Mirrored sampling in evolution strategies with weighted recombination

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.