Decomposition methods for polyhedral approximation of the Edgeworth–Pareto hull

Abstract

In the framework of multiobjective optimization (MOO) techniques, there is a group of methods that attract growing attention. These methods are based on the approximation of the Edgeworth–Pareto hull (EPH), that is, the largest set (in the sense of inclusion) that has the same Pareto frontier as the feasible objective set [1, 2]. The block separable structure of MOO problems is used in this paper to improve the efficiency of EPH approximation methods in the case when EPH is convex. In this case, polyhedral approximation can be applied to EPH. Its practical importance was shown, for example, in [3, 4]. In this paper, a two-level system is considered that consists of an upper (coordinating) level and a finite number of blocks interacting through the upper level. It is assumed that the optimization objectives are related only to the variables of the upper level. The approximation method is based on the polyhedral approximation of EPH for single blocks, followed by the application of these results for approximating the EPH for the whole MOO problem.