Enhancing the performance of differential evolution with covariance matrix self-adaptation

Abstract

Differential evolution (DE) is an efficient global optimizer, while the covariance matrix adaptation evolution strategy (CMA-ES) shows great power on local search. However, utilizing both of these advantages in one algorithm is difficult since the randomness introduced by DE may reduce the reliability of covariance matrix estimation. Moreover, the exploration ability of DE can be canceled out by CMA-ES because they use completely different mechanisms to control the search step. To take advantage of both DE and CMA-ES, we propose a novel DE variant with covariance matrix self-adaptation, named DECMSA. In DECMSA, a new mutation scheme named “DE/current-to-better/1” is implemented. This scheme uses a Gaussian distribution to guide the search and strengthens both exploration and exploitation capabilities of DE. The proposed algorithm has been tested on the CEC-13 benchmark suite. The experimental results demonstrate that DECMSA outperforms popular DE variants, and it is quite competitive with state-of-the-art CMA-ES variants such as IPOP-CMA-ES and BIPOP-CMA-ES. Moreover, equipped with a constraint handling method, DECMSA is able to produce better solutions than other comparative algorithms on three classic constrained engineering design problems.