Efficiency and mutation strength adaptation of the (μ/μi, λ)-ES in a noisy environment

Abstract

Noise is present in many optimization problems. Evolutionary algorithms are frequently reported to be robust with regard to the effects of noise. In many cases, there is a tradeoff between the accuracy with which the fitness of a candidate solution is determined and the number of candidate solutions that are evaluated in every time step. This paper addresses this tradeoff on the basis of recently established results from the analysis of the local performance of a recombinant multi-parent evolution strategy on a noisy sphere. It is shown that, provided that mutation strengths are appropriately adapted, the strategy is indeed able to cope with noise, and that results previously obtained for single-parent evolution strategies do not carry over to multi-parent strategies. Then, the problem of mutation strength adaptation in noisy environments is addressed. Mutative self-adaptation and the cumulative mutation strength adaptation algorithm are compared empirically in a simple fitness environment. The results suggest that both algorithms are prone to failure in the presence of noise.