  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.
