Towards a Matrix-free Covariance Matrix Adaptation Evolution Strategy

In this paper, we discuss a method for generating new individuals such that their mean vector and the covariance matrix are defined by formulas analogous to the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In contrast to CMA-ES, which generates new individuals using multivariate Gaussian distribution with an explicitly defined covariance matrix, the introduced method uses combinations of difference vectors between archived individuals and univariate Gaussian random vectors along directions of past shifts of the population midpoints. We use this method to formulate the Differential Evolution Strategy (DES) – an algorithm that is a crossover between Differential Evolution (DE) and CMA-ES. The numerical results presented in the paper indicate that DES is competitive against CMA-ES in performing both local and global optimization.