Evolutionary Multi-objective Optimization in Uncertain Environments

Issues and Algorithms

By: Chi-Keong Goh, Kay Chen Tan

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Hardcover | 9 March 2009

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Evolutionary algorithms are sophisticated search methods that have been found to be very efficient and effective in solving complex real-world multi-objective problems where conventional optimization tools fail to work well. Despite the tremendous amount of work done in the development of these algorithms in the past decade, many researchers assume that the optimization problems are deterministic and uncertainties are rarely examined.

The primary motivation of this book is to provide a comprehensive introduction on the design and application of evolutionary algorithms for multi-objective optimization in the presence of uncertainties. In this book, we hope to expose the readers to a range of optimization issues and concepts, and to encourage a greater degree of appreciation of evolutionary computation techniques and the exploration of new ideas that can better handle uncertainties. "Evolutionary Multi-Objective Optimization in Uncertain Environments: Issues and Algorithms" is intended for a wide readership and will be a valuable reference for engineers, researchers, senior undergraduates and graduate students who are interested in the areas of evolutionary multi-objective optimization and uncertainties.

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Introduction	p. 1
Multi-objective Optimization	p. 1
Totally Conflicting, Non-conflicting, and Partially Conflicting Multi-objective Problems	p. 2
Pareto Dominance and Optimality	p. 3
Multi-objective Optimization Goals	p. 5
Evolutionary Multi-objective Optimization	p. 5
MOEA Framework	p. 6
Basic MOEA Components	p. 8
Benchmark Problems	p. 16
Performance Metrics	p. 18
Empirical Analysis and Performance Assessment Adequacy for EMO Techniques	p. 21
Preliminary Discussions	p. 21
Systematic Design for Empirical Assessment	p. 25
Survey on Experimental Specifications	p. 31
Conceptualizing Empirical Adequacy	p. 33
Case Studies	p. 36
Overview of This Book	p. 38
Conclusion	p. 39
Evolving Solution Sets in the Presence of Noise
Noisy Eyolutionary Multi-objective Optimization	p. 43
Noisy Multi-objective Optimization Problems	p. 44
Performance Metrics for Noisy Multi-objective Optimization	p. 45
Empirical Results of Noise Impact	p. 46
General MOEA Behavior under Different Noise Levels	p. 47
MOEA Behavior in the Objective Space	p. 50
MOEA Behavior in Decision Space	p. 53
Conclusion	p. 54
Handling Noise in Evolutionary Multi-objective Optimization	p. 55
Estimate Strength Pareto Evolutionary Algorithm	p. 56
Multi-Objective Probabilistic Selection Evolutionary Algorithm	p. 60
Noise Tolerant Strength Pareto Evolutionary Algorithm	p. 63
Modified Non-dominated Sorting Genetic Algorithm II	p. 65
Multi-objective Evolutionary Algorithm for Epistemic Uncertainty	p. 67
Indicator-Based Evolutionary Algorithm for Multi-objective Optimization	p. 70
Multi-Objective Evolutionary Algorithm with Robust Features	p. 72
Comparative Study	p. 80
Effects of the Proposed Features	p. 92
Further Examination	p. 97
Conclusion	p. 98
Handling Noise in Evolutionary Neural Network Design	p. 101
Singular Value Decomposition for ANN Design	p. 102
Rank-Revealing Decomposition	p. 102
Actual Rank of Hidden Neuron Matrix	p. 103
Estimating the Threshold	p. 106
Moore-Penrose Generalized Pseudoinverse	p. 107
Hybrid Multi-Objective Evolutionary Neural Networks	p. 107
Algorithmic Flow of HMOEN	p. 107
Multi-Objective Fitness Evaluation	p. 108
Variable-Length Representation for ANN Structure	p. 109
SVD-Based Architectural Recombination	p. 109
Micro-Hybrid Genetic Algorithm	p. 112
Experimental Study	p. 114
Experimental Setup	p. 114
Analysis of HMOEN Performance	p. 116
Conclusion	p. 121
Tracking Dynamic Multi-objective Landscapes
Dynamic Evolutionary Multi-objective Optimization	p. 125
Dynamic Multi-objective Optimization Problems	p. 126
Dynamic Multi-objective Problem Categorization	p. 126
Dynamic Multi-objective Test Problems	p. 128
TLK2 Dynamic Test Function	p. 129
FDA Dynamic Test Functions	p. 130
dMOP Test Functions	p. 131
DSW Test Functions	p. 133
JS Test Functions	p. 134
Performance Metrics for Dynamic Multi-objective Optimization	p. 135
Illustrating Performance Using Static Performance Measures	p. 135
Time Averaging Static Performance Measures	p. 136
Evolutionary Dynamic Optimization Techniques	p. 138
Design Issues	p. 138
Directional-Based Dynamic Evolutionary Multi-objective Optimization Algorithm	p. 141
Dynamic Non-dominated Sorting Genetic Algorithm II	p. 142
Dynamic Multi-objective Evolutionary Algorithm Based on an Orthogonal Design	p. 144
Dynamic Queuing Multi-objective Optimizer	p. 146
Multi-objective Immune Algorithm	p. 148
Conclusion	p. 152
A Coevolutionary Paradigm for Dynamic Multi-Objective Optimization	p. 153
Competition, Cooperation, and Competitive-Cooperation in Coevolution	p. 154
Competitive Coevolution	p. 154
Cooperative Coevolution	p. 155
Competitive-Cooperative Coevolution	p. 158
Applying Competitive-Cooperation Coevolution for Multi-objective Optimization	p. 160
Cooperative Mechanism	p. 161
Competitive Mechanism	p. 162
Implementation	p. 164
Adapting COEA for Dynamic Multi-objective Optimization	p. 165
Introducing Diversity via Stochastic Competitors	p. 165
Handling Outdated Archived Solutions	p. 167
Static Environment Empirical Study	p. 168
Comparative Study of COEA	p. 168
Effects of the Competitive Mechanism	p. 172
Effects of Different Competition Schemes	p. 174
Dynamic Environment Empirical Study	p. 177
Comparative Study	p. 177
Effects of Stochastic Competitors	p. 182
Effects of Temporal Memory	p. 182
Conclusion	p. 185
Evolving Robust Solution Sets
Robust Evolutionary Multi-objective Optimization	p. 189
Robust Multi-objective Optimization Problems	p. 189
Robust Measures	p. 190
Robust Optimization Problems	p. 191
Robust Continuous Multi-objective Test Problem Design	p. 192
Robust Multi-objective Problem Categorization	p. 192
Empirical Analysis of Existing Benchmark Features	p. 194
Robust Continuous Multi-objective Test Problem Design	p. 197
Basic Landscape Generation	p. 199
Changing the Decision Space	p. 202
Changing the Solution Space	p. 202
Example of a Robust Multi-objective Test Suite	p. 203
Vehicle Routing Problem with Stochastic Demand	p. 207
Problem Features	p. 208
Problem Formulation	p. 210
Conclusion	p. 211
Evolving Robust Solutions in Multi-Objective Optimization	p. 213
Evolutionary Robust Optimization Techniques	p. 214
Single-Objective Approach	p. 214
Multi-objective Approach	p. 215
Robust Multi-Objective Optimization Evolutionary Algorithm	p. 216
Empirical Analysis	p. 219
Fitness Inheritance for Robust Optimization	p. 219
Evaluating GTCO Test Suite	p. 219
Evaluating VRPSD Test Problems	p. 225
Conclusion	p. 227
Evolving Robust Routes	p. 229
Overview of Existing Works	p. 229
Hybrid Evolutionary Multi-Objective Optimization	p. 230
Variable-Length Chromosome	p. 231
Local Search Exploitation	p. 232
Route-Exchange Crossover	p. 232
Multi-mode Mutation	p. 233
Route Simulation Method	p. 235
Computing Budget	p. 236
Algorithmic Flow of HMOEA	p. 237
Simulation Results and Analysis	p. 238
Performance of Hybrid Local Search	p. 239
Comparison with a Deterministic Approach	p. 241
Effects of Sample Size, H	p. 244
Effects of M	p. 246
Conclusion	p. 247
Final Thoughts	p. 249
References	p. 253
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Evolutionary Multi-objective Optimization in Uncertain Environments

Issues and Algorithms

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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