Cooperative-Coevolution-CMA-ES with Two-Stage Grouping

摘要

The Cooperative Coevolution (CC) framework is the state of the art for solving large scale global optimization (LSGO) problems. A particular challenge in using CC lies in the decomposition of variables and resource allocation. In this work, the decomposition phase of the framework is performed in two stages to address both variable interaction and efficient resource allocation. The algorithm starts with differential analysis followed by differential grouping. The differential analysis allows efficient resource allocation while the differential grouping will detect variable interactions. The differential grouping will act on a small number of variables and will not consume as much computational budget as a single-stage grouping. While not all variable interactions will be detected, separable variables will be recognized hence specialized solvers for separable problems can be employed on these subproblems. In this work, the twostage grouping CC (TSCC) is paired with a hybrid algorithm where sep-CMA-ES is used to solve the separable subproblem and CMA-ES is used to solve the non-separable subproblems, the algorithm is referred as TSCC-CMAES. A comparison between TSCC and CC with groups based on either differential analysis or differential grouping is carried out. In general, TSCC could outperform the two single-stage grouping methods. Additionally, the TSCC-CMAES shows a competitive advantage on a number of more complex problems against state-of-the-art algorithms and it is shown that the effect of the population size and group size is crucial in achieving these results.