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An exponential (matching based) neighborhood for the vehicle routing problem

Author

Listed:
  • Eric Angel

    (Université d’Évry Val d’Essonne)

  • Evripidis Bampis

    (Université d’Évry Val d’Essonne)

  • Fanny Pascual

    (Université d’Évry Val d’Essonne)

Abstract

We introduce an exponential neighborhood for the Vehicle Routing Problem (vrp) with unit customers’ demands, and we show that it can be explored efficiently in polynomial time by reducing its exploration to a particular case of the Restricted Complete Matching (rcm) problem that we prove to be polynomial time solvable using flow techniques. Furthermore, we show that in the general case with non-unit customers’ demands the exploration of the neighborhood becomes an $\mathcal{NP}$ -hard problem.

Suggested Citation

  • Eric Angel & Evripidis Bampis & Fanny Pascual, 2008. "An exponential (matching based) neighborhood for the vehicle routing problem," Journal of Combinatorial Optimization, Springer, vol. 15(2), pages 179-190, February.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:2:d:10.1007_s10878-007-9075-3
    DOI: 10.1007/s10878-007-9075-3
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    References listed on IDEAS

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    1. Paul M. Thompson & Harilaos N. Psaraftis, 1993. "Cyclic Transfer Algorithm for Multivehicle Routing and Scheduling Problems," Operations Research, INFORMS, vol. 41(5), pages 935-946, October.
    2. Richard K. Congram & Chris N. Potts & Steef L. van de Velde, 2002. "An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 52-67, February.
    3. Jiefeng Xu & James P. Kelly, 1996. "A Network Flow-Based Tabu Search Heuristic for the Vehicle Routing Problem," Transportation Science, INFORMS, vol. 30(4), pages 379-393, November.
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