Solving the Multiple Objective Integer Linear Programming Problem

Abstract

In this work, an exact method for generating the efficient set of the multiple objective integer linear programming problem (MOILP) is described. When many of the published methods consist of solving initially an ILP program, our method has the advantage of starting with an optimal solution of an LP program whose objective is a positive combination of the criteria, and uses a branching procedure to generate an integer feasible solution. Whenever such a solution is found, the increasing directions of the criteria are recognized and an efficient cutting plane is built in order to delete some of the non efficient solutions without computing them. Compared to the Sylva & Crema’s method where at each stage, the ILP programs considered are augmented by (q + 1) new constraints and q bivalent variables, our method does not depend on q, where q is the number of the criteria.