Mirrored Sampling in Evolution Strategies With Weighted Recombination

Anne Auger 1 Dimo Brockhoff 2, * Nikolaus Hansen 1, 3, 4
* Corresponding author
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 LRI - Laboratoire de Recherche en Informatique
4 MSR - INRIA - Microsoft Research - Inria Joint Centre
Abstract : This paper introduces mirrored sampling into evolution strategies (ESs) with weighted multi-recombination. Two further heuristics are introduced: pairwise selection selects at most one of two mirrored vectors in order to avoid a bias due to recombination. Selective mirroring only mirrors the worst solutions of the population. Convergence rates on the sphere function are derived that also yield upper bounds for the convergence rate on any spherical function. The optimal fraction of offspring to be mirrored is regardless of pairwise selection one without selective mirroring and about 19% with selective mirroring, where the convergence rate reaches a value of 0.390. This is an improvement of 56% compared to the best known convergence rate of 0.25 with positive recombination weights.
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Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Mirrored Sampling in Evolution Strategies With Weighted Recombination. Genetic and Evolutionary Computation Conference (GECCO 2011), SIGEVO, Jul 2011, Dublin, Ireland. pp.861-868, ⟨10.1145/2001576.2001694⟩. ⟨inria-00612522⟩

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