Solving large-scale many-objective optimization problems by covariance matrix adaptation evolution strategy with scalable small subpopulations

Despite the recent development in evolutionary multi- and many-objective optimization, the problems with large-scale decision variables still remain challenging. In this work, we propose a scalable small subpopulations based covariance matrix adaptation evolution strategy, namely S³-CMA-ES, for solving many-objective optimization problems with large-scale decision variables. The proposed S³-CMA-ES attempts to approximate the set of Pareto-optimal solutions using a series of small subpopulations instead of a whole population, where each subpopulation converges to only one solution. In the proposed S³-CMA-ES, a diversity improvement strategy is designed to generate and select new solutions. The performance of S³-CMA-ES is compared with five representative algorithms on 36 test instances with 5–15 objectives and 500–1500 decision variables. The empirical results demonstrate the superiority of the proposed S³-CMA-ES.