Optimal Weighted Recombination

Weighted recombination is a means for improving the local search performance of evolution strategies. It aims to make effective use of the information available, without significantly increasing computational costs per time step. In this paper, the potential speed-up resulting from using rank-based weighted recombination is investigated. Optimal weights are computed for the sphere model, and comparisons with the performance of strategies that do not make use of weighted recombination are presented. It is seen that unlike strategies that rely on unweighted recombination and truncation selection, weighted multirecombination evolution strategies are able to improve on the serial efficiency of the (1+1)-ES on the sphere. The implications of the use of weighted recombination for noisy optimization are studied, and parallels to the use of rescaled mutations are drawn. The cumulative step length adaptation mechanism is formulated for the case of an optimally weighted evolution strategy, and its performance is analyzed.

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