Adaptive Parent Population Sizing in Evolution Strategies

Adaptive population sizing aims at improving the overall progress of an evolution strategy. At each generation, it determines the parental population size that promises the largest fitness gain, based on the information collected during the evolutionary process. In this paper, we develop an adaptive variant of a (μ/μ, λ) evolution strategy. Based on considerations on the sphere, we derive two approaches for adaptive population sizing. We then test these approaches empirically on the sphere model using a normalized mutation strength and cumulative mutation strength adaption. Finally, we compare the methodology on more general functions with a fixed population, covariance matrix adaption evolution strategy (CMA-ES). The results confirm that our adaptive population sizing methods yield better results than even the best fixed population size.