Mirrored sampling and sequential selection for evolution strategies

Authors:
Dimo Brockhoff;Anne Auger;Nikolaus Hansen;Dirk V. Arnold;Tim Hohm
Affiliations:
INRIA Saclay, LRI Paris Sud University, Orsay Cedex, France;INRIA Saclay, LRI Paris Sud University, Orsay Cedex, France;INRIA Saclay, LRI Paris Sud University, Orsay Cedex, France;Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada;Department of Medical Genetics, University of Lausanne, Lausanne, Switzerland
Venue:
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Year:
2010

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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.