Incorporation of a decision space diversity maintenance mechanism into MOEA/D for multi-modal multi-objective optimization

Abstract

A Multi-objective optimization problem with several different Pareto optimal solution sets is defined as a multi-modal multi-objective optimization problem. Finding all the Pareto optimal solution sets for this type of problem can provide more options for the decision maker, which is important in some real-world situations. The Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been proved to perform well in various multi-objective problems but it does not perform well in finding all the Pareto optimal solution sets for multi-modal multi-objective optimization problems. In this paper, a MOEA/D variant is proposed to solve these problems. K solutions are assigned to each weight vector in the MOEA/D variant and the solutions are evaluated by not only the scalarizing function values but also the minimum distance from other solutions with the same weight vector and the average distance from the neighboring solutions in the same weight vector grid. Experimental results show that the MOEA/D variant performs much better than the original MOEA/D on the multi-modal distance minimization problems.