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Solving the robust shortest path problem with interval data using a probabilistic metaheuristic approach

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  • Nikulin, Yury

Abstract

This paper addresses the robust shortest path problem with interval data, i.e. the case of classical shortest path problem with given source and sink when arc weights are not fixed but take their values from some intervals associated with arcs. The problem consists in finding a shortest path that minimizes so called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in [9], the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for the large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop metaheuristic approach for solving the robust shortest path problem.

Suggested Citation

  • Nikulin, Yury, 2005. "Solving the robust shortest path problem with interval data using a probabilistic metaheuristic approach," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 597, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:597
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    References listed on IDEAS

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    1. Nikulin, Yury, 2005. "Simulated annealing algorithm for the robust spanning tree problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 591, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
    3. Nikulin, Yury V., 2004. "Robustness in combinatorial optimization and scheduling theory: An annotated bibliography," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 583, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
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