Multi-Objective Optimization using Artificial Intelligence Techniques

By Seyedali Mirjalili and Jin Song Dong

This book focuses on the most well-regarded and recent nature-inspired algorithms capable of solving optimization problems with multiple objectives. Firstly, it provides preliminaries and essential definitions in multi-objective problems and different paradigms to solve them. It then presents an in-depth explanations of the theory, literature review, and applications of several widely-used algorithms, such as Multi-objective Particle Swarm Optimizer, Multi-Objective Genetic Algorithm and Multi-objective GreyWolf Optimizer Due to the simplicity of the techniques and flexibility, readers from any field of study can employ them for solving multi-objective optimization problem. The book provides the source codes for all the proposed algorithms on a dedicated webpage.

• Language: English
• Publisher: Springer
• Release date: Jul 24, 2019
• ISBN: 9783030248352

Seyedali Mirjalili

Dr. Mirjalili has gained international recognition for his contributions to nature-inspired artificial intelligence techniques. He has been on the list of the top 1% of highly-cited researchers since 2019, and the Web of Science named him one of the most influential researchers in the world. In 2022 and 2023, The Australian newspaper recognized him as a global leader in Artificial Intelligence and a national leader in the Evolutionary Computation and Fuzzy Systems fields. He also holds a post as Adjunct Principal Research Fellow at the Institute for Integrated and Intelligent Systems, Griffith University (Australia). He serves as a senior member of IEEE and covers editorial positions at several top AI-related journals published by Elsevier, including Engineering Applications of Artificial Intelligence, Applied Soft Computing, Neurocomputing, Advances in Engineering Software, Computers in Biology and Medicine, Healthcare Analytics, and Decision Analytics.

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Seyedali Mirjalili and Jin Song Dong

Multi-Objective Optimization using Artificial Intelligence Techniques

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Seyedali Mirjalili

Torrens University Australia, Fortitude Valley, Brisbane, QLD, Australia

Jin Song Dong

Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD, Australia

Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

ISSN 2191-530Xe-ISSN 2191-5318

SpringerBriefs in Applied Sciences and Technology

ISSN 2625-3704e-ISSN 2625-3712

SpringerBriefs in Computational Intelligence

ISBN 978-3-030-24834-5e-ISBN 978-3-030-24835-2

https://doi.org/10.1007/978-3-030-24835-2

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

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To my father and mother

Preface

This book focuses on the most well-regarded and recent nature-inspired algorithms capable of solving optimization problems with multiple objectives. First, the book provides preliminaries and essential definitions in multi-objective problems and different paradigms to solve them. It then provides an in-depth explanation of the theory, literature review, and applications of several widely used algorithms. The algorithms are Multi-objective Particle Swarm Optimizer (MOPSO), Multi-Objective Genetic Algorithm (NSGA-II), and Multi-objective Grey Wolf Optimizer (MOGWO).

Dr.Seyedali Mirjalili

Prof.Jin Song Dong

Brisbane, Australia

July 2019

Acronyms

$$ \text{EA} $$

Evolutionary algorithm

$$ \text{GA} $$

Genetic Algorithm

$$ \text{PSO} $$

Particle Swarm Optimization

$$ \text{GWO} $$

Grey Wolf Optimizer

$$ \text{SA} $$

Simulated Annealing

$$ \text{MOPSO} $$

Multi-Objective Particle Swarm Optimization

$$ \text{MOGWO} $$

Multi-Objective Grey Wolf Optimizer

$$ \text{NSGA} $$

Non-dominated Sorting Genetic Algorithm

$$ \text{PF} $$

Pareto Optimal Front

Contents

1 Introduction to Multi-objective Optimization 1

1.​1 Introduction 1

1.​2 Uninformed and Heuristic AI Search Methods 1

1.​3 Popularity of AI Heuristics and Metaheuristics 2

1.​4 Exploration Versus Exploitation in Heuristics and Metaheuristics 4

1.​5 Different Methods of Multi-objective Search (Optimization) 7

1.​6 Scope and Structure of the Book 8

References 8

2 What is Really Multi-objective Optimization?​ 11

2.​1 Introduction 11

2.​2 Essential Definitions 11

2.3 A Classification $$ f $$ Multi-objective Optimization Algorithms 14

2.​4 A Priori Multi-objective Optimization 16

2.​5 A Posteriori Multi-objective Optimization 18

2.​6 Interactive Multi-objective Optimization 19

2.​7 Conclusion 19

References 19

3 Multi-objective Particle Swarm Optimization 21

3.​1 Introduction 21

3.​2 Particle Swarm Optimization 22

3.​3 Multi-objective Particle Swarm Optimization 27

3.​4 Results 30

3.​4.​1 The Impact of the Mutation Rate 30

3.​4.​2 The Impact of the Inertial Weight 32

3.4.3 The Impact of Personal ( $$ c_1 $$ ) and Social ( $$ c_2 $$ ) Coefficients 32

3.​5 Conclusion 35

References 35

4 Non-dominated Sorting Genetic Algorithm 37

4.​1 Introduction 37

4.​2 Multi-objective Genetic Algorithm 38

4.​3 Results 39

4.3.1 The Impact of the Mutation Rate ( $$ P_m $$ ) 39

4.3.2 The Impact of the Crossover Rate ( $$ P_c $$ ) 42

4.​3.​3 Conclusion 45

References 45

5 Multi-objective Grey Wolf Optimizer 47

5.​1 Introduction 47

5.​2 Grey Wolf Optimizer 48

5.​3 Multi-objective Grey Wolf Optimizer 50

5.​4 Literature Review of MGWO 52

5.​4.​1 Variants 52

5.​4.​2 Applications 53

5.​5 Results of MOGWO 54

5.5.1 The Impact of the Parameter $$ a $$ 54

5.5.2 The Impact of the Parameter $$ c $$ 54

5.​6 Conclusion 56

References 57

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Seyedali Mirjalili and Jin Song DongMulti-Objective Optimization using Artificial Intelligence TechniquesSpringerBriefs in Applied Sciences and Technologyhttps://doi.org/10.1007/978-3-030-24835-2_1

1. Introduction to Multi-objective Optimization

Seyedali Mirjalili¹  and Jin Song Dong², ³

(1)

Torrens University Australia, 90 Bowen Terrace, Fortitude Valley, Brisbane, QLD, 4006, Australia

(2)

Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD, Australia

(3)

Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

1.1 Introduction

In the field of Artificial Intelligence (AI), search algorithms have been popular since their invention. A search algorithm is typically designed to search and find a desired solution from a given set of all possible solutions to maximize/minimize one or multiple objectives. Depending on the mechanism of a search method, this set of solution can be searched entirely or partially. A search algorithm starts with an initial state (solution), and the ultimate goal is to find a target state (solution). Note that there might be multiple targets in case of multi-objective search that will be discussed in a later section. One of the main challenges in the field of AI is that the set that should be searched by a search algorithm exponentially grows proportional to the size of the problem and the number of objectives. This was not an issue in the past when the problems were less complex and challenging. These days, however, this issue should be addressed when solving a wide range of problems.

1.2 Uninformed and Heuristic AI Search Methods

One of the most well-regarded classifications in the