Many-objective evolutionary algorithms (MOEAs), especially the decomposition-based MOEAs, have attracted wide attention in recent years. Recent studies show that a well designed combination of the decomposition method and the domination method can improve the performance ,i.e., convergence and diversity, of a MOEA. In this paper, a novel way of combining the decomposition method and the domination method is proposed. More precisely, a set of weight vectors is employed to decompose a given many-objective optimization problem(MaOP), and a hybrid method of the penalty-based boundary intersection function and dominance is proposed to compare local solutions within a subpopulation defined by a weight vector. A MOEA based on the hybrid method is implemented and tested on problems chosen from two famous test suites, i.e., DTLZ and WFG. The experimental results show that our algorithm is very competitive in dealing with MaOPs. Subsequently, our algorithm is extended to solve constraint MaOPs, and the constrained version of our algorithm also shows good performance in terms of convergence and diversity. These reveals that using dominance locally and combining it with the decomposition method can effectively improve the performance of a MOEA.
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