized Fractional Order Differentiators (GFOD) and Generalized Fractional Hilbert Transformer (GFHT). The fitness function used in this implementation is the error between the frequency response and the desired response of the FIR filter. The least square error averaged over the total frequency range is the cost function considered, as given in the Eqs. (4) and (5). The formula for FIR filter is F(z) =

M−1 



f (n)z −n



(9)

n=0

π E 1 (ω) =

    Fc (ω) − F e− jω 2 dω

(10)

    Pd (ω) − F e− jω 2 dω

(11)

0

π E 2 (ω) = 0

Fc (ω) = |ω| p e

jsgn(ω) p 2

(12)

Pd (ω) = P(ω)e− jn 0 ω

(13)

P(ω) = e− j π/2 |ω| < π

(14)

Results show an improved performance over genetic algorithm and particle swarm optimization.

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137

2.2 Signal Recovery Bat algorithm has been applied for the signal recovery of compression sensor (CS) system which is an important field of signal sampling and compression [8]. Bat algorithm in combination with pruning technique in subspace pursuit is applied for CS. In compression sensing, let y = (y1 , y2 , . . . , yn )T an n-dimensional signal which can be represented on a basis  ∈ R n×n and y = x, where x = (x1 , x2 , . . . , xn )T , if K nonzero elements only exists in x, y, is known as K – sparse signal with sparsity K. All locations of the nonzero elements in x are named as support set E and is given asE = {1 ≤ i ≤ n|xi = 0}. The sampled signal of y using the projection on the measurement matrix is denoted by b which is given as b = y = x = Ax

(15)

where A is the sensing matrix. To recover the sparse signal y from b, the following l0 minimization is used min x0 x

(16)

s.t Ax = b where .0 represents l0 -norm. For the condition K < spark(A), the Eq. (16) is approximated as argminx Ax − b2 ,

(17)

s.t x0  ≤ K . In greedy pursuit algorithms, a two-step procedure is used to detect the signal as follows: Step 1: Estimation of the support set Step 2: Signal estimation by least square method.

x



E

x 

= A+ b E

(18)

=0

(19)





S− E

Estimation where E represents the estimated support set and S = {1, 2, . . . , n}. x E is a vector that consists of the elements of x ∈ R n .

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A E is the sub-matrix of matrix A. The condition to be satisfied after the accurate estimation of support set is as follows:      A A+ b − b = 0 (20)   E E 2 



where .2 denotes l2 -norm. Since,      A A+ b − b ≥ 0  E E  



2

the cost function is formulated as     +  f E =  A A b − b  E E 2 





(21)

Pseudocode of BA based sparse recovery algorithm for CS Step 1: Initialization of BA parameters, K, terminated threshold σ and iterations limit as N _max Step 2: generate the positions and velocities of bats randomly. Step 3: generate Q i (t) with the random elements selected from the best solution E∗. Step 4: If |Ui (t)| ≤ q, a set Q i (t) consists randomly chosen elements of q −Ui (t) from the set S − Ui (t). Update the velocity of bats using the following equation. Vi (t + 1) = Ui (t) ∪ G i (t) If |Ui (t)| > q, the set G i (t) consists randomly chosen elements of q − K from the set Q i (t) − E i (t). Determine the velocity of bats using the following equation. Vi (t + 1) = E i (t) ∪ G i (t) Step 5: The location of i-th bat E i (t + 1) consists of the elements corresponding to the K maximum absolute values of A+ Vi (t+1) . Step 6: If rand1 > ri (t), select an optimal solution among best solutions and then replace ε· L i (t) · K elements of this solution with remaining elements in S − E ∗j . Step 7: Compute the new fitness value using f (E i (t + 1)). Step 8: If rand2 > L i (t), adjust  ri (t) and L i (t). Step 9: If f (E i (t + 1)) < f E i∗ update the best solutions and set E i∗ = E i (t + 1).

8 Bat Algorithm with Applications to Signal, Speech …

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If f (E i (t + 1)) < f (E ∗ ) update the best solution E ∗ = E i (t + 1) Step 10: Stop iterations if condition of termination satisfied otherwise repeat.

2.3 Feature Selection Feature selection (FS) is the method of choosing appropriate feature sets that are used for the model construction. The broad classifications of FS approaches are filter, wrapper, and embedded methods. All the approaches of feature selection can be applied for both the supervised learning and unsupervised learning. Supervised learning uses the class labels to guide the selection process whereas in unsupervised learning there are no class labels. Meta heuristic feature selection methods are the latest literature where Genetic Algorithm [9], Simulated Annealing [10], Ants Colony [11], and Particle Swarm Optimization [12] have already been explored for feature selection. Recently, Bat Algorithm is also adopted for FS. Taha et al. [13] applied a hybrid of the Bat algorithm and Naïve Bayes algorithm (BANB) as an intelligent approach for feature selection. The pseudocode for the implementation of BANB is given below: Pseudocode Naïve Bayes—based BA (BANB) Initialize the algorithm parameters: A, Amin , Amax , r, f qmin , f qmax , Pmax , Imax , Vmax , Vmin , ϕ, δ, γ and α Create a population with Pmax bats Compute fitness function for all bats Identify the best bat ps∗ at the moment While (t < maximum runs) Get new solutions by changing frequency, and velocities given by   f qi = f qmin + f qmax − f qmin β   vlit = vlit−1 + psit − psi f qi If Vi > Vmax then Vi = Vmax End If Vi < Vmin then Vi = Vmin End Update positions by using the following Eq. psit = psit−1 + vlit

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If (rand > r i ) t Determine  tε A  If ε A > Amax ε At = Amax ) End   If ε At < Amin ε At = Amin ) End  Build a local solution for the best solution ( ps∗ ) x gb = xold + ε At End t Determine  tε A  If ε A > Amax ε At = Amax ) End   If ε At < Amin ε At = Amin ) End  t  t Create a new  solution for the current solution psi psl = psold + ε A  If x1 ≥ x gb f x = xl Else f x = x gb End If(rand < Ai & f ( psi ) < f ( ps∗ )) Take the new solution Increment of ri and decrement of Ai End Acquire current best solution End Ramasamy and Rani [14] applied a modified Binary Bat algorithm for unsupervised feature selection and named it as UFS-MBBA. In this method, k-means clustering algorithm is utilized as wrapper. Authors also employed the mutation operation to ensure the diversity of the search space. The cost function is defined using the cluster quality measure given by [15] fitness(bi ) =

k n      psi − m j 2 j=1 i=1,xi ∈c j

where bi is each bat in the swarm and psi is the location of each bat. Pseudocode of UFS-MBBA Initialize the swarm of bat Apply mutation on the bats

(22)

8 Bat Algorithm with Applications to Signal, Speech …

141

Define pulse frequency f qi at psi Determine the performance of initial bats using objective function Find the lowest fitness value of bat While (t < maximum number of iterations) Set the velocity and frequency Determine cost function given in (22) If (T < rand Build new solutions If(rand < Ai & f ( psi ) < f ( ps∗ )) Find the new solutions Increment of ri and decrement of Ai End Determine the currently available best solutions by ranking the bats End Yang et al. [16] suggested an enhanced version of Bat algorithm named MBAFS for feature selection. Using this approach, the evolution of bats will be guided by a randomly chosen additional bat in order to improve the diversity. Authors also utilized mutation technique for local optimum. The classification accuracy of MBAFS algorithm achieved higher performance than Binary Bat algorithm, Binary PSO [17], and improved binary PSO [18] algorithms. The mutation operator is formulated as

j psi

=

j

− psi , r ≤ dr j psi , otherwise

(23) g

Bat’s velocity consists of two components, known as vir (t) and vi (t), given by   ps (t) × τ vir (t) = TT−t × di f ps (t), i  vi (t) g g vi (t) = w × vi (t − 1) + di f ps (t), psi (t) × f qi 





(24)

g

The local search space is divided as two parts based on vir (t) and vi (t), given as ⎧ ⎨

g

1, vi (t) < 0 = Dmax , vig (t) ≥ Dmax ⎩ g vi (t) + 1, otherwise ⎧ 1, vir (t) < 0 ⎨ g Di (t) = Dmax , vir (t) ≥ TT−t Dmax ⎩  r vi (t) + 1, otherwise Dir (t)

(25)

(26)

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The fitness function is given as fit(x) = α × accuracy + (1 − α) ×

n − S(x) n

(27)

where n is the number of bits in a string, S(x) is the selected features, and accuracy is the accuracy of the classifier. Pseudocode of MBAFS Set the velocity vi and population of bats ( psi = 1, 2, . . . , n b ) Set pulse frequency f qi , pulse rate ri , and the loudness Ai Determine the best bat ps While (t < T ) For each bat Select a random bat psr g Calculate Dir (t) and Di (t) End for If (rand > r i ) Pick a bat ps1 from the best bats Build a local solution ps2 around ps Select a better solution psbr between ps1 and ps2 End if If (rand < Ai If( psbr x ) > f ( ps ) Accepting the new solutions xbr Increase ri and reduce Ai 





MI = 0 Else MI + + End if If MI = 3 Compute a new solution with the mutation operator for each bat End if End while Saleem et al. [19] applied Niche-Based Bat Algorithm (NBBA) to get the optimal feature subsets, for the problem of feature selection. In NBBA algorithm, each bat is considered as a solution and represented with bits (binary representation). The features of dataset refer to the number of bits. For each bit, the value of “0” indicates

8 Bat Algorithm with Applications to Signal, Speech …

143

that this feature was not chosen, and the value of “1” indicates the presence of a function in the selection process. The classification accuracy which is computed by using four performance metrics has been considered as the fitness function for evaluation of the algorithm and is given as Accuracy =



TP + TN TP + TN + FP + FN

(28)

where TP = True positive, TN = True negative, FP = false positive, and FN = false negative. Pseudocode of NBBA Generate the bat swarm S randomly Repeat Train the population with local random walk for first iteration Compute the fitness for each bat For each sub-population Sk Training of Sk using BA for global search Compute fitness for every bat Determine the radius of sub-population Sk · R End Combine sub-populations, if possible Enable Sk to get solutions from S which are moved into any radius of (Sk ) Generate new sub-populations Until we met the stopping criteria Accept the new solutions Return best solution Sk · y for each sub-population Sk .

3 BA Applications to Speech Processing 3.1 Speech Enhancement Prajna et al. [20] applied BA for speech enhancement application. Authors implemented BA based dual-channel enhancement system. The dual-channel speech enhancement system consists of two channels namely primary and secondary. The first channel input is the noisy speech and the second channel input is the noise reference. The path of the signal that audio signal travels from first channel to second channel is estimated using an adaptive filter. Since the majority of the speech signals are non-stationary, the input signal is segmented and processed as frames. The aim is therefore to optimize filter solution that would give the least mean square error

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output between the first and second channels. To assess each bat’s fitness the fitness function is proposed as N 1 Ji = (d(k) − yi (k))2 L k=0

(29)

where L is each frame’s length and yi (k) is the adaptive filter output at i-th agent. In this optimization problem, Ji is minimized utilizing BA. Each solution’s fitness value reflects bat’s quality in the search process. To generate new solutions the frequencies, loudness, and pulse emission rates are varied. The new solutions are accepted depending on the reliability of the solutions depicted by loudness and pulse levels, in effect refers to the proximity or fitness of the bats to the optimal global bat. The best solution is obtained after some iterations, when the fitness value is minimum, i.e., Ji is minimum. The convolution of the noisy signal with the error signal gives the noise estimation. Then, the subtraction of measured noise estimation from the noisy signal extracts the clean speech.

3.2 Speech Emotion Recognition A hybrid of Bat algorithm and Simulated Annealing (SA) algorithm is proposed for speech emotion recognition and named as EBSA (emotion classification enhanced BA with SA algorithm) [21]. This hybrid approach could overcome the issues related to fast convergence and high computational complexity of BA algorithm. It also helps improving the accuracy of the speech emotion recognition system. The emotions are classified as happy, normal, and sad by drawing-out the Mel Frequency Cepstral Coefficients (MFCC) [22], PS-ZCPA [23], and energy features from the speech sample input and the classification is done by applying the enhanced BA with SA. Emotion Classification Enhanced Bat Algorithm with Simulated Annealing (EBSA) Algorithm is described as follows: Cost function is f (x) = [ ps1 , ps2 , ps3 , . . . , psd ]T . Initialization of bat population psi (i = 0, 1, 2 . . . , n) and vli Initialize pulse frequency f qi , pulse rates ri and the loudness Ai While (t < maximum runs) For each psi Obtain new features by adjusting frequency Updating of positions and velocities of bats if (rand > r i ) Choose one feature among the best features Create a local solution for the chosen best solution

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End if Build a new solution with random flight Apply SA algorithm Compute the fitness of cost function  −Eβ T e kβ z= β

E β —energy, T —temperature Compute the accuracy and error value using above equation Accept the new state Until the number of accepted transitions is below a threshold level Choose a neighbor feature at random from the given input If(rand < Ai & f ( psi ) < f ( ps∗ )) Consider the new features eliminate the noise features Increment ri and decrease Ai End if Rate the bats and select the current best bat Check for better pitch frequency, energy, and MFCC Classification of optimized signal with high accuracy and less error rate End while

4 BA Applications to Image Processing 4.1 Image Compression Several techniques have been proposed for image compression, and vector quantization is the widely used technique among them because of its better performance. Linde–Buzo–Gray (LBG) [24] is a classical approach of Vector Quantization (VQ) that generates a local optimal codebook with less PSNR value. Bat algorithm is applied for the generation of global codebook of VQ [25]. Fitness values are computed using Eq. (30) for each codebook Fitness(C) =

Nb 1 = N N  2 c b   D(c) j=1 i=1 u i j · X i − C j

(30)

where Nb is the number of subdivided blocks of the image of size N × N, X i (i = 1, 2, …, N b ) is the pixel representation of these blocks, Nc is the number of codebooks, and D is the distortion between codebooks which is given by

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D=

Nc  Nb  2 1  ui j ·  X i − C j  Nc j=1 i=1

(31)

Step 1: Initialize the parameters of codebook number (bats), loudness, velocity V, pulse rate r, minimum, and maximum frequencies Qmin and Qmax, respectively. The LBG algorithm codebook is allocated as initial codebook X 1 . Remaining codebooks X i , (i = 2, 3, . . . , N − 1) are randomly chosen. Step 2: Use Eq. (30) to determine all codebooks fitness, and assign X best as best fitness codebook. Step 3: Every component of each codebook is zoomed using Eq. (3) Step 4: If (rand > r) Find the neighborhood of best codebooks using Eq. (4) Step 5: Build a random number, accept the new codebook if its loudness is less and fitness beats the old one. Step 6: Rate the bats to find the current best X best . Step 7: Follow steps 2–6 until the condition of maximum runes is met.

4.2 Image Enhancement Contrast enhancement techniques are used to provide better visual perception. Histogram Equalization (HE) is an easiest and popularly used approach for contrast improvement. Authors proposed a new HE variant named as weighted and thresholded Bi-HE (WTBHE). They developed an improved version of Bat algorithm (BA) by employing dynamic inertia weight and proposed self-adaptive parameters of BA [26]. They also utilized the concept of chaotic sequence for local search, and the initial population is also improved using the population diversity metric method. The algorithm for Weighted and thresholded Bi.HE (WTBHE) is given as follows: 1. Histogram separation of the image by threshold level helps to get least absolute mean brightness error. 2. To change the lower and upper histograms, define the lower and upper weight constraints. 3. Use the BA and its variants to optimize the constraints. 4. Use HE process separately over the lower and upper histograms 5. Unite lower and upper histograms to obtain an enhanced image Chaotic sequences are mainly used for three purposes in meta-heuristic algorithms: generating (1) random numbers, (2) inertia weight, and (3) to carry out local. Authors used chaotic sequences to conduct local search and to produce random numbers. Various chaotic generators are available such as logistic map, tent map, gauss map, sinusoidal iterator, lozi map, Chua’s oscillator, etc. [27]. Authors utilized logistic equation in their study. The fitness function is defined as follows:

8 Bat Algorithm with Applications to Signal, Speech …

  Fitness(vl , rl , vu , ru ,) = log Icon × exp(HE ) /Ien

147

(32)

where HE is the enhanced image entropy, Icon and Ien are the contrast and energy of the co-occurrence matrix. The problem of optimization is defined as  (vl0 , rl0 , vu0 , ru0 ) = arg maxvl ,rl ,vu ,ru {Fit(vl , rl , vu , ru )}

(33)

The pseudocode of DAWBA: Step 1: Initialize n bats, Y = {Yi |i = 1, 2, 3, . . . , n} according to Eq. (33), where ∂ is generated by means of a logistic equation. Then it has been chosen by the following rule:   i f D t ≤ 0.4 here, D t is the Diversity Factor. The appropriate population was then used in the proposed BA for further processing. Step 2: Initialize each bat’s frequency, loudness, and pulse rate with the aid of logistic equation Step 3: Produce new solutions by changing the frequency using following equations:   f qit = f qmin + f qmax − f qmin β f qit = min( f qit , E S Fit )   Vit+1 = Uit ∗ Vit + Y∗ − Yit f qit Yit+1 = Yit + Vit+1 where β ∈ [0, 1] is the random number created by logistic equation and f qi regulates the velocity and range of the each bat’s movement. Step 4: Choose the best solution Ybest and use the following equation to generate new solutions if(rand > ri ) Z = Ybest + L M × sign(rand − 0.5) × Aavg If not, same will remain where rand ∈ [0, 1], L_M ∈ [0, 1] are the chaotic sequences generated by logistic equation and Aavg is the average loudness. Step 5: This step is a SA step required to maintain the population diversity if(rand3 < Ai & fit(Z ) < fit(Yi )) Consider local search solution Step 6: Increment of ri and decrement of Ai Step 7. Rate the bats to obtain current best Y∗ . Step 8. Follow steps 4–7 until the stopping criterion has been met. Step 9. Display the result

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4.3 Image Thresholding Image segmentation thresholding is an essential and is the first step in the image processing for many applications. Segmentation is a low-level operation that can segment an image in non-overlapping regions. In a gray level image, the optimal thresholds are identified by maximizing entropy-based thresholding. Bat algorithm and modified Bat algorithm have been applied for finding optimal thresholds. Tuba and Alihodzic [28] applied BA based multilevel image thresholding algorithm for segmentation. The multilevel thresholding problem is modeled as a problem of optimization with k-variables. Let L gray levels in a given image I having n pixels and these gray levels are in the range {0, 1, …, L − 1}. The objective is to maximize the fitness function given as f ([t1 , t2 , . . . , tk ]) = H0 + H1 + H2 + · · · + Hk

(34)

where the entropies Hi are given as H0 = −

t1 −1 t1 −1   Pi Pi ln , w0 = Pi , w0 w0 i=0 i=0

(35)

H1 = −

t2 −1 t2 −1   Pi Pi ln , w1 = Pi , w1 w1 i=t i=t

(36)

t3 −1 t3 −1   Pi Pi ln , w2 = Pi , w2 w2 i=t i=t

(37)

1

H2 = −

1

2

Hk = −

L−1  i=tk

2

Pi Pi ln , wk = wk wk

L−1 

Pi

(38)

i=tk

  [t1 , t2 , . . . , tk ] = [X 1 , X 2 , . . . , X N ], xi = xi,1 , xi,2 , . . . , xi,k

(39)

Here, BA attempts to achieve the optimal K dimensional vector [t1 , t2 , . . . , tk ] by maximizing the entropy in Eq. (34). The pseudocode of algorithm: Step 1. BA creates a swarm of k dimensional N solutions (bats) randomly. The fitness values of all solutions xi are evaluated and set cycle = 1. Observe the best solution X best . Step 2. Create new solutions by varying the vector of frequencies f i and by updating the matrix of velocities V using the Eqs. (1) and (2), respectively. Step 3. The local search is initiated with propinquity based on pulse rate as per the Eq. (3)

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Step 4. In this step, the fitness function is evaluated for the current best solution vector resulted in step 3. If the solution’s fitness is greater than the old fitness and the loudness value A obtained by Eq. (6) is low Take new solution and change the old fitness value. If not, maintain the old fitness. Step 5. Choose the best optimal vector with the currently highest objective function value and the best optimum as X best . Add the cycle by one. Step 6. If the cycle is equal to the max runs Stop Else Go to Step 2. The main limitation of the aforementioned BA based multilevel image thresholding is that it cannot produce good results for large number of thresholds. To overcome this problem, an Improved Bat Algorithm (IBA) is adopted for multilevel thresholding. IBA is a hybrid of Differential Evolution (DE) and two different solution search equations of BA. It uses the advantages of crossover and mutation operators of DE to improve the convergence performance and maintain good intensification and diversification. The image thresholding algorithm with IBA is shown below: Step 1 Define random swarm of bats with k dimensions. Each threshold value xi, j (i = 1, 2, . . . , n; j = 1, 2, . . . , k) of the matrix X generated by the bat i is confined to set {0, 1, . . . , L − 1}. Define the variable limit that refers the maximum attempts to improve a bat, the loudness Ai and pulse rate ri0 . Define the variables of the DE algorithm such as the differential weight F and crossover probability Cr . Then evaluate the fitness value for each bat xi . Determine the best solution as xbest , using IBA. Then set the variable cycle to one. Step 2 Calculation of a new threshold is performed by moving virtual bats xit−1 . The velocity vit and frequency f i are calculated. In this stage, the IBA regulates the boundary conditions for new solution. If the value of the xit is less than 0 or is greater than L − 1, then xit is updated with the value of the closer limit value to the xit . Step 3 For each solution xit calculate new solution defined by  t xdif , if rand1 >rti (40) xnew = xtdif , otherwise where rand1 is a random value inbetween 0 and 1, r is the pulse rate function, xdif is the differential operator for mutation and crossover, and xloc is the operator based on the local search in the BA. The differential mutation and crossover operations are performed by



t t xc,t j + F xa, t j − x b, j , if(rand2 > Cr or j = jr ) (41) xdif, j = xi,t j , otherwise

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Similar to classical BA, parameters ε and A i, denote the scaling factor and the loudness function, respectively. Also, inside the local search operator xloc ,





t t t xlbest, t j , i f ( f xlbest, j > f x i, j ) (42) xloc, j = xi,t j , otherwise t−1 t−1 t xlbest, j = x best, j + ε Ai, j

(43)

the boundary conditions for all j (j = 1, …, k) are checked. In our proposed approach, we found that it is beneficial to replace (13) by r. Step 4 In this step, the solution x new obtained in Step 3 is accepted as a new solution and (x new ) as a new objective function value by using    t   t   t  t   ), if rand3 > Ait and f xnew > f xit−1 (xnew , f xnew  (44) xi , f it xit = tri = tri + 1, otherwise (xit−1 , f xit−1 ) where rand is a random value in between 0 and 1, tri is a vector keeping the number of trails through which solution xi cannot be bettered at cycle t, and Ait loudness. In case the location xit−1 cannot be bettered, then the new location xnew is neglected and the value of tri is incremented by one. As the cycles proceed, if the location xi could not be further enhanced, neglect it and create a new solution/location. Step 5 Observe the best solution. Step 6. If the condition for termination is satisfied or the value of cycle is the total number of runs Stop the algorithm Else Increment the value of cycle by one and go to Step 2. Image segmentation is performed using Modified chaotic Bat algorithm (MCBA) [29]. In this approach, MCBA optimizes the threshold values for image segmentation. The objective function considered is the maximization of the 2D Tsallis entropy. For implementation, the swarm of bats is initialized with n, where each bat’s location is a D-dimensional solution. Since each bat’s solution refers to a 2D candidate threshold, D is set of 2. X i denotes the i -th bat position in the population, which refers a candidate threshold pair and its fitness is calculated by 2D Tsallis function. The MCBA-based 2D Tsallis entropy algorithm is as follows: The objective function is defined as sq (t, s) = sq (O) + sq (B) + (1 − q)sq (O)sq (B)

(45)

where sq (O) and sq (B) are 2D entropy of Tsallis linked with object and background sets given as follows:

8 Bat Algorithm with Applications to Signal, Speech …

sq (O) =

sq (B) = where PA (t, s) =

t i=0

s j=0

1−

1−

t

s

i=0

255

151



j=0

p(i, j) PA (t,s)

q −1 255

i=t+1

j=s+1

q

p(i, j) PB (t,s)

(46)

q (47)

q −1 p(i, j) and PB (t, s) =

255 i=t+1

255 j=s+1

p(i, j)

Pseudocode of MCBA Step 1: Initialization of velocity vector Vi , pulse rates ri , and the loudness Ai . Specify the pulse frequency f i at X i , and set iterations of MCBA, k = 0. Step 2: Compute the cost function sq (t, s) using Eq. (45) Step 3: Reproduction loop: k = k + 1 Step 4: Bats random walk 4.1: Build new solutions by changing frequency, velocities, and positions by using Eqs. (1)–(3). 4.2: Generate a chaotic process with the logistic Equations. 4.3: Calculate the value of fitness function using Eq. (45) 4.4: Enable local search with Levy flight. Step 5: If Ai > 1.4 && H (X i ) < H (X ∗ ) Obtain the new solutions. Increment of ri and decrement of Ai . Step 6: Rate bats to get current best X ∗ Step 7: If (k < Max_gen) go to Step 3. Else Acquire image with optimal parameters.

5 Conclusions Bat Algorithm, being a potential optimization algorithm, is utilized to optimize many engineering problems. This chapter provided a brief review of signal processing techniques that are developed based on BA. Application of BA for FIR filtering, signal recovery, speech enhancement, image thresholding, and enhancement and compression techniques are presented in detail. Some of the new versions of BA such as improved bat algorithm, dynamically adapted and weighted bat algorithm, modified chaotic bat algorithm, naïve based bat algorithm have been briefly reviewed. BA has been widely applied for image processing research. In particular, many researchers have adopted BA for image thresholding whereas in speech processing very few studies are reported based on BA. There are many open problems in speech

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processing such as recognition and feature extraction areas where BA can be applied to achieve improved performance with optimal solutions. In signal processing applications, BA is most popular for feature selection and classification tasks. There is a large potential to develop new operators and variants of BA and to investigate the effect of parameters on converging in particular applications. There is also huge potential for researchers to apply BA for complex engineering problems specifically signal, image, and speech processing.

References 1. Yang X-S (2010) A new metaheuristic bat-inspired algorithm, pp 65–74 2. Satapathy SC, Raja NSM, Rajinikanth V, Ashour AS, Dey N (2018) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29(12):1285–1307 3. Rajinikanth V et al (2019) Skin melanoma assessment using Kapur’s entropy and level set—a study with bat algorithm. In: Smart intelligent computing and applications. Springer, Singapore, pp 193–202 4. Dey N, Ashour AS, Bhattacharyya S (2019) Applied nature-inspired computing: algorithms and case studies. Springer tracts in nature-inspired computing 5. Dey N (ed) (2017) Advancements in applied metaheuristic computing. IGI Global 6. Dey N (2020) Applications of firefly algorithm and its variants. Springer tracts in nature-inspired computing 7. Goyanka A, Rachuri B, Rawat TK, Barsainya R (2017) Bat algorithm for the design of fractional order FIR differentiators and fractional FIR Hilbert transformers: a comparative study. In: 2017 8th international conference on computing, communication and networking technologies (ICCCNT), pp 1–7 8. Bao W, Liu H, Huang D, Hua Q, Hua G (2018) A bat-inspired sparse recovery algorithm for compressed sensing. Comput Intell Neurosci 2018:1–9 9. Langdon WB, Poli R, McPhee NF, Koza JR (2008) Genetic programming: an introduction and tutorial, with a survey of techniques and applications, pp 927–1028 10. Granville V, Krivanek M, Rasson J-P (1994) Simulated annealing: a proof of convergence. IEEE Trans Pattern Anal Mach Intell 16(6):652–656 11. Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2– 3):243–278 12. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95— international conference on neural networks, vol 4, pp 1942–1948 13. Taha AM, Mustapha A, Chen S-D (2013) Naive Bayes-guided bat algorithm for feature selection. Sci World J 2013:1–9 14. Ramasamy R, Rani S (2018) Modified binary bat algorithm for feature selection in unsupervised learning. Int Arab J Inf Technol 15(6):1060–1067 15. Jiawei Han MK, Pei J (2012) Data mining: concepts and techniques. Elsevier 16. Yang B, Lu Y, Zhu K, Yang G, Liu J, Yin H (2017) Feature selection based on modified bat algorithm. IEICE Trans Inf Syst E100.D(8):1860–1869 17. Lee S, Soak S, Oh S, Pedrycz W, Jeon M (2008) Modified binary particle swarm optimization. Prog Nat Sci 18(9):1161–1166 18. Chuang L-Y, Chang H-W, Tu C-J, Yang C-H (2008) Improved binary PSO for feature selection using gene expression data. Comput Biol Chem 32(1):29–38 19. Saleem N, Zafar K, Sabzwari A (2019) Enhanced feature subset selection using Niche based bat algorithm. Computation 7(3):49 20. Prajna K, Sasibhushana Rao G, Reddy KVVS, Uma Maheswari R (2014) Application of bat algorithm in dual channel speech enhancement. In: 2014 international conference on communication and signal processing, pp 1457–1461

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21. Kumuthaveni R, Chandra E (2017) An enhanced bat algorithm with simulated annealing method for speech emotion recognition. J Adv Res Dyn Control Syst 01:125–138 22. Mustafa MB, Yusoof MAM, Don ZM, Malekzadeh M (2018) Speech emotion recognition research: an analysis of research focus. Int J Speech Technol 21(1):137–156 23. Li X et al (2007) Stress and emotion classification using jitter and shimmer features. In: 2007 IEEE international conference on acoustics, speech and signal processing—ICASSP ’07, pp. IV-1081–IV-1084 24. Lin Y-C, Tai S-C (1998) A fast Linde-Buzo-Gray algorithm in image vector quantization. IEEE Trans Circuits Syst II Analog Digit Signal Process 45(3):432–435 25. Karri C, Jena U (2016) Fast vector quantization using a bat algorithm for image compression. Eng Sci Technol Int J 19(2):769–781 26. Dhal KG, Das S (2019) A dynamically adapted and weighted bat algorithm in image enhancement domain. Evol Syst 10(2):129–147 27. Caponetto R, Fortuna L, Fazzino S, Xibilia MG (2003) Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans Evol Comput 7(3):289–304 28. Tuba M, Alihodzic A (2013) Bat algorithm (BA) for image thresholding. In: Recent researches in telecommunications, informatics, electronics and signal processing, pp 364–369 29. Ye Z, Yang J, Wang M, Zong X, Yan L, Liu W (2018) 2D Tsallis entropy for image segmentation based on modified chaotic bat algorithm. Entropy 20(4):239

Chapter 9

Bat Algorithm Aided System to Extract Tumor in Flair/T2 Modality Brain MRI Slices V. Sindhu, M. Singaravelan, J. Ramadevi, S. Vinitha, and S. Hemapriyaa

1 Introduction Brain is the fundamental part in humans and is responsible to evaluate the entire physiological signal coming from other sensory parts and take essential control actions. This operation is badly affected, if any infection or disease arises in brain and the unnoticed and untreated brain sickness may lead to various troubles including death [1–4]. The normal condition of the brain may be affected due to various causes, such as birth defects, head injury due to major/minor accident, and the Abnormal-CellGrowth (ACG) in interior brain section [5–7]. Due to the various preventive measures and the availability of the modern caring conditions, children with birth defects can be considerably reduced [8, 9]. Also, the intellect shortcoming due to the head injury is also less compared to the brain abnormality due to ACG [10–12]. Recently, a considerable number of awareness programs and preventive measures are taken to preserve the brain from abnormality. But, due to various unavoidable reasons, such as modern lifestyle, food habits, heredity, and age [13, 14], most of the humans are suffering due to various brain abnormalities in which Brain Tumor (BT) is one such abnormality. If the BT is diagnosed in its early phase, then possible measures can be implemented to cure/control the disease. The brain consists of a large number of soft tissues along with the associated signal transceivers (nerves) and hence, the biopsy methods are not recommended to diagnose these tumors, like in other tumor evaluation procedures followed in hospitals [15]. Hence, brain-signal (EEG) and brain-image (MRI or CT) are widely considered to diagnose the abnormalities in the brain. Assessment of brain abnormalities with EEG V. Sindhu (B) · M. Singaravelan · J. Ramadevi · S. Vinitha · S. Hemapriyaa Department of Information Technology, Kingston Engineering College, Katpadi, Vellore 632059, TN, India e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 N. Dey and V. Rajinikanth (eds.), Applications of Bat Algorithm and its Variants, Springer Tracts in Nature-Inspired Computing, https://doi.org/10.1007/978-981-15-5097-3_9

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is quite complex and requires various pre-processing and post-processing methods. Hence, most of the clinical level tumor evaluation techniques require the brainimages recorded with the chosen imaging methodology (MRI/CT). The visibility of the brain infection is good in MRI compared to the CT and the MRI also can be recorded in various modalities, such as T1, T1C, T2, Flair, and Diffusion-Weighting (DW) [16–18]. In the proposed research, the examination of the BT obtained using the Flair/T2 modalities is used for the examination and these essential images are obtained from the Brats2015 database [19, 20]. The raw MRI database is available in the form of a three-dimensional (3D) image with different orientations, such as Axial, Sagittal, and Coronal; and in this work, the axial orientation 2D MRI slices are considered for the assessment. Initially, the required MRI slices are obtained by using the ITK-Snap software [21], which helped to extract the 2D slices with a dimension of 240 × 240 × 1 pixels. In this work, 20 volunteers dataset are considered for the assessment and from each volunteer, 10 number of slices (20 × 10 = 200 slices) are extracted for Flair as well as T2 modality. The plan of this research is to build an Automated Tumor Examination System (ATES) using the Bat Algorithm (BA). This work considered the following phases: (1) Extraction of 2D slices using ITK-Snap, (ii) Multi-thresholding using the BA and Kapur’s technique, (iii) Mining of the tumor using Watershed Segmentation Method (WSM), (iv) Comparison of tumor section with the Ground-Truth Image (GTI), (v) Computation of Quality Measures (QM), and confirmation of the practical significance of the proposed method. This work employed the globally accepted BA primarily used by Yang (2010) and this algorithm uses the Levy-Flight-Search (LFS) for the algorithm’s convergence. The earlier works depicted a number of image processing applications by the BA, and these work proved that BA is one of the globally accepted heuristic technique of the twenty-first century, and still the traditional and enhanced forms of the BA is used to resolve various optimization tasks [22–25]. This work considered the BA to find the optimal threshold of the chosen MRI slice, which maximizes the Kapur’s entropy value. This thresholding work helped to segregate the chosen MRI slice into tumor, normal element, and background; and with the help of WSM, the tumor section is effectively mined. Finally, a comparison of this tumor with the GTI will help to assess the performance of the proposed ATES. In this work, the Flair and T2 modality slices are separately assessed and the average values attained with this procedure helped to compute the practical significance of the developed ATES. The other sections are prearranged as follows: Sect. 2 outlines the related existing methods, Sects. 3 and 4 presented the problem description and its solution. Section 5 presents the conclusion of this work.

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2 Related Research Recently, a considerable number of brain tumor evaluation procedures are proposed and implemented using the Machine-Learning (ML) and Deep-Learning (DL) techniques. Every technique has its own merits and demerits and from the recent research work, it can be noted that the segmentation approach will help to enhance the results of the ML and DL techniques, and even the number of image samples is less. The segmentation outcome will help to get the essential shape and dimension features of the tumor section, which will improve the classification accuracy of the ML and DL methods and this procedure plays a vital role in ensemble approaches [26, 27]. The summary of the existing brain segmentation procedures can be accessed from Table 1; which offers the details regarding the approach, considered dataset, outcome, and the validation process. From this table, it can be noted that a considerable number of heuristic algorithm assisted techniques are already implemented due to its significance.

3 Problem Formulation During the clinical evaluation, the recorded MRI is initially evaluated by a radiologist, and the image and the report is then sent to an expert member for further analysis. The hospital-level analysis involves in identifying the location and the severity of the tumor; to plan for essential handling course. The manual examination of the MRI slices by an experienced doctor depends on the availability of the doctor and in most of the cases, this process needs more time and the evaluation of all these slides are time-consuming. Hence, recently a number of automated diagnostic methodologies are developed to assist the doctor in the evaluation process. The proposed technique aims to implement ATES based on the BA. This system aims to extort the tumor piece from the Flair/T2 modality images using a chosen threshold and segmentation methods. The outcome of this approach is then evaluated based on the attained performance values computed based on a comparison with the GTI. This work aims to find the feasibility of ATES on the Flair and T2 modality slices. The outline of ATES is depicted in Fig. 1. Figure 1 shows the arrangement of the ATES developed in this research. This work considered the 2D MRI slices of Flair/T2 modality for the examination. Later, a conventional BA working with LFS is considered to identify the optimal threshold using Kapur’s entropy. The threshold image is then subjected to a WSM and the extracted tumor section is then compared with the GTI. This comparison helped to get a considerable number of performance values and based on these values, the presentation of the constructed ATES is validated.

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Table 1 Summary of brain tumor assessment techniques References

Methodology

Abnormality

[1]

Heuristic algorithm based early detection of tumor using MRI slices

Tumor

[2]

Combination of thresholding and segmentation methodology

Tumor

[3]

Machine-learning based classification of brain MRI into normal/tumor class

Tumor

[4]

Jaya algorithm based assessment of brain MRI

Tumor

[28]

Brain MRI assessment with fuzzy-entropy and level-set is implemented

Tumor

[29]

Kapur’s threshold and Chan-Vese segmentation for tumor detection were discussed.

Tumor

[30]

A hybrid methodology to analyze CT/MRI is discussed

Tumor

[31]

Tsallis entropy assisted analysis is discussed

Tumor

[32]

MRI of Flair/DW modality assessment with heuristic technique is presented

Stroke

[33]

This work implemented Kapur’s threshold and Markov random field based evaluation for brain abnormality detection

Tumor

[34]

A detailed analysis of MRI assessment techniques are presented

Tumor

[35]

Random forest based brain abnormality classification was discussed

Tumor

[36]

Deep-learning technique for MRI assessment is presented

Tumor

[37]

A survey of MRI analysis is discussed

Tumor

[38]

Multi-level thresholding based assessment of MRI is discussed in detail

Tumor

[39]

MRI based detection of brain-related disease is presented

Alzheimer’s disease

[40]

Brain tumor detection with big-data concept is presented with appropriate experiment

Tumor

3.1 Brain MRI Database This work considered the clinical grade brain MRI data of the Brats2015 [19, 20]. This is one of the benchmark MRI image collections available in T1, T1C, T2, and Flair modality. This dataset is free from the skull-section and it is also coming with the associated GTI for comparing and validating the result obtained with a chosen algorithm. This research considered 240 × 240 × 1 pixel-sized images and in each modality case (Flair/T2), 200 images (20 volunteer × 10 image/volunteer) are considered for examination. The chief advantage of Flair/T2 MRI is the visibility of the tumor section. In these two modalities, the tumor section is more visible

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Bat Algorithm

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Segmentation (Watershed)

Extracted Tumour

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Comparison of performance values Performance validation of ATES on Flair/T2 slices Fig. 1 Different stages involved in the proposed ATES

compared to the T1 and T1C. Hence, Flair/T2 slices are used to test the presentation of ATES.

3.2 Pre-processing This section of the chapter describes the initial processing implemented to improve the tumor section by grouping the related pixels based on the thresholding process. Recently, a considerable amount of heuristic and meta-heuristic approaches are proposed and implemented to solve a variety of optimization tasks. Bat algorithm invented by Yang (2010) is proven to be a successful technique, widely used by the researchers to resolve assortment of optimization tasks [22]. Even though a number of modern modifications were proposed earlier, the traditional BA with the Levy-FlightSearch (LFS) seems to be fast and reliable in a considerable number of optimization tasks [23–25, 41–44]. Hence, in this work, the BA with LFS (BA-LFS) is considered to discover the optimal threshold for the brain MRI images. The BA was originally projected by reproducing the pathway actions of microbats. The mathematical model for the BA-LFS can be found below: X i(n+1) = Yi(n) + (X i(n) − G) · Q i

(1)

Yi(n+1) = Yi(n) + X i(n+1)

(2)

Q i = Q min + (Q max − Q min ) · β 1

(3)

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where X i(n+1) and Yin+1 are the speed and place of bat, respectively, Qmin = least frequency and Qmax = utmost frequency. The place revision depends on X new = X old + ε I t

(4)

where ε = LFS and I is the strength of bats’ released sound during the search of a new area. Other details on BA-LFS can be found in [41–44]. The role of the BA is to recognize the best thresholds for the image by maximizing the Kapur’s Entropy (KE). The maximized KE can be represented as Jmax = Z kapur (T h) =

n 

T jC

(5)

j=1

where T jC is the probability allotment. The implementation of KE is common in image processing domain and its information can be found in [45–50]. In this study, the BA parameters are allocated as follows; number of bats = 35, search dimension = 3, iteration = 2500, and the stopping function = J max . Sometimes, this algorithm will stop when the maximum iteration is reached.

3.3 Watershed Segmentation Segmentation is an essential method in image testing, which helps to extract the required part of the image for further evaluation. A considerable number of segmentation techniques are available in the literature to extort the tumor division from the brain MRI. Among them, the WSM seems to be a fast and automated technique and works well on a class of image modalities. The WSM consists of various operations, such as the edge detection, watershed fill, morphological manipulation, and extraction of the tumor. In this work, the operator is to assign only the pixel size to be considered in the test image. Based on the allotted pixel size, the WSM will extract the tumor region. The essential information and the recent application of WSM are found from [51–55].

3.4 Evaluation and Validation The performance assessment and validation procedure is an essential step to confirm the working of the image examination procedure. This is the final step in the proposed ATES. In this, a comparison is executed between the tumor and the GTI, and the

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essential performance values are then computed. Based on these values, the eminence of the proposed tool is confirmed. In this work, the following performance values are used [56–60], TPR = Sensitivity = SE =

TP TP + FN

TNrate = Specificity = SP =

TN TN + FP

(6) (7)

FNrate =

FN FN + TP

(8)

FPrate =

FP FP + TN

(9)

 Jaccard Index = JI = Igti ∩ It Igti ∪ It

(10)

    Dice = DC = 2 Igti ∩ It  Igti  ∪ |It |

(11)

Accuracy = AC =

TP + TN TP + TN + FP + FN

(12)

TP TP + FP

(13)

2TP 2TP + FN + FP

(14)

Precision = PR = F1Score = F1S =

where I gti = GTI, I t = tumor, ∪ is the union process, and ∩ is the intersection function. TP, TN, FP, and FN indicate the true-positive, true-negative, false-positive, and false-negative, correspondingly [61–63].

4 Problem Solution The experiment executed and the corresponding results are shown in this section. All these results are attained using Matlab software. Initially, the essential test image of dimension 240 × 240 × 1 is extracted using the ITK-Snap. This work considers the Flair/T2 modality image for the demonstration and 400 images (200 Flair + 200 T2) are considered for the investigation with the constructed ATES. Figure 2 shows the trial test MRI slices used for the examination. In which Fig. 2a depicts the imitation name for the slices, Fig. 2b and c, the images of Flair and T2, respectively, and Fig. 2d the GTI. The GTI consists of the tumor-core, tumor, and edema; and is displayed in a variety of shades like white, dark-gray, and gray,

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S1

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S10 (a) Slice value

(b) Flair

Fig. 2 Sample MRI slices for the investigation

(c) T2

(d) GTI

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Flair

Pixel distribution

respectively. The aim of the ATES is to extract the whole infected sector from MRI which includes the tumor-core, tumor, and edema. Initially, an image is used in the demonstration and similar procedure is then implemented for other images. The histogram of the image resents the essential pixel distribution value of the image and in the histogram the X-axis normally represents the threshold level and the Y-axis denotes the pixel distribution. The chosen test images and the corresponding histogram is depicted in Fig. 3. Figure 3a shows the image and Fig. 3b presents the histogram. From Fig. 3b, it can be observed that, for the normal image, the distribution is uniform and for the GTI, the threshold shows only three-pixel groups, such as white, gray, and dark-gray. After preferring the picture, a pre-processing is executed to improve the tumor piece of brain MRI. This work implemented the BA-based KE to identify the optimal threshold. In this work, a three-level threshold is applied, which helps to segregate 1800 1600 1400 1200 1000 800 600 400 200 0 0

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(a) Image Fig. 3 Trial images and its corresponding histogram

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Fig. 4 Sample results attained in threshold operation

the picture into background, tumor and normal tissue. Figure 4 depicts the results of the pre-processing operation, in which Fig. 4a presents the convergence of KE search and Fig. 4b illustrates the attained optimal thresholds. The outcome of the pre-processing is then accounted to implement the WSM. During thresholding, the BA randomly assigns the thresholds and computes the KE. This process is continued until the search identifies a threshold cluster which maximizes the KE. If required KE is attained; this process stops and displays the value of the image and the threshold values. Figure 5 shows the results of WSM, in which Fig. 5a is the threshold image, Fig. 5b is the initial result of WSM, like edge detection and watershed fill and Fig. 5c is the extracted tumor. In order to confirm the performance of the ATES, it is mandatory to compare the tumor with GTI. The assessment of performance values are based on the comparison of the tumor with GTI and the related results are presented in Tables 2 and 3. From this table, it is clear that the performance measure attained with the ATES on Flair modality image is better than T2. Similar procedure is then implemented on other images of Fig. 2 and the related outcome is depicted in Fig. 6. Similar procedure is then implemented on all other images (200 + 200 images) and the average of the performance values of Flair/T2 is considered for the validation. The results confirmed that the Flair modality offers a mean accuracy of 95.73% and T2 modality offered accuracy of 95.14%. This confirms that the proposed ATES helped to achieve an accuracy >95% on both the modalities. These results are depicted in Fig. 7.

165

T2

Flair

9 Bat Algorithm Aided System to Extract Tumor …

(a) Threshold

(b) Segmentation

(c) Tumor

Fig. 5 Results of watershed segmentation

Table 2 Initial performance values attained with sample image Modality

TP

FP

TN

FN

TPrate

FPrate

TNrate

FNrate

Flair

2699

140

54713

44

0.9840

0.0026

0.9974

0.0160

T2

2490

349

54289

468

0.8418

0.0064

0.9936

0.1582

Table 3 Essential performance measures achieved for the sample image Modality

JI

DC

SE

SP

AC

PR

F1S

Flair

0.9362

0.9670

0.9840

0.9974

0.9968

0.9507

0.9670

T2

0.7529

0.8591

0.8418

0.9936

0.9858

0.8771

0.8591

Figure 8 represents the other patient’s data considered for the assessment, and the corresponding GTIs are shown in Fig. 9. The sample result attained with the proposed tool is depicted in Fig. 10. In future, the performance of the ATES can be enhanced by considering other threshold methods and segmentation methods. Further, the performance of the BALFS can be validated with the other versions of the Bas and other heuristic algorithms.

5 Conclusion This work aims to develop an ATES to mine the tumor from Flair/T2 modality MRI slices. This work implemented a pre-processing and the segmentation techniques on the Brats2015 database (200 + 200 = 400 images). The initial work enhances the test image using the BA assisted KE. In this work, the BS-LFS is used to discover the

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Fig. 6 Results of ATES for test images

Flair

100

T2

90

Performance (%)

80 70 60 50 40 30 20 10 0

JI

DC

SE

SP

AC

Fig. 7 Comparison of the performance of ATES on Flair/T2 images

PR

F1S

167

Pattient6

Pattient5

Pattient4

Pattient3

Pattient2

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 8 Sample test images considered in this work. a Pseudo name, b–f Various MRI slices

finest threshold. After threshold, the tumor section is then extracted using the WSM. The comparison of tumor and GTI is then employed and the essential performance standards are then calculated. The outcome of this experiment confirms that the proposed work helped to achieve a mean accuracy of >95% for Flair/T2 slices. The overall result obtained with the Flair modality case is superior to the T2 case.

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(b)

(c)

(d)

(e)

(f)

Fig. 9 Ground-Truth images of considered test images. a Pseudo name, b–f Various GTs

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(b) Edge detection

(d) Tumor

Fig. 10 Sample result for a chosen test image

Appendix See Figs. 8, 9, and 10.

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