Generating maximal efficient faces for the multiobjective multicommodity flow problem

Multicommodity flow problems (MCFPs) arise when several commodities are to be transmitted within a capacitated network. MCFP has received a great attention in the literature for the single objective case, while only few works addressed the problem in a multiobjective framework. In this paper, we study the MCFP with multiple objectives. This problem is modeled as multiobjective linear program with continuous decision variables. In order to solve this problem, we propose to apply an exact solution approach operating in the objective space, called the Efficient Solutions Adjacency based Method (ESAM) to generate all the maximal efficient faces and extreme points. An experimental study is conducted to test the efficiency of the ESAM on solving small and medium sized multiobjective MCFPs.