Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications

Authors:
George Tsaggouris;Christos Zaroliagis
Affiliations:
Patras University Campus, R.A. Computer Technology Institute, N. Kazantzaki Str, 26500, Patras, Greece and University of Patras, Department of Computer Engineering and Informatics, 26500, Patras, ...;Patras University Campus, R.A. Computer Technology Institute, N. Kazantzaki Str, 26500, Patras, Greece and University of Patras, Department of Computer Engineering and Informatics, 26500, Patras, ...
Venue:
Theory of Computing Systems
Year:
2009

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Abstract

We provide an improved FPTAS for multiobjective shortest paths—a fundamental (NP-hard) problem in multiobjective optimization—along with a new generic method for obtaining FPTAS to any multiobjective optimization problem with non-linear objectives. We show how these results can be used to obtain better approximate solutions to three related problems, multiobjective constrained [optimal] path and non-additive shortest path, that have important applications in QoS routing and in traffic optimization. We also show how to obtain a FPTAS to a natural generalization of the weighted multicommodity flow problem with elastic demands and values that models several realistic scenarios in transportation and communication networks.