Advanced Optimization-by-Nature-inspired-Algorithms.pdf

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Preface

Contents

Figures

Tables

Introduction

Optimization: Core Principles and Technical Terms

Brief History of CI-Based Optimization Algorithms

Classi ﬁ cation of CI-Based Optimization Algorithms

No Free Lunch Theorem: The Reason Behind New Algorithms

Conclusion

References

Cat Swarm Optimization (CSO)

Introduction

Natural Process of the Cat Swarm Optimization Algorithm

Seeking Mode (Resting)

Tracing Mode (Movement)

Termination Criteria

Performance of the CSO Algorithm

Pseudo Code of the CSO Algorithm

Conclusion

References

League Championship (LCA)

Introduction

Review of LCA and Its Terminology

League Championship Algorithm

Generating League Schedule

Determining the Winner or Loser

Setting Up a New Team Formation

Pseudo Code of LCA

Conclusions

References

Anarchic Society Optimization (ASO)

Introduction

Formulation

Algorithm Procedure

Movement Policy Based on Current Positions

Movement Policy Based on Positions of Other Members

Movement Policy Based on Previous Positions

Combination of Movement Policies

Pseudo Code of the ASO

Conclusion

References

Cuckoo Optimization (COA)

Introduction

Cuckoo Life Style

Details of COA

Cuckoos’ Initial Residence Locations

Cuckoos’ Egg Laying Approach

Cuckoos Immigration

Demising Cuckoos Laid in Inappropriate Positions

Pseudo Code for COA

Capabilities of COA

Conclusion

References

Teaching-Learning-based Optimization (TLBO)

Introduction

Mapping a Classroom into the Teaching-Learning-Based Optimization Algorithm

Teacher Phase

Learner Phase

Pseudo Code of the TLBO Algorithm

Conclusion

References

Flower Pollination (FPA)

Introduction

Flower Pollination Process

Flower Pollination Algorithm

User-De ﬁ ned Parameters of the FPA

Pseudo Code of FPA

Conclusion

References

Krill Herd (KHA)

Introduction

Krill Swarms’ Herding Pattern

Motion Induced by the Krill Herd

Foraging Motion

Physical Diffusion

Motion Process of the KHA

Pseudo Code of KHA

Conclusion

References

Grey Wolf Optimization (GWO)

Introduction

Natural Process of the GWO Algorithm

Mathematical Model of the GWO Algorithm

Social Hierarchy

Encircling the Prey

Attacking the Prey

Searching for the Prey (Exploration)

Optimization Process in GWO Algorithm

Pseudocode of GWO

Conclusions

References

Shark Smell Optimization (SSO)

Introduction

Underlying Idea of SSO

Formulation of the SSO Algorithm

Initialization of SSO: Finding Initial Odor Particles

Shark Movement Toward the Prey

Pseudo-Code of SSO

Conclusion

References

Ant Lion Optimizer (ALO)

Introduction

Mapping Antlions Hunting Mechanism into the ALO

Initialization of Positions of Ants and Antlions and Evaluation of Their Fitness Functions

Digging Trap

Sliding Ants Toward Antlion

Entrapping Ants Inside Pits

Random Walk of Ants

Elitism

Catching Prey and Reconstruct the Trap

Termination Criteria

User-De ﬁ ned Parameters of the ALO Algorithm

Pseudo-Code of the ALO Algorithm

Conclusion

References

Gradient Evolution (GE)

Introduction

Underlying Idea of the GE Algorithm

Gradient

Gradient-Based Algorithm

Mathematical Formulation of the GE Algorithm

Solution Representation and Algorithm Initialization

Vector Updating

Vector Jumping

Vector Refreshing

Pseudo-Code of GE

Conclusion

References

Moth-Flame Optimization (MFO)

Introduction

Mapping the Navigation Method of Moths into Moth-Flame Optimization

Creating the Initial Population of Moths

Updating the Moths’ Positions

Updating the Number of Flames

Termination Criteria

Performance of the MFO

Pseudocode of the MFO

Conclusion

References

Crow Search (CSA)

Introduction

Crow Flock’s Food Gathering Imitation

CSA Implementation for Optimization

Pseudo Code of the CSA

Conclusion

References

Dragonﬂy (DA)

Introduction

Dragonﬂies’ Swarming Patterns

Optimization Procedure of the DA

Pseudo-Code of the DA

Conclusion

References

Omid Bozorg-Haddad Editor Advanced Optimization by Nature-inspired Algorithms 123

Editor Omid Bozorg-Haddad Department of Irrigation & Reclamation Engineering College of Agriculture & Natural Resources, University of Tehran Karaj Iran ISSN 1860-949X Studies in Computational Intelligence ISBN 978-981-10-5220-0 DOI 10.1007/978-981-10-5221-7 ISSN 1860-9503 (electronic) ISBN 978-981-10-5221-7 (eBook) Library of Congress Control Number: 2017943829 © Springer Nature Singapore Pte Ltd. 2018 This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface From the early 1990s, the introduction of the term “Computational Intelligence” (CI) highlighted the potential applicability of this ﬁeld. One of the preliminary applications of the ﬁeld was in the realm of optimization. Undoubtedly, the tasks of design and operation of systems can be approached systematically by the application of optimization. And while in most real-life problems, including engineering problems, application of the classical optimization techniques were limited due to the complex nature of the decision space and numerous variables, and the CI-based optimization techniques, which imitated the nature as a source of inspiration, have proven quite useful. Consequently, during the last passing decades, a considerable number of novel nature-based optimization algorithms have been proposed in the literature. While most of these algorithms hold considerable promise, a majority of them are still in their infancy. For such algorithms to bloom and reach their full potential, they should be implemented in numerous optimization problems, so that not only their most suitable sets of optimization problems are recognized, but also adaptive strategies need to be introduced to make them more suitable for wider sets of optimization problems. For that, this book speciﬁcally aimed to introduce some of these potential nature-based algorithms that could be useful for multidisciplinary students including those in aeronautic engineering, mechanical engineering, indus- trial engineering, electrical and electronic engineering, chemical engineering, civil engineering, computer science, applied mathematics, physics, economy, biology, and social science, and particularly those pursuing postgraduate studies in advanced subjects. Chapter 1 of the book is a review of the basic principles of optimization and nature-based optimization algorithms. Chapters 2–15 are respectively dedicated to Cat Swarm Optimization (CSO), League Championship Algorithm (LCA), Anarchies Society Optimization (ASO), Cuckoo Optimization Algorithm (COA), Teacher-Learning-Based Optimization (TLBO), Flower Pollination Algorithm (FPA), Krill Herd Algorithm (KHA), Grey Wolf Optimization (GWO), Shark Smell Optimization (SSO), Ant Lion Optimization (ALO), Gradient Evolution (GE), Moth-Flame Optimization (MFO), Crow Search Algorithm (CSA), and Dragonﬂy Algorithm (DA). The order of the chapters corresponds to the order of chronological appearance of these algorithms, from earlier algorithms to newly introduced ones. Each chapter describes a speciﬁc algorithm and starts with a brief literature review of its development and subsequent modiﬁcation since the time of inception. This is followed by the presentation of the basic concept on which the algorithm is based and the steps of the algorithm. Each chapter closes with a pseudocode of the algorithm. Karaj, Iran Omid Bozorg-Haddad

Contents 1 2 3 4 5 6 7 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Babak Zolghadr-Asli, Omid Bozorg-Haddad and Xuefeng Chu Cat Swarm Optimization (CSO) Algorithm. . . . . . . . . . . . . . . . . . . . Mahdi Bahrami, Omid Bozorg-Haddad and Xuefeng Chu League Championship Algorithm (LCA). . . . . . . . . . . . . . . . . . . . . . Hossein Rezaei, Omid Bozorg-Haddad and Xuefeng Chu Anarchic Society Optimization (ASO) Algorithm . . . . . . . . . . . . . . . Atiyeh Bozorgi, Omid Bozorg-Haddad and Xuefeng Chu Cuckoo Optimization Algorithm (COA) . . . . . . . . . . . . . . . . . . . . . . Saba Jafari, Omid Bozorg-Haddad and Xuefeng Chu Teaching-Learning-Based Optimization (TLBO) Algorithm . . . . . . Parisa Sarzaeim, Omid Bozorg-Haddad and Xuefeng Chu Flower Pollination Algorithm (FPA) . . . . . . . . . . . . . . . . . . . . . . . . . Marzie Azad, Omid Bozorg-Haddad and Xuefeng Chu 8 Krill Herd Algorithm (KHA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Babak Zolghadr-Asli, Omid Bozorg-Haddad and Xuefeng Chu 9 Grey Wolf Optimization (GWO) Algorithm . . . . . . . . . . . . . . . . . . . Hossein Rezaei, Omid Bozorg-Haddad and Xuefeng Chu 10 Shark Smell Optimization (SSO) Algorithm . . . . . . . . . . . . . . . . . . . Sahar Mohammad-Azari, Omid Bozorg-Haddad and Xuefeng Chu 1 9 19 31 39 51 59 69 81 93 11 Ant Lion Optimizer (ALO) Algorithm. . . . . . . . . . . . . . . . . . . . . . . . 105 Melika Mani, Omid Bozorg-Haddad and Xuefeng Chu 12 Gradient Evolution (GE) Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . 117 Mehri Abdi-Dehkordi, Omid Bozorg-Haddad and Xuefeng Chu 13 Moth-Flame Optimization (MFO) Algorithm . . . . . . . . . . . . . . . . . . 131 Mahdi Bahrami, Omid Bozorg-Haddad and Xuefeng Chu 14 Crow Search Algorithm (CSA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Babak Zolghadr-Asli, Omid Bozorg-Haddad and Xuefeng Chu 15 Dragonﬂy Algorithm (DA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Babak Zolghadr-Asli, Omid Bozorg-Haddad and Xuefeng Chu

Figures Fig. 2.1 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 4.1 Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. 6.1 Fig. 7.1 Fig. 8.1 Fig. 8.2 Fig. 9.1 Fig. 9.2 Fig. 9.3 Fig. 9.4 Fig. 9.5 Fig. 10.1 Fig. 10.2 Fig. 10.3 Fig. 11.1 Fig. 11.2 Fig. 11.3 Fig. 12.1 Fig. 12.2 13 23 24 26 33 43 45 46 54 64 Flowchart of the CSO algorithm . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the basic LCA . . . . . . . . . . . . . . . . . . . . . . . . . . . A simple example of league championship scheduling . . . . . . . Procedure of the artiﬁcial match analysis in LCA . . . . . . . . . . . Flowchart of the ASO algorithm . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the COA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Random egg laying in ELR (the black circle is the cuckoo’s initial habitat with three eggs; and the white circles are the eggs at new positions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Immigration of a sample cuckoo to the target habitat . . . . . . . . Flowchart of the TLBO algorithm . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the FPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic representation of the sensing ambit around a krill individual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simpliﬁed ﬂowchart of the KHA. . . . . . . . . . . . . . . . . . . . . . . . Social hierarchy of grey wolves. . . . . . . . . . . . . . . . . . . . . . . . . Attacking toward prey versus searching for prey . . . . . . . . . . . . Updating of positions in the GWO algorithm . . . . . . . . . . . . . . Attacking toward prey and searching for prey . . . . . . . . . . . . . . Flowchart of the GWO algorithm . . . . . . . . . . . . . . . . . . . . . . . Schematic of shark’s movement toward the source of the smell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Rotational movement of a shark . . . . . . . . . . . . . . . . . . . . . . . . 99 Flowchart of the SSO algorithm . . . . . . . . . . . . . . . . . . . . . . . . 100 Antlion hunting behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Flowchart of the ALO algorithm (It = iteration counter; and IT = number of iterations). . . . . . . . . . . . . . . . . . . . . . . . . . 108 Three random walk curves in one dimension started at zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Gradient determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Search direction for the original gradient-based method . . . . . . 122 73 77 82 85 86 86 89

Fig. 12.3 Fig. 12.4 Search direction for the GE algorithm . . . . . . . . . . . . . . . . . . . . 123 Gradient approximation method modiﬁed from individual-based search to population-based search: a individual-based, b population-based . . . . . . . . . . . . . . . . . . . 123 Vector jumping operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Fig. 12.5 Fig. 12.6 Flowchart of the GE algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 127 Fig. 13.1 Moth’s spiral ﬂying path around a light source . . . . . . . . . . . . . 134 Flowchart of the MFO algorithm . . . . . . . . . . . . . . . . . . . . . . . . 135 Fig. 13.2 Fig. 14.1 Flowchart of the standard CSA . . . . . . . . . . . . . . . . . . . . . . . . . 147 Primitive corrective patterns of dragonﬂy individuals Fig. 15.1 in a swarm: a Separation; b Alignment; c Cohesion; d Food Attraction; and e Predator distraction . . . . . . . . . . . . . . 153 Flowchart of the DA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Fig. 15.2

Tables Table 2.1 Characteristics of the CSO algorithm. . . . . . . . . . . . . . . . . . . . . Table 3.1 Characteristics of the LCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 3.2 Hypothetical SWOT analysis derived from the artiﬁcial 12 21 match analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Table 4.1 Characteristics of the ASO algorithm. . . . . . . . . . . . . . . . . . . . . 34 Table 5.1 Characteristics of the COA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Table 6.1 Characteristics of the TLBO algorithm . . . . . . . . . . . . . . . . . . . 55 Table 7.1 Characteristics of the FPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Table 8.1 The characteristics of the KHA . . . . . . . . . . . . . . . . . . . . . . . . . 77 Table 9.1 Characteristics of the GWO algorithm . . . . . . . . . . . . . . . . . . . . 87 Table 10.1 Characteristics of the SSO algorithm . . . . . . . . . . . . . . . . . . . . . 101 Table 11.1 Characteristics of the ALO algorithm . . . . . . . . . . . . . . . . . . . . 108 Table 12.1 Characteristics of the GE algorithm . . . . . . . . . . . . . . . . . . . . . . 128 Table 13.1 Characteristics of the MFO algorithm . . . . . . . . . . . . . . . . . . . . 135 Table 14.1 Characteristics of the CSA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Table 15.1 Characteristics of the DA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Chapter 1 Introduction Babak Zolghadr-Asli , Omid Bozorg-Haddad and Xuefeng Chu Abstract In this chapter, some general knowledge relative to the realm of nature-inspired optimization algorithms (NIOA) is introduced. The desirable merits of these intelligent algorithms and their initial successes in many ﬁelds have inspired researchers to continuously develop such revolutionary algorithms and implement them to solve various real-world problems. Such a truly interdisciplinary environment of the research and development provides rewarding opportunities for scientiﬁc breakthrough and technology innovation. After a brief introduction to computational intelligence and its application in optimization problems, the history of the NIOA was reviewed. The relevant algorithms were then categorized in different manners. Finally, one the most groundbreaking theorems regarding the nature-inspired optimization techniques was brieﬂy discussed. 1.1 Introduction Artiﬁcial intelligence (AI) refers to any sort of intelligence that is exhibited by machines. The term of computational intelligence (CI), a branch of AI, was coined by Bezdek in the early 1990s (Bezdek 1992), which inspired the development of a B. Zolghadr-Asli O. Bozorg-Haddad (&) Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, College of Agriculture and Natural Resources, University of Tehran, 3158777871 Karaj, Iran e-mail: obhaddad@ut.ac.ir B. Zolghadr-Asli e-mail: zolghadrbabak@ut.ac.ir X. Chu Department of Civil and Environmental Engineering, North Dakota State University, Dept 2470, Fargo, ND 58108-6050, USA e-mail: xuefeng.chu@ndsu.edu

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