Parameter Setting of CMA-ES: A Numerical Study on CEC2019 100-Digit Challenge

The evolution strategy with covariance matrix adaptation (CMA-ES) is a well-known algorithm in the family of evolution strategies. It consists of three main mechanisms: derandomized adaptation, cumulative step size, and covariance matrix adaptation. In this paper we aim to improve the CMA- ES and its performance by proper parameter values, better repair mechanism, removal of rank-one update, and a spread-based step size adaptation mechanism. We tested the proposed algorithm by ten test functions in the CEC2019 100-Digit Challenge. The results showed that our algorithm can achieve similar solution quality compared with two recent hybrid adaptive evolutionary algorithms and needs fewer fitness function evaluations.