Solving scalarized multi-objective network flow problems using an interior point method

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 infeasible dual feasible inexact interior point method for multi-objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi-objective instances are reported. The multi-objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision-making methods.