Improved Fptas for Multiobjective Shortest Paths with Applications

We consider multiobjective shortest paths, a fundamental (NP-hard) problem in multiobjective optimization, where we are interested not in optimizing a single objective, but in finding a set of paths that captures the trade-off (the so-called Pareto curve) among several objectives in a digraph whose edges are associated with multidimensional cost vectors. We provide a new FPTAS for computing an approximate Pareto curve for multiobjective shortest paths that significantly improves upon previous approaches, especially in the case of more than two objective functions. We show how our new FPTAS can be used to provide better approximate solutions to three related problems (multiobjective constrained optimal paths, multiobjective constrained paths, and non-additive shortest paths) that have important applications in the areas of quality of service routing in communication networks, and in computing traffic equilibria in transportation networks. We also show how our new FPTAS for multiobjective shortest paths can provide efficient approximate solutions in a completely different context – to a natural generalization of the weighted multicommodity flow problem with elastic demands and values that models several realistic design scenarios in transportation and communication networks. Finally, as a byproduct of our framework, we provide a generic method for constructing FPTAS for any multiobjective optimization problem with non-linear objective functions of a rather general form. ∗This work was partially supported by the IST Programme (6th FP) of EC under contract No. IST-2002-001907 (integrated project DELIS), and the Action PYTHAGORAS of the Operational Programme for Educational & Vocational Training II, with matching funds from the European Social Fund and the Greek Ministry of Education. †Computer Technology Institute, P.O. Box 1122, 26110 Patras, Greece, and Dept of Computer Engineering and Informatics, University of Patras, 26500 Patras, Greece. Emails: {tsaggour,zaro}@ceid.upatras.gr