Investigating Adaptive Population Control Strategies With Cumulative Step-Size Adaptation

Three state-of-the-art adaptive population control strategies (PCS) are theoretically and empirically investigated for a multi-recombinative, cumulative step-size adaptation Evolution Strategy μλ-CSA-ES. First, scaling properties for the generation number and mutation strength rescaling are derived on the sphere in the limit of large population sizes. Then, the adaptation properties of three standard CSA variants are studied for varying population size and dimensionality, and compared to the predicted scaling results. Thereafter, three PCS are implemented along the CSA-ES and studied on a test bed of sphere, random, and Rastrigin functions. The CSA properties significantly influence the performance and stability of PCS, which is shown in greater detail. Given the test bed, well-performing parameter sets (in terms of scaling, efficiency, and success rate) for both the CSA-and PCS-subroutines are identified.