An Empirical Comparison of CMA-ES in Dynamic Environments

Abstract

This paper empirically investigates the behavior of three variants of covariance matrix adaptation evolution strategies (CMA-ES) for dynamic optimization. These three strategies include the elitist (1+1)-CMA-ES, the non-elitist (μ,λ)-CMA-ES and sep-CMA-ES. To better understand the influence of covariance matrix adaptation methods and of the selection methods to the strategies in dynamic environments, we use the state-of-art dynamic optimization benchmark problems to evaluate the performance. We compare these CMA-ES variants with the traditional (1+1)-ES with the one-fifth success rule. Our experimental results show that the simple elitist strategies including the (1+1)-ES and the (1+1)-CMA-ES generally outperform those non-elitist CMA-ES variants on one out of the six dynamic functions. We also investigate the performance when the dynamic environments change with different severity and when the problems are in higher dimensions. The elitist strategies are robust to different severity of dynamic changes, but the performance is worse when the problem dimensions are increased. In high dimensions, the performance of the elitist and the non-elitist versions of CMA-ES are marginally the same.