A Decomposition-based Multi-modal Multi-objective Evolutionary Algorithm with Problem Transformation into Two-objective Subproblems

In some real-world multi-objective optimization problems, Pareto optimal solutions with different design parameter values are mapped to the same point with the same objective function values. Such problems are called multi-modal multi-objective optimization problems (MMOPs). For MMOPs, multi-modal multi-objective evolutionary algorithms (MMOEAs) have been developed for approximating both the Pareto front (PF) and the Pareto sets (PSs). However, most MMOEAs use population convergence in the objective space as the primary evaluation criterion. They do not necessarily have a high PS approximation ability. To better approximate both PF and PSs, we propose a decomposition-based MMOEA where an MMOP is transformed into a number of two-objective subproblems. One objective of each subproblem is a scalarizing function defined by a weight vector for the original MMOP, while the other is defined by a decision space diversity. Experimental results show a high approximation ability of the proposed method for both PF and PSs.