In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal-dual infeasible and inexact interior point method for multi-objective linear network flow problems. A comparison with standard interior point methods is provided and experimental results on bi-objective instances are reported in this paper as well. The multi-objective instances are converted into single objective problems with the help of an achievement function, which is particularly adequate for interactive decision-making methods.
AT&T Labs Technical Report, AT&T Labs Research, Florham Park, NJ 07932, January 12, 2009.