Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems

  • Paul Shaw
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1520)


We use a local search method we term Large Neighbourhood Search (LNS) to solve vehicle routing problems. LNS is analogous to the shuffing technique of job-shop scheduling, and so meshes well with constraint programming technology. LNS explores a large neighbourhood of the current solution by selecting a number of “related” customer visits to remove from the set of planned routes, and re-inserting these visits using a constraint-based tree search. Unlike similar methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We analyse the performance of our method on benchmark problems. We demonstrate that results produced are competitive with Operations Research meta-heuristic methods, indicating that constraint-based technology is directly applicable to vehicle routing problems


Time Window Local Search Benchmark Problem Constraint Programming Insertion Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    D. Applegate and W. Cook. A computational study of the job-shop scheduling problem. ORSA Journal On Computing, 3:149–156, 1991.zbMATHGoogle Scholar
  2. 2.
    B. De Backer, V. Furnon, P. Prosser, P. Kilby, and P. Shaw. Local search in constraint programming: Application to the vehicle routing problem. In A. Davenport and C. Beck, editors, Proceedings of the CP-97 workshop on Industrial Constraintbased Scheduling, 1997.Google Scholar
  3. 3.
    P. Baptiste, C. Le Pape, and W. Nuijten. Constraint-based optimization and approximation for job-shop scheduling. In Proceedings of the AAAI-SIGMAN Workshop on Intelligent Manufacturing Systems, IJCAI-95, Montreal, Canada, 1995.Google Scholar
  4. 4.
    Y. Caseau and F. Laburthe. Disjunctive scheduling with task intervals. Technical report, LIENS Technical Report 95-25, école Normale Supérieure Paris, France, July 1995.Google Scholar
  5. 5.
    Y. Caseau and F. Laburthe. Solving small TSPs with constraints. In L. Naish, editor, Proceedings the 14th International Conference on Logic Programming. The MIT Press, 1997.Google Scholar
  6. 6.
    N. Christofides, A. Mingozzi, and P. Toth. The vehicle routing problem. Combinatorial Optimization, pages 315–338, 1979.Google Scholar
  7. 7.
    M. Desrochers, J. Desrosiers, and M. Solomon. A new optimization algorithm for the vehicle routing problems with time windows. Operations Research, 40(2):342–354, 1992.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Fisher. Optimal solution of vehicle routing problems using minimum K-trees. Operations Research, 42:626–642, 1994.zbMATHMathSciNetGoogle Scholar
  9. 9.
    W. D. Harvey and M. L. Ginsberg. Limited discrepancy search. In Proceedings of the 14th IJCAI, 1995.Google Scholar
  10. 10.
    P. Kilby, P. Prosser, and P. Shaw. A comparison of traditional and constraint-based heuristic methods on vehicle routing problems with side constraints. Submitted to the Constraints Special Issue on Industrial Scheduling, 1998.Google Scholar
  11. 11.
    G. A. P. Kindervater and M. W. P. Savelsbergh. Vehicle routing: Handling edge exchanges. In E. H. L. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 337–360. Wiley, Chichester, 1997.Google Scholar
  12. 12.
    T. Mautor and P. Michelon. MIMAUSA: A new hybrid method combining exact solution and local search. In Proceedings of the 2nd International Conference on Meta-heuristics, 1997.Google Scholar
  13. 13.
    Pedro Meseguer and Toby Walsh. Interleaved and discrepancy based search. In Proceedings of the 13th European Conference on AI—ECAI-98, 1998. To appear.Google Scholar
  14. 14.
    G. Pesant and M. Gendreau. A view of local search in constraint programming. In Proceedings of CP’ 96, pages 353–366. Springer-Verlag, 1996.Google Scholar
  15. 15.
    G. Pesant, M. Gendreau, J.-Y. Potvin, and J.-M. Rousseau. An exact constraint logic programming algorithm for the traveling salesman problem with time windows. Transportation Science, 1998. To appear.Google Scholar
  16. 16.
    G. Pesant, M. Gendreau, and J.-M. Rousseau. GENIUS-CP: A generic single-vehicle routing algorithm. In Proceedings of CP’ 97, pages 420–433. Springer-Verlag, 1997.Google Scholar
  17. 17.
    J.-Y. Potvin and S. Bengio. A genetic approach to the vehicle routing problem with time windows. Technical Report CRT-953, Centre de Recherche sur les Transports, University of Montreal, 1994.Google Scholar
  18. 18.
    Y. Rochat and E. D. Taillard. Probabilistic diversi_cation and intensification in local search for vehicle routing. Journal of Heuristics, 1(1):147–167, 1995.zbMATHCrossRefGoogle Scholar
  19. 19.
    M. W. P. Savelsbergh. The vehicle routing problem with time windows: Minimizing route duration. ORSA Journal on Computing, 4(2):146–154, 1992.zbMATHGoogle Scholar
  20. 20.
    M. M. Solomon. Algorithms for the vehicle routing and scheduling problem with time window constraints. Operations Research, 35:254–265, 1987.zbMATHMathSciNetGoogle Scholar
  21. 21.
    E. Taillard, P. Badeau, M. Gendreau, F. Guertain, and J.-Y. Potvin. A tabu search heuristic for the vehicle routing problem with soft time windows. Transportation Science, 32(2), 1997.Google Scholar
  22. 22.
    E. D. Taillard. Parallel iterative search methods for vehicle routing problems. Networks, 23:661–676, 1993.zbMATHCrossRefGoogle Scholar
  23. 23.
    S. R. Thangiah, I. H. Osman, and T. Sun. Hybrid genetic algorithm, simulated annealing, and tabu search methods for vehicle routing problems with time windows. Working paper UKC/OR94/4, Institute of Mathematics and Statistics, University of Kent, Canterbury, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Paul Shaw
    • 1
  1. 1.ILOG S.A.Gentilly CedexFrance

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