On finding representative non-dominated points for bi-objective integer network flow problems

This paper proposes a new algorithm to find a representation of the set of all non-dominated points of the bi-objective integer network flow problem. The algorithm solves a sequence of ε-constraint problems with a branch-and-bound algorithm to find a subset of non-dominated points that represents the set of all non-dominated points well in the sense of coverage or uniformity. At each iteration of the algorithm, one non-dominated point, determined by solving one ε-constraint problem, is added to the representation until it is guaranteed that the representation has the desired quality. Computational experiments on different problem types show the efficacy of the algorithm.