Genetic Programming and Evolvable Machines

, Volume 5, Issue 4, pp 327–360

On the Impact of Systematic Noise on the Evolutionary Optimization Performance—A Sphere Model Analysis

  • Hans-Georg Beyer
  • Markus Olhofer
  • Bernhard Sendhoff
Article

DOI: 10.1023/B:GENP.0000036020.79188.a0

Cite this article as:
Beyer, HG., Olhofer, M. & Sendhoff, B. Genetic Programming and Evolvable Machines (2004) 5: 327. doi:10.1023/B:GENP.0000036020.79188.a0

Abstract

Quality evaluations in optimization processes are frequently noisy. In particular evolutionary algorithms have been shown to cope with such stochastic variations better than other optimization algorithms. So far mostly additive noise models have been assumed for the analysis. However, we will argue in this paper that this restriction must be relaxed for a large class of applied optimization problems. We suggest “systematic noise” as an alternative scenario, where the noise term is added to the objective parameters or to environmental parameters inside the fitness function. We thoroughly analyze the sphere function with systematic noise for the evolution strategy with global intermediate recombination. The progress rate formula and a measure for the efficiency of the evolutionary progress lead to a recommended ratio between μ and λ. Furthermore, analysis of the dynamics identifies limited regions of convergence dependent on the normalized noise strength and the normalized mutation strength. A residual localization error R can be quantified and a second μ to λ ratio is derived by minimizing R.

evolution strategies noisy optimization performance analysis robust optimization 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Hans-Georg Beyer
    • 1
  • Markus Olhofer
    • 2
  • Bernhard Sendhoff
    • 2
  1. 1.Department of Computer Science XIUniversity of DortmundGermany
  2. 2.Honda Research Institute Europe GmbHGermany

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