A median success rule for non-elitist evolution strategies: Study of feasibility

Success rule based step-size adaptation, namely the one-fifth success rule, has shown to be effective for single parent evolution strategies (ES), e.g. the (1+1)-ES. The success rule remains feasible in non-elitist single parent strategies, where the target success rate must be roughly inversely proportional to the population size. This success rule is, however, not easily applicable to multi-parent strategies. In this paper, we introduce the median success rule for step-size adaptation, applicable to non-elitist multi-recombinant evolution strategies. The median success rule compares the median fitness of the population to a fitness from the previous iteration. The comparison fitness is chosen to achieve a target success rate of 1/2, thereby a deviation from the target can be measured reliably in comparatively few iteration steps. As a prerequisite for feasibility of the median success rule, we studied the way the fitness comparison quantile depends on the search space dimension, the population size, the parent number, the recombination weights and the objective function. The findings are encouraging: the choice of the comparison quantile appears to be relatively uncritical and experiments on a variety of functions, also in combination with CMA, reveal reasonable behavior.