A Decomposition-Based Multi-Modal Multi-Objective Evolutionary Algorithm Transforming to Two-Objective Problems

Abstract

In a multi-modal multi-objective optimization problem, there exist some Pareto optimal solutions for any point on the Pareto front. A multi-modal multi-objective evolutionary algorithm needs the abilities of approximating better both the Pareto front and the Pareto set. However, most of existing multi-modal multi-objective evolutionary algorithms use the population convergence in the objective space as the primarily evaluation criterion. As a result, they do not always have a high approximation ability of the Pareto set in the decision space. To approximate better both the Pareto front and the Pareto set, we propose a decomposition-based multi-modal multi-objective evolutionary algorithm. In our proposed algorithm, a multi-modal multi-objective optimization problem is transformed into a number of two-objective subproblems. In each subproblem, solutions are optimized in terms of the corresponding scalarizing function and the decision space diversity. The proposed algorithm can maintain not only solutions with good convergence to the Pareto front but also diverse solutions in the decision space. Experimental results show that the proposed algorithm has a high approximation ability to both the Pareto front and the Pareto set.