sigma-Self-Adaptive Weighted Multirecombination Evolution Strategy with Scaled Weights on the Noisy Sphere

This paper presents a performance analysis of the recently proposed σ-self-adaptive weighted recombination evolution strategy (ES) with scaled weights. The steady state behavior of this ES is investigated for the non-noisy and noisy case, and formulas for the optimal choice of the learning parameter are derived allowing the strategy to reach maximal performance. A comparison between weighted multirecombination ES with σ-self-adaptation (σSA) and with cumulative step size adaptation (CSA) shows that the self-adaptive ES is able to reach similar (or even better) performance as its CSA counterpart on the noisy sphere.