Handling bound constraints in CMA-ES: An experimental study

Bound constraints are the lower and upper limits defined for each coordinate of the solution. There are many methods to deal with them, but there is no clear guideline for which of them should be preferred. This paper is devoted to handling bound constraints in the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm. It surveys 22 Bound Constraint Handling Methods (BCHMs). The experiments cover both unimodal and multimodal functions taken from the CEC 2017 and the BBOB benchmarks. The performance of CMA-ES was found to change when different BCHMs were used. The worst and the best BCHMs were identified. The results of CMA-ES with the best BCHM and restarts were compared on CEC 2017 with the results of recently published derivatives of Differential Evolution (DE).