In this paper, we present a new algorithm for solving the multi-objective shortest path problem (MSPP) which consists of finding all the non-dominated paths between two nodes s and t (ND s-t paths), on a network where a multiple criteria function is defined over the set of arcs. The main feature of the algorithm is that, contrarily to the previous most efficient approaches for the MSPP, not all of the ND sub-paths on the network need to be found. Additionally, the algorithm fully exploits the fact that ND s-t paths are generated at a very early stage of the ranking procedure. The computational experience reported in the paper shows that, for large size general type networks, the new algorithm clearly outperforms the labelling approach.

This paper is devoted to the study of labelling techniques for solving the multi-objective shortest path problem (MSPP) which is an extension of the shortest path problem (SPP) resulting from considering simultaneously more than one cost function (criteria) for the arcs. The generalization of the well known SPP labelling algorithm for the multiobjective situation is studied in detail and several different versions are considered combining two labelling techniques (setting and correcting), with different data structures and ordering operators. The computational experience was carried out making use of a large and representative set of test problems, consisting of around 9000 instances, involving three types of network (random, complete and grid) and a reasonable range for the number of criteria. The computational results show that the labelling algorithm is able to solve large size instances of the MSPP, in a reasonable computing time. The computational experience reported in this paper is complemented by the results presented in a twin paper [22] showing that the label correcting technique proves to be the fastest procedure when the computation of the full set of non-dominated paths is required.