A multiobjective linear programming method based on the projection of the objective function gradients

This paper presents an interactive method for decision support to multiobjective linear programming problems. This method is based on the projection of the objective function gradients over the non-dominated region of the problem. It allows an oriented and continuous search for the preferred solution. The method uses also the dual variables, according to the achievement scalarizing program used in the projections, to characterize the non-dominated hyper-faces of the problem. The most representative multiobjective linear programming methods and systems, based on reference points, are also reviewed in this paper. The purpose of this revision is to transmit a global view of the evolution of these methods and systems, allowing their comparison with the new presented method. Finally the method's usage is illustrated through a small example.