2022/12/19 by Ryoki Hamano, Shota Saito, Hamano, Ryoki +5
Computer Science · Engineering · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE) #Optimization and Control (math.OC) #Optimization and Mathematical Programming
paper · pdf · doi:10.48550/arxiv.2212.09260
openalex publication_date 2022/12/19 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that samples solution candidates from a multivariate Gaussian distribution (MGD), which shows excellent performance in continuous BBO. The parameters of MGD, mean and (co)variance, are updated based on the evaluation value of candidate solutions in the CMA-ES. If the CMA-ES is applied to the MI-BBO with straightforward discretization, however, the variance corresponding to the integer variables becomes much smaller than the granularity of the discretization before reaching the optimal solution, which leads to the stagnation of the optimization. In particular, when binary variables are included in the problem, this stagnation more likely occurs because the granularity of the discretization becomes wider, and the existing integer handling for the CMA-ES does not address this stagnation. To overcome these limitations, we propose a simple integer handling for the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD. The numerical experiments on the MI-BBO benchmark problems demonstrate the efficiency and robustness of the proposed method. Furthermore, in order to demonstrate the generality of the idea of the proposed method, in addition to the single-objective optimization case, we incorporate it into multi-objective CMA-ES and verify its performance on bi-objective mixed-integer benchmark problems.