On a multicriteria shortest path problem

Connectedness of efficient solutions in multiple criteria combinatorial optimization

“…The connectedness result for multiple criteria linear programming was uaed in [8] to derive an algorithm for finding all efficient paths from node • to node t in a given directed graph G = (V, A).…”

Speeding up Martins’ algorithm for multiple objective shortest path problems

“…In this article the main goal was to speed up the multiple objective shortest path (MOSP) algorithm as presented by Martins [24], while still maintaining the guarantee to find all Pareto optimal paths. The improvements prove to be very useful, especially in large transportation networks.…”

“…The basic algorithm presented in this section is based on the multiple objective shortest path algorithm of Martins [24], which is, in turn, based on the algorithm of Dijkstra [10]. Instead of only one label, nodes will now contain a set of labels.…”

“…In this article we will focus on the exact label setting algorithm of Martins [24] with additive objectives, and propose a number of adaptations to speed up the calculation in the case where we want to find all non-dominated paths between a single origin node and a single destination node. In the following section more details are given on the objectives and the contributions that are made in this research.…”

Generalized multiple objective bottleneck problems

“…Polynomial algorithms considering a sum and a bottleneck objective are presented in [11][12][13][14]. More recently, shortest path problems involving two bottleneck and a sum objective were analyzed in [15] and [16].…”