A guideline for CMA-ES parameter selection using statistical analysis

Abstract

The covariance matrix adaptation evolution strategy (CMA-ES) is an evolutionary algorithm that is used to solve difficult non-linear, non-convex black-box optimization problems in continuous domain. The performance of the CMA-ES algorithm is highly dependent on the setting of the CMA-ES parameters such as population size, parent number, and initial step-size. Many studies have focused on CMA-ES parameter setting. In this study, we present a method for parameter tuning in which the parameter values are set before the CMA-ES algorithm is applied. This method reduces the heavy computational burden that is usually required for parameter tuning. In real-world manufacturing problems, we must consider the accuracy, and efficiency. First, we determine the value of the error criterion, and we then adopt an optimal Latin hypercube design (OLHD) in which the parameters of a CMA-ES algorithm are set as factors. After selecting the parameter settings sampled by the OLHD, we run the CMA-ES to solve all the test problems with replications and we then estimate the performance of the parameter settings. Twenty-two test problems, which represent a variety of applications to a large category of problems, were selected for this study. The result of the statistical analysis shown the appropriate values of the maximum number of function evaluations (Max_FEs). We therefore recommended parameter settings that are appropriate for the test problems, and compared them to the initial parameter ranges of the parameters. The range of population size, parent number, and initial step-size were reduced by 69%, 42%, and 42%, respectively. In order to validate the effectiveness of the recommended parameter ranges, we compared the accuracy and robustness of the initial and recommended parameter ranges. The proposed parameter tuning method demonstrated remarkable improvements in accuracy and robustness when the recommended parameter ranges were used instead of the initial parameter ranges. Therefore, based on these results, we recommended a guideline for the CMA-ES parameter selection