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Solving the shortest path tour problem

Author

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  • Festa, P.
  • Guerriero, F.
  • Laganà, D.
  • Musmanno, R.

Abstract

In this paper, we study the shortest path tour problem in which a shortest path from a given origin node to a given destination node must be found in a directed graph with non-negative arc lengths. Such path needs to cross a sequence of node subsets that are given in a fixed order. The subsets are disjoint and may be different-sized. A polynomial-time reduction of the problem to a classical shortest path problem over a modified digraph is described and two solution methods based on the above reduction and dynamic programming, respectively, are proposed and compared with the state-of-the-art solving procedure. The proposed methods are tested on existing datasets for this problem and on a large class of new benchmark instances. The computational experience shows that both the proposed methods exhibit a consistent improved performance in terms of computational time with respect to the existing solution method.

Suggested Citation

  • Festa, P. & Guerriero, F. & Laganà, D. & Musmanno, R., 2013. "Solving the shortest path tour problem," European Journal of Operational Research, Elsevier, vol. 230(3), pages 464-474.
    • Handle: RePEc:eee:ejores:v:230:y:2013:i:3:p:464-474
    DOI: 10.1016/j.ejor.2013.04.029
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    References listed on IDEAS

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    1. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    2. Francesca Guerriero & Roberto Musmanno & Valerio Lacagnina & Antonio Pecorella, 2001. "A Class of Label-Correcting Methods for the K Shortest Paths Problem," Operations Research, INFORMS, vol. 49(3), pages 423-429, June.
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    Cited by:

    1. F. Carrabs & R. Cerulli & R. Pentangelo & A. Raiconi, 2018. "A two-level metaheuristic for the all colors shortest path problem," Computational Optimization and Applications, Springer, vol. 71(2), pages 525-551, November.
    2. L. Di Puglia Pugliese & D. Ferone & P. Festa & F. Guerriero, 2022. "A generalized shortest path tour problem with time windows," Computational Optimization and Applications, Springer, vol. 83(2), pages 593-614, November.
    3. Di Puglia Pugliese, Luigi & Ferone, Daniele & Festa, Paola & Guerriero, Francesca, 2020. "Shortest path tour problem with time windows," European Journal of Operational Research, Elsevier, vol. 282(1), pages 334-344.
    4. Coelho, Leandro Callegari & De Maio, Annarita & Laganà, Demetrio, 2020. "A variable MIP neighborhood descent for the multi-attribute inventory routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).

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