A Decomposition-Based Evolutionary Algorithm for Multi-modal Multi-objective Optimization

This paper proposes a novel decomposition-based evolutionary algorithm for multi-modal multi-objective optimization, which is the problem of locating as many as possible (almost) equivalent Pareto optimal solutions. In the proposed method, two or more individuals can be assigned to each decomposed subproblem to maintain the diversity of the population in the solution space. More precisely, a child is assigned to a subproblem whose weight vector is closest to its objective vector, in terms of perpendicular distance. If the child is close to one of individuals that have already been assigned to the subproblem in the solution space, the replacement selection is performed based on their scalarizing function values. Otherwise, the child is newly assigned to the subproblem, regardless of its quality. The effectiveness of the proposed method is evaluated on seven problems. Results show that the proposed algorithm is capable of finding multiple equivalent Pareto optimal solutions.