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A promising idea for evolutionary constrained optimization is to efficiently utilize not only feasible solutions (feasible individuals) but also infeasible ones. In this paper, we propose a simple implementation of this idea in MOEA/D. In the proposed method, MOEA/D has two grids of weight vectors. One is used for maintaining the main population as in the standard MOEA/D. In the main population, feasible solutions always have higher fitness than infeasible ones. Among infeasible solutions, solutions with smaller constraint violations have higher fitness. The other grid is for maintaining a secondary population where non-dominated solutions with respect to scalarizing function values and constraint violations are stored. More specifically, a single non-dominated solution with respect to the scalarizing function and the total constraint violation is stored for each weight vector. A new solution is generated from a pair of neighboring solutions in the two grids. That is, there exist three possible combinations of two parents: both from the main population, both from the secondary population, and each from each population. The proposed MOEA/D variant is compared with the standard MOEA/D and other evolutionary algorithms for constrained multiobjective optimization through computational experiments.
Ishibuchi et al. (2018) studied this question.