Adapting the population size in CMA-ES using nearest-better clustering method for multimodal optimization

Abstract

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the advanced algorithms for solving continuous single-objective optimization. In this algorithm, the population size is an important parameter which represents the number of candidate points generated in each iteration. A larger population size allows for better exploration of the search space and is typically required for handling multimodal functions, while a smaller population size facilitates quicker convergence. Adapting the population size in this algorithm raises a question about how to increase/decrease/keep it in an efficient way to solve specific problems. In this paper, we propose a novel approach for this purpose based on the information of niches observed during the evolution process. Firstly, the nearest-better clustering (NBC) technique is employed to detect the number of niches in each iteration, then the information will be used to adapt the population size accordingly. Additionally, a quasi-Newton method, which serves as a local search, can be incorporated into the algorithm in order to speed it up. We evaluate the effectiveness of our method through numerical simulations on multimodal test functions, the black-box optimization benchmarking (BBOB) noiseless testbed, and the CEC 2014 and CEC 2017 benchmark testing suites.