A modified version of a Benson-type algorithm proposed for obtaining solutions with better dispersion on the non-dominated set of a non-convex multi-objective programming problem

Abstract

This paper proposes a new method to approximate the non-dominated set of a general multi-objective programming (MOP) problem with continuous variables (that is, without any convexity assumption). The algorithm is based on a recent modification of Benson's method [14], and like Benson's idea, generates an inner approximation and an outer approximation of the (weakly) non-dominated set of an MOP. It is proved that this method provides a set of (weakly) $ \varepsilon $-non-dominated points. To evaluate the performance of the proposed algorithm, some different test problems are presented. The results show that the algorithm provides a reliable and practical approach to the approximation of non-dominated sets.