A Tabu Search Heuristic for a Full-Load, Multi-Terminal, Vehicle Scheduling Problem with Backhauling and Time Windows


The problem considered is the full-load pickup and delivery problem with time windows (PDPTW), and heterogeneous products and vehicles, where the assignment of pickup points to requests is not predetermined. Elements associated with tabu search, such as diversification by reversion to ‘junctions’ and the use of soft aspiration criteria, are embedded into our tabu search implementation. This metaheuristic is evaluated using random instances and selected data from a construction company in the U.K. The obtained results are compared against lower bounds from LP relaxation and also solutions from an existing multi-level heuristic.

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  1. 1.

    Bodin, L., Mingozzi, A., Baldacci, R. and Ball, M.: The rollon-rolloff vehicle routing problem, Transport. Sci.34(3) (2000), 271–288.

    Google Scholar 

  2. 2.

    Calvo, R.: A new heuristic for the travelling salesman problem with time windows, Transport. Sci.34(1) (2000), 113–124.

    Google Scholar 

  3. 3.

    Cordeau, J.-F., Laporte, G. and Mercier, A.: A unified tabu search heuristic for vehicle routing problems with time windows, J. Oper. Res. Soc.52(8) (2001), 928–936.

    Google Scholar 

  4. 4.

    Currie, R. and Salhi, S.: Exact and heuristic methods for a full-load, multi-terminal, vehicle scheduling problem with backhauling and time windows, J. Oper. Res. Soc.54 (2003), 390–400.

    Google Scholar 

  5. 5.

    Dumas, Y., Desrosiers, J. and Soumis, F.: The pickup and delivery problem with time windows, European J. Oper. Res.54 (1991), 7–22.

    Google Scholar 

  6. 6.

    Gendreau, M., Laporte, G. and Vigo, D.: Heuristics for the travelling salesman problem with pickup and delivery,Comput. Oper. Res.26 (1999), 699–714.

    Google Scholar 

  7. 7.

    Glover, F. and Laguna, M.: Tabu Search, Kluwer Acad. Publ., Boston, 1997.

    Google Scholar 

  8. 8.

    Ichoua, S., Gendreau, M. and Potvin, J.-Y.: Diversion issues in real-time vehicle dispatching, Transport. Sci.34(4) (2000), 426–438.

    Google Scholar 

  9. 9.

    James, J. C. and Salhi, S.: A tabu search heuristic for the location of multi-type protection devices on electrical supply tree networks, J. Combin. Optim.6 (2002), 81–98.

    Google Scholar 

  10. 10.

    Kelly, J., Laguna, M. and Glover, F.: A study of diversification strategies for the quadratic assignment problem, Comput. Oper. Res.29 (1994), 665–695.

    Google Scholar 

  11. 11.

    Lokketangen, A. and Glover, F.: Solving zero-one mixed integer programming problems using tabu search, European J. Oper. Res.106 (1998), 624–658.

    Google Scholar 

  12. 12.

    Osman, I. H.: Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem, Ann. Oper. Res.41 (1993).

  13. 13.

    Osman, I. H. and Salhi, S.: Local search strategies for the vehilce fleet mix problem, in V. J. Rayward-Smith, I. H. Osman, C. R. Reeves and G. D. Smith (eds),Modern Heuristic Search Methods, Wiley, Chichester, 1996, Chapter 8, pp. 131–154.

  14. 14.

    Potvin, J.-Y., Kervahut, T., Garcia, B.-L. and Rousseau, J.-M.: The vehicle routing problem with time windows. Part 1: Tabu search, INFORMS J. Comput.8(2) (1995), 158–184.

    Google Scholar 

  15. 15.

    Renaud, J., Boctor, F. and Laporte, G.: Perturbation heuristics for the pickup and delivery travelling salesman problem, Comput. Oper. Res.29 (2002), 1129–1141.

    Google Scholar 

  16. 16.

    Rochat, Y. and Taillard, E.: Probabilistic diversification and intensification in local search for vehicle routing, J. Heuristics1 (1995), 147–167.

    Google Scholar 

  17. 17.

    Salhi, S.: Defining tabu list size and aspiration criterion within tabu search methods, Comput. Oper. Res.29 (2002), 67–86.

    Google Scholar 

  18. 18.

    Savelsbergh, M. and Sol, M.: Drive: Dynamic routing of independent vehicles, Oper. Res.46(4) (1998), 474–490.

    Google Scholar 

  19. 19.

    Taillard, E., Badeau, P., Gendreau, M., Guertin, F. and Potvin, J.-Y.: A tabu search heuristic for the vehicle routing problem with soft time windows, Transport. Sci.31(2) (1997), 170–186.

    Google Scholar 

  20. 20.

    Thangiah, S. R., Potvin, J.-Y. and Tong, S.: Heuristic approaches to vehicle routing with backhauls and time windows, Comput. Oper. Res.23(11) (1996), 1043–1058.

    Google Scholar 

  21. 21.

    Thomas, P. and Salhi, S.: A tabu search approach for the resource constrained project management problem, J. Heuristics4 (1998), 123–139.

    Google Scholar 

  22. 22.

    Van Der Bruggen, L. J. J., Lenstra, J. K. and Schuur, P. C.: Variable-depth search for the singlevehicle pickup and delivery problem with time windows, Transport. Sci.27(3) (1993), 298–310.

    Google Scholar 

  23. 23.

    Wassan, N. A. and Osman, I. H.: Tabu search variants for the mix fleet vehicle routing problem, J. Oper. Res. Soc.53(7) (2002), 768–782.

    Google Scholar 

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Currie, R.H., Salhi, S. A Tabu Search Heuristic for a Full-Load, Multi-Terminal, Vehicle Scheduling Problem with Backhauling and Time Windows. Journal of Mathematical Modelling and Algorithms 3, 225–243 (2004). https://doi.org/10.1023/B:JMMA.0000038616.99798.f2

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  • tabu search
  • heuristics
  • LP relaxation
  • distribution scheduling