Weighted Multirecombination Evolution Strategies on the Parabolic Ridge

Weighted recombination is a means for improving the local search performance of evolution strategies. Optimal weights for the infinite-dimensional sphere model have been computed previously. This paper extends that work by considering the parabolic ridge. It is found that in the limit of infinite search space dimensionality the speed-up resulting from optimal weighted recombination is the same as on the sphere, and that, importantly, optimal weights are the same in both cases. The effect of weighted recombination on cumulative step length adaptation on the parabolic ridge is also examined. Experiments are used to study the significance of the findings in finite-dimensional search spaces, and to arrive at recommendations with regard to the setting of strategy parameters.