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

This paper presents a performance analysis of the recentlyproposed σ-self-adaptive weighted recombinationevolution strategy (ES) with scaled weights. The steady statebehavior of this ES is investigated for the non-noisy and noisycase, and formulas for the optimal choice of the learning parameterare derived allowing the strategy to reach maximal performance. Acomparison between weighted multirecombination ES withσ-self-adaptation (σSA) and withcumulative step size adaptation (CSA) shows that the self-adaptiveES is able to reach similar (or even better) performance as its CSAcounterpart on the noisy sphere.