Mirrored Sampling and Sequential Selection for Evolution Strategies

  • Dimo Brockhoff
  • Anne Auger
  • Nikolaus Hansen
  • Dirk V. Arnold
  • Tim Hohm
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6238)

Abstract

This paper reveals the surprising result that a single-parent non-elitist evolution strategy (ES) can be locally faster than the (1+1)-ES. The result is brought about by mirrored sampling and sequential selection. With mirrored sampling, two offspring are generated symmetrically or mirrored with respect to their parent. In sequential selection, the offspring are evaluated sequentially and the iteration is concluded as soon as one offspring is better than the current parent. Both concepts complement each other well. We derive exact convergence rates of the (1,λ)-ES with mirrored sampling and/or sequential selection on the sphere model. The log-linear convergence of the ES is preserved. Both methods lead to an improvement and in combination the (1,4)-ES becomes about 10% faster than the (1+1)-ES. Naively implemented into the CMA-ES with recombination, mirrored sampling leads to a bias on the step-size. However, the (1,4)-CMA-ES with mirrored sampling and sequential selection is unbiased and appears to be faster, more robust, and as local as the (1+1)-CMA-ES.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dimo Brockhoff
    • 1
  • Anne Auger
    • 1
  • Nikolaus Hansen
    • 1
  • Dirk V. Arnold
    • 2
  • Tim Hohm
    • 3
  1. 1.TAO Team, INRIA SaclayLRI Paris Sud UniversityOrsay CedexFrance
  2. 2.Faculty of Computer ScienceDalhousie UniversityHalifax, Nova ScotiaCanada
  3. 3.Department of Medical GeneticsUniversity of LausanneLausanneSwitzerland

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