Article Dans Une Revue 4OR: A Quarterly Journal of Operations Research Année : 2006

Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function

Résumé

This paper presents a direct extension of the label setting algorithm proposed by Martins in 1984 for the shortest path problem with multiple objectives. This extended version computes all the efficient paths from a given source vertex, to all the other vertices of the network. The algorithm copes with problems in which the "cost values" associated with the network arcs are positive. The proposed extension can handle objective functions that are either of the "sum" type or of the "bottleneck" type. The main modifications to Martins' algorithm for multi-objective shortest path problems are linked to the dominance test and the procedure for identifying efficient paths. The algorithmic features are described and a didactic example is provided to illustrate the working principle. The results of numerical experiments concerning the number of efficient solutions produced and the CPU time consumed for several configurations of objectives, on a set of randomly generated networks, are also provided.

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Dates et versions

hal-00462028 , version 1 (08-03-2010)

Identifiants

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Xavier Gandibleux, Frédéric Beugnies, Sabine Randriamasy. Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function. 4OR: A Quarterly Journal of Operations Research, 2006, 4 (1), pp.47-59. ⟨10.1007/s10288-005-0074-x⟩. ⟨hal-00462028⟩
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