Parallel Problem Solving from Nature, PPSN XI

Volume 6238 of the series Lecture Notes in Computer Science pp 11-21

Mirrored Sampling and Sequential Selection for Evolution Strategies

  • Dimo BrockhoffAffiliated withTAO Team, INRIA Saclay, LRI Paris Sud University
  • , Anne AugerAffiliated withTAO Team, INRIA Saclay, LRI Paris Sud University
  • , Nikolaus HansenAffiliated withTAO Team, INRIA Saclay, LRI Paris Sud University
  • , Dirk V. ArnoldAffiliated withFaculty of Computer Science, Dalhousie University
  • , Tim HohmAffiliated withDepartment of Medical Genetics, University of Lausanne

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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.