On the use of evolution strategies for optimization on spherical manifolds

Abstract

We study the behaviour of evolution strategies applied to a simple class of unimodal optimization problems on spherical manifolds. The techniques used are the same as those commonly employed for the analysis of the behaviour of evolution strategies in Euclidean search spaces. However, we find that there are significant differences in strategy behaviour unless the vicinity of an optimal solution has been reached. Experiments with cumulative step size adaptation reveal the existence of metastable states associated with large step sizes, which can preclude reaching optimal solutions.