Convergence Analysis of Evolution Strategies with Random Numbers of Offspring

  • Olivier François
Conference paper

DOI: 10.1007/978-3-540-87700-4_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)
Cite this paper as:
François O. (2008) Convergence Analysis of Evolution Strategies with Random Numbers of Offspring. In: Rudolph G., Jansen T., Beume N., Lucas S., Poloni C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg

Abstract

Hitting times of the global optimum for evolutionary algorithms are usually available for simple unimodal problems or for simplified algorithms. In discrete problems, the number of results that relate the convergence rate of evolution strategies to the geometry of the optimisation landscape is restricted to a few theoretical studies. This article introduces a variant of the canonical (μ + λ)-ES, called the Poisson-ES, for which the number of offspring is not deterministic, but is instead sampled from a Poisson distribution with mean λ. After a slight change on the rank-based selection for the μ parents, and assuming that the number of offspring is small, we show that the convergence rate of the new algorithm is dependent on a geometric quantity that measures the maximal width of adaptive valleys. The argument of the proof is based on the analogy of the Poisson-ES with a basic Mutation-or-Selection evolutionary strategy introduced in a previous work.

Keywords

Evolution Strategies Discrete Optimisation Convergence Theory Markov Chains Large Deviations Mutation or Selection 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Olivier François
    • 1
  1. 1.Institut National Polytechnique de Grenoble, TIMC-IMAG, Faculté de MédecineLa TroncheFrance

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