On the Benefits of Distributed Populations for Noisy Optimization

While in the absence of noise, no improvement in local performance can be gained from retaining but the best candidate solution found so far, it has been shown experimentally that in the presence of noise, operating with a non-singular population of candidate solutions can have a marked and positive effect on the local performance of evolution strategies. So as to determine the reasons for the improved performance, we study the evolutionary dynamics of the -ES in the presence of noise. Considering a simple, idealized environment, a moment-based approach that utilizes recent results involving concomitants of selected order statistics is developed. This approach yields an intuitive explanation for the performance advantage of multi-parent strategies in the presence of noise. It is then shown that the idealized dynamic process considered does bear relevance to optimization problems in high-dimensional search spaces