CMA-ES with Restarts for Solving CEC 2013 Benchmark Problems

This paper investigates the performance of 6 versions of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with restarts on a set of 28 noiseless optimization problems (including 23 multi-modal ones) designed for the special session on real-parameter optimization of CEC 2013. The experimental validation of the restart strategies shows that: i). the versions of CMA-ES with weighted active covariance matrix update outperform the original versions of CMA-ES, especially on ill-conditioned problems; ii). the original restart strategies with increasing population size (IPOP) are usually outperformed by the bi-population restart strategies where the initial mutation step-size is also varied; iii). the recently proposed alternative restart strategies for CMA-ES demonstrate a competitive performance and are ranked first w.r.t. the proportion of function-target pairs solved after the full run on all 10-, 30- and 50-dimensional problems.