Multi-Objective Optimization Using Coupled Discrete Gradient Model

Abstract

Optimization problems in which multiple objective functions are optimized simultaneously are called “multi-objective optimization problem”. Multi-objective optimization problems appear naturally in the decision making process for complex systems. Recently, a number of multi-objective optimization methods which search Pareto optimal solutions covering Pareto front have been proposed and have attracted much interests. Such methods are based on meta-heuristics, and a multi-objective optimization method based on gradient dynamics which takes a similar approach has not been proposed yet to our knowledge. In this paper, we propose a new multi-objective optimization method using a coupled discrete gradient dynamics. In the proposed method, firstly, we consider multiple search points driven by discrete gradient dynamics which optimize respective objective functions independently. Next, trajectories of the search points are synchronized by a coupling among the search points. Then, Pareto optimal solutions that cover whole Pareto front are obtained by the modulation of dynamic characteristics of each optimization model. We confirm effectiveness of the proposed method through applications to benchmark problems which have various types of Pareto fronts.