Adaptive Differential Evolution (eBook)

A Robust Approach to Multimodal Problem Optimization

Jingqiao Zhang, Arthur C. Sanderson (Autoren)

eBook Download: PDF

2009
XIII, 164 Seiten
Springer Berlin (Verlag)
978-3-642-01527-4 (ISBN)

Infos

The fundamental theme of this book is theoretical study of differential evolution and algorithmic analysis of parameter adaptive schemes. The book offers real-world insights into a variety of large-scale complex industrial applications.

Inhalt

Foreword 6
Contents 9
Acronyms 13
Introduction 14
Research Motivation 15
Research Contribution 16
Related Work and Background 18
Evolutionary Algorithms 18
Evolution Strategies 19
Evolutionary Programming 20
Genetic Algorithms 20
Genetic Programming 20
Differential Evolution 21
Parameter Control 22
Multi-objective Optimization 24
No Free Lunch Theorem and Domain Knowledge Utilization 25
Theoretical Analysis of Differential Evolution 27
Introduction 27
Properties of Differential Evolution 29
DE/rand/k/bin without Crossover 29
Properties of Mutation 29
Properties of Selection 30
An Approximate Model of DE 31
Analyses of the Evolution Process of DE 33
Mathematical Formulation of DE 33
Calculation of E(z) 34
Calculation of $/sigma_{z1}$ 38
Calculation of $/sigma_{z2}$ 39
From $/{/vec{z}_{i,g}/}$ to $/{/vec{x} _{i,g+1}/}$ 41
Numerical Evaluation and Discussions 42
Performance Metrics 42
Progress Rate 43
Evolution of $/sigma^{*}_{x1}$ and $/sigma^{*}_{x2}$ 43
Steady Point 45
Dynamic Behavior of DE 45
Effect of Mutation Factor 46
Summary 48
Appendix 49
Proof of Property 3.3 49
Proof of Eqs. (3.16) and (3.34) 50
Parameter Adaptive Differential Evolution 51
Introduction 51
Adaptive DE Algorithms 53
DESAP 53
FADE 53
SaDE 54
SaNSDE 55
jDE 55
Algorithms Comparison 56
JADE: A New Adaptive Differential Evolution Algorithm 58
Initialization 58
Mutation 58
Crossover 60
Selection 60
Adaptation of $µ_{CR}$ 61
Adaptation of $µ_{F}$ 62
Explanation of Parameter Adaptation 63
Discussion of Parameter Settings 64
Algorithm Complexity 64
Performance Analysis for Low- to Moderate-Dimensional Problems 64
Comparison of JADE with Other Evolutionary Algorithms 66
Benefit of JADE’s Components 74
Evolution of $µ_{F}$ and $µ_{CR}$ in JADE 75
Parameter Values of JADE 76
Performance Analysis in a Noisy Environment 76
Scalability Analysis for High-Dimensional Problems 79
Comparison of Different Adaptive DE Algorithms 80
Scalability of Different Adaptive DE Algorithms 85
Comparison of JADE+ with Coevolutionary Algorithms 87
Summary 88
Appendix: Stochastic Properties of the Mutation and Crossover of JADE 89
A Simplified Model 89
Mathematical Analysis 90
Proof of Proposition 4.1 91
Surrogate Model-Based Differential Evolution 95
Introduction 95
Adaptive Differential Evolution 96
RBF Surrogate Model 97
DE-AEC: Differential Evolution with Adaptive Evolution Control 98
Procedure of DE-AEC 98
Explanation of q, S and K 100
Performance Evaluation 101
Success Rate and Success Performance 101
Simulation Results 101
Summary 104
Adaptive Multi-objective Differential Evolution 106
Introduction 106
Multi-objective Evolutionary Algorithms 108
PAES 108
SPEA2 108
PESA 109
NSGA and NSGA-II 109
Differential Evolution Based MOEAs 109
JADE for Multi-objective Optimization 111
Pareto Dominance and Crowding Density 111
Selection 111
Mutation 113
Performance Comparison 114
Comparison Based on Conventional Performance Metrics 115
Pareto-Compliant Performance Metrics 116
Experimental Results 121
Summary 124
Application to Winner Determination Problems in Combinatorial Auctions 125
Introduction 125
Problem Description and Current Approaches 127
Winner Determination in Combinatorial Auctions 127
Current Approaches 127
Utilization of Domain Knowledge 128
Representation Scheme for Discrete Optimization 128
Regeneration Operation 129
Seeding JADE 131
Performance Comparison 131
Experimental Setting 132
Comparison Results 132
Summary 135
Application to Flight Planning in Air Traffic Control Systems 136
Introduction 136
Problem Formulation 137
Utilization of Domain Knowledge 139
Simulation 140
Summary 143
Application to the TPM Optimization in Credit Decision Making 144
Introduction 144
Problem Formulation 146
Utilization of Domain Knowledge 148
Simulation 149
Performance Comparison 150
Comparison of Optimized TPM with Empirical Data 153
Summary 154
Conclusions and Future Work 155
Summary 155
Future Work 156
Coevolutionary Algorithms 157
Constrained Optimization 157
Optimization in a Noisy Environment 158
References 159
Index 170

Produkt-Details

• Erscheint lt. Verlag: 9.7.2009
• Reihe/Serie: Adaptation, Learning, and Optimization
• Reihe/Serie: Adaptation, Learning, and Optimization
• Zusatzinfo: XIII, 164 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Schlagworte: adaptive parameter control • algorithms • Combinatorial auction • Differential evolution • Evolution • evolutionary algorithm • evolutionary optimization • expensive optimization • flight-route planning • Multi-Objective Optimization • Optimization • Racter • transition probability matrix optimization
• ISBN-10: 3-642-01527-1 / 3642015271
• ISBN-13: 978-3-642-01527-4 / 9783642015274