Use of Radial Basis Functions and Rough Sets for Evolutionary Multi-Objective Optimization

Abstract

This paper presents a new multi-objective evolutionary algorithm (MOEA) which adopts a radial basis function (RBF) approach in order to reduce the number of fitness function evaluations performed to reach the Pareto front. The specific method adopted is derived from a comparative study conducted among several RBFs. In all cases, the NSGA-II (which is an approach representative of the state-of-the-art in the area) is adopted as our search engine with which the RBFs are hybridized. The resulting algorithm can produce very reasonable approximations of the true Pareto front with a very low number of evaluations, but is not able to spread solutions in an appropriate manner. This led us to introduce a second stage to the algorithm in which it is hybridized with rough sets theory in order to improve the spread of solutions. Rough sets, in this case, act as a local search approach which is able to generate solutions in the neighborhood of the few nondominated solutions previously generated. We show that our proposed hybrid approach only requires 2,000 fitness function evaluations in order to solve test problems with up to 30 decision variables. This is a very low value when compared with today's standards reported in the specialized literature