A New Step-Size Adaptation Rule for CMA-ES Based on the Population Midpoint Fitness

In this paper, we present the CMA-ES algorithm with a step-size adaptation rule which is inspired by the 1/5th success rule. The method, called PPMF (Previous Population Midpoint Fitness), adjusts the step-size multiplier sigma using the comparison of fitness values of the current population of points and the midpoint of the previous population. In the paper we compare the performance of CMA-ES coupled with PPMF and with two other step-size adaptation rules: Cumulative Step-size Adaptation (CSA) and Median Success Rule (MSR). For the comparison we apply a version of the IPOP-CMA-ES strategy and we test its performance using three benchmark suites: CEC 2013, CEC 2017 and CEC 2021. The results evidence that the efficiency of PPMF is comparable with CSA and superior to MSR.