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 1/5-th success rule. The method, called PPMF (Previous Population Midpoint Fitness), adjusts the step-size multiplier σ 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.