A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives

In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p > 2 objectives. We apply the method to the assignment problem with three objectives. We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description. Experimental results on the three-objective assignment problem where we use a ranking algorithm to explore the search area show the efficiency of the method. (C) 2010 Elsevier B.V. All rights reserved.