A decomposition-based many-objective evolutionary algorithm with weight grouping and adaptive adjustment

Multiobjective evolutionary algorithms based on decomposition (MOEA/D) have attracted tremendous interest and have been thoroughly developed because of their excellent performance in multi/many-objective optimization problems. In general, MOEA/D methods use a set of uniformly distributed weight vectors to decompose a multiobjective problem into multiple single-objective subproblems and solve them cooperatively. However, a set of uniformly distributed weight vectors tends to perform well over smooth, continuous, and well-spread Pareto fronts (PFs) but poorly over irregular PFs, such as discontinuous PFs, degenerate PFs and PFs with long peaks and tails. Many weight vector adjustment strategies have been proposed to alleviate this issue. In this article, we propose a novel weight grouping strategy and an adaptive adjustment strategy. Specifically, we dynamically divide the weight vectors into three groups, normal weight vectors, invalid weight vectors and crowded weight vectors; then, the invalid weight vectors and crowded weight vectors are deleted in order, and new weight vectors are added according to the external archived individuals. The proposed method can be combined with a penalty-based boundary intersection approach or the Tchebycheff aggregation function. In the experiments, we compare our algorithm with several state-of-the-art many-objective evolutionary algorithms in several many-objective problem test instances with PFs of varying degrees of difficulty, and the results show that the proposed algorithm performs best on most test instances, which further demonstrates that it outperforms all the comparison algorithms.