The Multi-Commodity One-to-One Pickup-and-Delivery Traveling Salesman Problem: A Matheuristic

  • I. Rodríguez-Martín
  • Juan José Salazar-González
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6701)

Abstract

This paper addresses an extension of the TSP where a vehicle with a limited capacity must transport certain commodities from their origins to their destinations. Each commodity has a weight, and the objective is to find a minimum length Hamiltonian tour satisfying all the transportation requests without ever violating the capacity constraint. We propose for this problem a heuristic approach that combines mathematical programming and metaheuristic techniques. The method is able to improve the best known solutions for a set of instances from the literature in a reasonable amount of computation time.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ascheuer, N., Jünger, M., Reinelt, G.: A branch & cut algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints. Computational Optimization and Applications 17, 61–84 (2000)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Berbeglia, G., Cordeau, J.-F., Gribkovskaia, I., Laporte, G.: Static Pickup and Delivery Problems: A Classification Scheme and Survey. TOP 15, 1–31 (2007)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Danna, E., Rothberg, E., Le Pape, C.: Exploring relaxation induced neighborhoods to improve MIP solutions. Mathematical Programming A 102, 71–90 (2005)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Fischetti, M., Lodi, A.: Local Branching. Mathematical Programming B 98, 23–47 (2003)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Gambardella, L.M., Dorigo, M.: An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem. INFORMS Journal on Computing 13, 237–255 (2000)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Gouveia, L., Pesneau, P.: On extended formulations for the Precedence Constrained Asymmetric Traveling Salesman Problem. Networks 48, 77–89 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hernández-Pérez, H., Salazar-González, J.J.: A branch-and-cut algorithm for a Traveling Salesman Problem with Pickup and Delivery. Discrete Applied Mathematics 145, 126–139 (2004)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Hernández-Pérez, H., Salazar-González, J.J.: Heuristics for the One-Commodity Pickup-and-Delivery Traveling Salesman Problem. Transportation Science 38, 245–255 (2004)CrossRefGoogle Scholar
  9. 9.
    Hernández-Pérez, H., Salazar-González, J.J.: The multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem. Europoean Journal of Operational Research 196, 987–995 (2009)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Maniezzo, V., Stützle, T., Voß, S. (eds.): Matheuristics. Hybridizing Metaheuristics and Mathematical Programming, Annals of Information Systems. Springer, Heidelberg (2009)Google Scholar
  11. 11.
    Mosheiov, G.: The traveling salesman problem with pickup and delivery. European Journal of Operational Research 79, 299–310 (1994)CrossRefMATHGoogle Scholar
  12. 12.
    Parragh, S.N., Doerner, K.F., Hartl, R.F.: A survey on pickup and delivery problems. Part I: Transportation between customers and depot. Journal für Betriebswirtschaft 58, 21–51 (2008)CrossRefGoogle Scholar
  13. 13.
    Parragh, S.N., Doerner, K.F., Hartl, R.F.: A survey on pickup and delivery problems. Part II: Transportation between pickup and delivery locations. Journal für Betriebswirtschaft 58, 81–117 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • I. Rodríguez-Martín
    • 1
  • Juan José Salazar-González
    • 1
  1. 1.DEIOCUniversidad de La LagunaSpain

Personalised recommendations