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Evolutionary algorithms are bio-inspired algorithms based on Darwin's theory of evolution. They are expected to provide non-optimal but good quality solutions to problems whose resolution is impracticable by exact methods.

In six chapters, this book presents the essential knowledge required to efficiently implement evolutionary algorithms.

Chapter 1 describes a generic evolutionary algorithm as well as the basic operators that compose it. Chapter 2 is devoted to the solving of continuous optimization problems, without constraint. Three leading approaches are described and compared on a set of test functions. Chapter 3 considers continuous optimization problems with constraints. Various approaches suitable for evolutionary methods are presented. Chapter 4 is related to combinatorial optimization. It provides a catalog of variation operators to deal with order-based problems. Chapter 5 introduces the basic notions required to understand the issue of multi-objective optimization and a variety of approaches for its application. Finally, Chapter 6 describes different approaches of genetic programming able to evolve computer programs in the context of machine learning.



Table of Contents

Preface xi

Chapter 1 Evolutionary Algorithms 1

1.1 From natural evolution to engineering 1

1.2 A generic evolutionary algorithm 3

1.3 Selection operators 5

1.4 Variation operators and representation 21

1.5 Binary representation 25

1.6 The simple genetic algorithm 30

1.7 Conclusion 31

Chapter 2 Continuous Optimization 33

2.1 Introduction 33

2.2 Real representation and variation operators for evolutionary algorithms 35

2.3 Covariance Matrix Adaptation Evolution Strategy 46

2.4 A restart CMA Evolution Strategy 55

2.5 Differential Evolution (DE) 57

2.6 Success-History based Adaptive Differential Evolution (SHADE) 65

2.7 Particle Swarm Optimization 70

2.8 Experiments and performance comparisons 77

2.9 Conclusion 88

2.10 Appendix: set of basic objective functions used for the experiments 89

Chapter 3 Constrained Continuous Evolutionary Optimization 93

3.1 Introduction 93

3.2 Penalization 98

3.3 Superiority of feasible solutions 112

3.4 Evolving on the feasible region 117

3.5 Multi-objective methods 123

3.6 Parallel population approaches 130

3.7 Hybrid methods 132

3.8 Conclusion 132

Chapter 4 Combinatorial Optimization 135

4.1 Introduction 135

4.2 The binary representation and variation operators 140

4.3 Order-based Representation and variation operators 143

4.4 Conclusion 163

Chapter 5 Multi-objective Optimization 165

5.1 Introduction 165

5.2 Problem formalization 166

5.3 The quality indicators 167

5.4 Multi-objective evolutionary algorithms 169

5.5 Methods using a "Pareto rankingö 169

5.6 Many-objective problems 176

5.7 Conclusion 181

Chapter 6 Genetic Programming for Machine Learning 183

6.1 Introduction 183

6.2 Syntax tree representation 186

6.3 Evolving the syntax trees 187

6.4 GP in action: an introductory example 194

6.5 Alternative Genetic Programming Representations 200

6.6 Example of application: intrusion detection in a computer system 210

6.7 Conclusion 215

Bibliography 217

Index 233