PSA-CMA-ES

Abstract

The population size, i.e., the number of candidate solutions generated at each iteration, is the most critical strategy parameter in the covariance matrix adaptation evolution strategy, CMA-ES, which is one of the state-of-the-art search algorithms for black-box continuous optimization. The population size is required to be larger than its default value when the objective function is well-structured multimodal and/or noisy, while we want to keep it as small as possible for optimization speed. However, the strategy parameter tuning based on trial and error is, in general, prohibitively expensive in black-box optimization scenario. This paper proposes a novel strategy to adapt the population size for CMA-ES. The population size is adapted based on the estimated accuracy of the update of the normal distribution parameters. The CMA-ES with the proposed population size adaptation mechanism, PSA-CMA-ES, is tested both on noiseless and noisy benchmark functions, and compared with existing strategies. The results revealed that the PSA-CMA-ES works well on well-structured multimodal and/or noisy functions, but causes inefficient increase of the population size on unimodal functions. Furthermore, it is shown that the PSA-CMA-ES can tackle noise and multimodality at the same time.