DMCA
Performance Analysis of Evolution Strategies with Multi-Recombination
| Venue: | in High-Dimensional R N -Search Spaces Disturbed by Noise. Theoretical Computer Science |
| Citations: | 14 - 10 self |
BibTeX
@INPROCEEDINGS{Arnold_performanceanalysis,
author = {Dirk V. Arnold and Hans-georg Beyer},
title = {Performance Analysis of Evolution Strategies with Multi-Recombination},
booktitle = {in High-Dimensional R N -Search Spaces Disturbed by Noise. Theoretical Computer Science},
year = {}
}
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Abstract
The presence of noise in real-world optimization problems poses difficulties to optimization strategies. It is frequently observed that evolutionary algorithms are quite capable of succeeding in noisy environments. Intuitively, the use of a population of candidate solutions alongside with some implicit or explicit form of averaging inherent in the algorithms is considered responsible. However, so as to arrive at a deeper understanding of the reasons for the capabilities of evolution-ary algorithms, mathematical analyses of their performance in select environments are necessary. Such analyses can reveal how the performance of the algorithms scales with parameters of the problem — such as the dimensionality of the search space or the noise strength — or of the algo-rithms — such as population size or mutation strength. Recommendations regarding the optimal sizing of such parameters can then be derived. The present paper derives an asymptotically exact approximation to the progress rate of the (µ=µI;λ)-Evolution Strategy (ES) on a finite-dimensional noisy sphere. It is shown that, in con-trast to results obtained in the limit of infinite search space dimensionality, there is a finite optimal population size above which the efficiency of the strategy declines, and that therefore it is not possible to attain the efficiency that can be achieved in the absence of noise by increasing the population size. It is also shown that nonetheless, the benefits of genetic repair and an increased mutation strength make it possible for the multi-parent (µ=µI;λ)-ES to far outperform simple one-parent strategies.
Keyphrases
evolution strategy performance analysis mutation strength population size finite-dimensional noisy noisy environment progress rate finite optimal population size select environment search space optimization strategy optimal sizing exact approximation simple one-parent strategy evolutionary algorithm noise strength candidate solution mathematical analysis real-world optimization problem genetic repair evolution-ary algorithm infinite search space dimensionality present paper explicit form
