The Augmented Weighted Tchebychev Norm for Optimizing a Linear Function over an Integer Efficient Set of a Multicriteria Linear Program

In this paper, we propose a new exact algorithm, using an augmented weighted Tchebychev norm, for optimizing a linear function on the efficient set of a multiple objective integer linear programming problem. This norm is optimized progressively by improving the value of the linear criteria and going through some efficient solutions. The method produced not only the best efficient solution of the linear objective function but also a subset of nondominated solutions that can help decision makers to select the best decision among a large set of Pareto solutions.