Approximating Weak Pareto Solution Sets for Multi-Objective Optimization Problems Using Deep Generative Models

Abstract

The multi-objective evolutionary algorithm approximates the Pareto solution set by a finite number of solutions. In such an approach, as the number of objective functions increases, it is difficult to obtain the outline drawing of the Pareto solutions set. In this study, we propose a method to approximate the entire weak Pareto solution set by using a deep generative model. Focusing on the correspondence between the weight space of the Chebyshev scalarization approach and the set of weakly Pareto optimal solutions, we train a deep generative model that outputs the optimal solution of the Chebyshev scalarization function when a point on the standard unit is taken as the input and this is used as the weight vector. Experiments show that the proposed method obtains a more accurate Pareto solution set than some conventional methods when the number of objective functions is large.