Cumulative step length adaptation for evolution strategies using negative recombination weights

Abstract

Cumulative step length adaptation is a mutation strength control mechanism commonly employed with evolution strategies. When using weighted recombination with negative weights it can be observed to be prone to failure, often leading to divergent behaviour in low-dimensional search spaces. This paper traces the reasons for this breakdown of step length control. It then proposes a novel variant of the algorithm that reliably results in convergent behaviour for the test functions considered. The influence of the dimensionality as well as of the degree of ill-conditioning on optimisation performance are evaluated in computer experiments. Implications for the use of weighted recombination with negative weights are discussed. © 2008 Springer-Verlag Berlin Heidelberg.