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Analysis of FPTASes for the Multi-Objective Shortest Path Problem

Author

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  • Breugem, T.
  • Dollevoet, T.A.B.
  • van den Heuvel, W.

Abstract

We propose a new FPTAS for the multi-objective shortest path problem. The algorithm uses elements from both an exact labeling algorithm and an FPTAS proposed by Tsaggouris and Zaroliagis (2009). We analyze the running times of these three algorithms both from a the- oretical and a computational point of view. Theoretically, we show that there are instances for which the new FPTAS runs an arbitrary times faster than the other two algorithms. Fur- thermore, for the bi-objective case, the number of approximate solutions generated by the proposed FPTAS is at most the number of Pareto-optimal solutions multiplied by the number of nodes. By performing a set of computational tests, we show that the new FPTAS performs best in terms of running time in case there are many dominated paths and the number of Pareto-optimal solutions is not too small.

Suggested Citation

  • Breugem, T. & Dollevoet, T.A.B. & van den Heuvel, W., 2016. "Analysis of FPTASes for the Multi-Objective Shortest Path Problem," Econometric Institute Research Papers EI2016-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:79908
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    References listed on IDEAS

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    1. Matthias Müller-Hannemann & Karsten Weihe, 2006. "On the cardinality of the Pareto set in bicriteria shortest path problems," Annals of Operations Research, Springer, vol. 147(1), pages 269-286, October.
    2. Mote, John & Murthy, Ishwar & Olson, David L., 1991. "A parametric approach to solving bicriterion shortest path problems," European Journal of Operational Research, Elsevier, vol. 53(1), pages 81-92, July.
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    Cited by:

    1. Nir Halman & Mikhail Y. Kovalyov & Alain Quilliot & Dvir Shabtay & Moshe Zofi, 2019. "Bi-criteria path problem with minimum length and maximum survival probability," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 469-489, June.

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    Keywords

    Shortest Path Problem; Multi-Objective Optimization; FPTAS; Complexity Analysis;
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