Noisy Optimization with Evolution Strategies

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Format: Hardcover
Pub. Date: 2002-06-01
Publisher(s): Kluwer Academic Pub
List Price: $188.99

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Summary

Noise is a common factor in most real-world optimization problems. Sources of noise can include physical measurement limitations, stochastic simulation models, incomplete sampling of large spaces, and human-computer interaction. Evolutionary algorithms are general, nature-inspired heuristics for numerical search and optimization that are frequently observed to be particularly robust with regard to the effects of noise.Noisy Optimization with Evolution Strategies contributes to the understanding of evolutionary optimization in the presence of noise by investigating the performance of evolution strategies, a type of evolutionary algorithm frequently employed for solving real-valued optimization problems. By considering simple noisy environments, results are obtained that describe how the performance of the strategies scales with both parameters of the problem and of the strategies considered. Such scaling laws allow for comparisons of different strategy variants, for tuning evolution strategies for maximum performance, and they offer insights and an understanding of the behavior of the strategies that go beyond what can be learned from mere experimentation.This first comprehensive work on noisy optimization with evolution strategies investigates the effects of systematic fitness overvaluation, the benefits of distributed populations, and the potential of genetic repair for optimization in the presence of noise. The relative robustness of evolution strategies is confirmed in a comparison with other direct search algorithms.Noisy Optimization with Evolution Strategies is an invaluable resource for researchers and practitioners of evolutionary algorithms.

Table of Contents

Foreword vii
Acknowledgments ix
Introduction
1(6)
Preliminaries
7(14)
The Basic (μ/ρ + λ)-ES
7(3)
Mutation Strength Adaptation
10(3)
Fitness Environments
13(2)
Measuring Performance
15(2)
Modeling the Sphere
17(4)
The (1+1)-ES: Overvaluation
21(16)
Overvaluation
21(7)
Performance
28(4)
Discussion
32(5)
The (μ, λ)-ES: Distributed Populations
37(16)
Modeling the Population
38(1)
The Infinite Noise Limit
39(3)
Finite Noise Strength
42(6)
The Spherical Environment
48(5)
The (μ/μ,λ)-ES: Genetic Repair
53(26)
Simple Performance Analysis
54(6)
Improving the Accuracy
60(6)
Cumulative Mutation Strength Adaptation
66(13)
Comparing Approaches to Noisy Optimization
79(18)
The Competitors
80(9)
The Competition
89(8)
Conclusions
97(6)
Appendices 103(46)
A. Some Statistical Basics
105(8)
1 Random Variables and Probability Distributions
105(1)
2 Moments and Cumulants
106(3)
3 Some Important Distributions
109(1)
4 Expansions of Probability Distributions
110(2)
5 Order Statistics
112(1)
B. Some Useful Identities
113(10)
C. Computing the Overvaluation
123(8)
1 Preliminaries
123(1)
2 Obtaining the Distribution
124(3)
3 Determining the Stability of the Fixed Point
127(1)
4 Success Probability and Quality Gain
127(4)
D. Determining the Effects of Sampling and Selection
131(18)
1 Sample Moments as Sums of Products
132(2)
2 The Infinite Noise Limit
134(1)
3 Noisy Order Statistics
135(3)
4 Expanding the Probability Functions
138(7)
5 A Corollary for Normal Samples
145(1)
6 Mathematica Code
145(4)
References 149(8)
Index 157

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