Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems

Abstract

As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a posteriori methods convey much more information to the decision maker. Especially, the a posteriori (or generation) methods give the whole picture (i.e. the Pareto set) to the decision maker, before his/her final choice, reinforcing thus, his/her confidence to the final decision. However, the generation methods are the less popular due to their computational effort and the lack of widely available software. The present work is an effort to effectively implement the ε-constraint method for producing the Pareto optimal solutions in a MOMP. We propose a novel version of the method (augmented ε-constraint method – AUGMECON) that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations. The method AUGMECON has been implemented in GAMS, a widely used modelling language, and has already been used in some applications. Finally, an interactive approach that is based on AUGMECON and eventually results in the most preferred Pareto optimal solution is also proposed in the paper.