A New Step Size Update Strategy for CMA-ES in Multi-objective Optimisation
摘要
The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most widely used evolutionary algorithms in single-objective black-box optimisation. Unlike the popularity of the single-objective CMA-ES, its multi-objective variant - MO-CMA-ES - has not been extensively studied. In MO-CMA-ES, like CMA-ES the step size, which determines how far the mutation can go, depends on whether a newly generated solution is better than its parent in the population. However, unlike single-objective optimisation where all solutions are distinguishable about their objective values, in multi-objective optimisation there may exist many solutions incomparable (i.e., non-dominated to each other). Updating the step size based on the qualitative comparison between solutions may not work best for the multi-objective case. In this paper, we propose a simple step-size update strategy for MO-CMA-ES. The proposed strategy considers how much change the newly generated solution has compared with its parent. Specifically, we factor in the difference in the non-domination levels that the offspring and parent solutions are located in, attempting to make use of quantitative information that may better reflect the current search progress. Experimental results show the effectiveness of the proposed strategy - it can accelerate the convergence speed on almost all the test problems considered.