A Multi-modal Multi-objective Evolutionary Algorithm based on Transformation to Two-objective Optimization Problems

Abstract

Multi-modal multi-objective evolutionary algorithms can solve a problem with multiple Pareto optimal solutions that have the same objective function vector. Most of existing multi-modal multi-objective evolutionary algorithms use the convergence in the objective space as the primarily fitness evaluation criterion. As a result, they do not always have 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 multi-modal multi-objective evolutionary algorithm based on problem transformation. A multiobjective 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.