On the performance of (1, λ)-evolution strategies for the ridge function class

This paper presents the N-dependent analysis of the (1, λ)-evolution strategy (ES) with isotropic mutations for the ridge functions including the special cases of sharp and parabolic ridges. The new approach presented allows for the prediction of the dynamics in ridge direction as well as in radial direction. The central quantities are the corresponding progress rates which are determined in terms of analytical expressions. Its predictive quality is evaluated by ES simulations and the steady-state behavior is discussed in detail