An Exact Method for Optimizing a Linear Function over an Integer efficient Set

Abstract: In this article, a new methodology is proposed to solve the problem of optimizing a linear function over an integer efficient set, noted (OI). The great challenges on it were its classification as NP-hard and that only three methods were introduced in the literature during decades treating this issue. We propose in this study a generalization of our method [8], wherein all efficient solutions of a multiobjective integer linear program (MOILP) are achieved. Based upon the well known branch and bound technique and strengthened by efficient tests, the proposed methodology succeeds to find an optimal solution in a finite number of steps. The main feature is that it greatly saturates nodes in the tree, thus a large number of feasible solutions can be avoided for optimality or efficiency purposes. Also, we have chosen Jorge method to perform a comparative study.