On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation

Abstract

A new adaptation scheme for adapting arbitrary normal mutation distributions in evolution strategies is introduced. It can adapt correct scaling and correlations between object parameters. Furthermore, it is independent of any rotation of the objective function and reliably adapts mutation distributions corresponding to hyperellipsoids with high axis ratio. In simulations, the generating set adaptation is compared to two other schemes which also can produce non axisparallel mutation ellipsoids. It turns out to be the only adaptation scheme which is completely independent of the chosen coordinate system. 1 INTRODUCTION In evolution strategies (ESs), a mutation is usually carried out by adding a N( ~ 0; A) distributed random vector 1 . The symmetric and positive semi-definite n \\Theta n-matrix A represents the parameters of the mutation distribution. Assuming that the landscape of the objective function is unknown, in general A has to be adapted to get reasonable progre...