Improving the differential evolution strategy by coupling it with CMA-ES

Differential Evolution Strategy (DES) is a method that combines the differential mutation with the search direction adaptation mechanisms used by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Although earlier research on that algorithm proved its good efficiency, it was still outperformed by the combined and hybrid methods which have been the winners of single objective bound constrained numerical optimization competitions. This paper reports on research that was aimed at improving the efficiency of DES in such a way that the optimization process is initially performed by DES, and after it terminates, the result is finely tuned by CMA-ES, whose expectation vector and the covariance matrix are initialized with statistics of points generated by DES. The hybrid method is evaluated according to the problem definitions and evaluation criteria for the 2022 Special Session and Competition on Single Objective Bound Constrained Numerical Optimization. According to the numerical results, the proposed hybrid method outperforms the standard versions of both DES and CMA-ES. Moreover, the comparison of results on the CEC'2017 benchmark suite evidences that the presented method would be superior or comparable to other methods whose results for CEC'2017 have been reported by the competing teams.