Advertisement

Journal of Heuristics

, Volume 6, Issue 4, pp 501–523 | Cite as

Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics

  • Bruno De Backer
  • Vincent Furnon
  • Paul Shaw
  • Philip Kilby
  • Patrick Prosser
Article

Abstract

Constraint Programming typically uses the technique of depth-first branch and bound as the method of solving optimization problems. Although this method can give the optimal solution, for large problems, the time needed to find the optimal can be prohibitive. This paper introduces a method for using local search techniques within a Constraint Programming framework, and applies this technique to vehicle routing problems. We introduce a Constraint Programming model for vehicle routing, and a system for integrating Constraint Programming and local search techniques. We then describe how the method can be accelerated by handling core constraints using fast local checks, while other more complex constraints are left to the constraint propagation system. We have coupled our local search method with a meta-heuristic to avoid the search being trapped in local minima. Several meta-heuristics are investigated ranging from a simple Tabu Search method to Guided Local Search. An empirical study over benchmark problems shows the relative merits of these techniques. Investigations indicate that the specific long-term memory technique used by Guided Local Search can be used as a diversification method for Tabu Search, resulting in significant benefit. Several new best solutions on the Solomon problems are found in relatively few iterations of our algorithm.

vehicle routing Constraint Programming Tabu Search Guided Local Search 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. De Backer, B. and V. Furnon. (1997). “Meta-Heuristics in Constraint Programming: Experiments with Tabu Search on the Vehicle Routing Problem.” In Proceedings of the 2nd International Conference on Meta-heuristics.Google Scholar
  2. Caseau, Y. and F. Laburthe. (1997). “Solving Small TSPs with Constraints.” In L. Naish (ed.), Proceedings the 14th International Conference on Logic Programming. The MIT Press.Google Scholar
  3. Clarke, G. and G.W. Wright. (1964). “Scheduling of Vehicles from a Central Depot to a Number of Delivery Points.” Operations Research 12, 568–581.Google Scholar
  4. Desrochers, M., J. Desrosiers, and M. Solomon. (1992). “A new Optimization Algorithm for the Vehicle Routing Problems with Time Windows.” Operations Research 40(2), 342–354.Google Scholar
  5. Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman.Google Scholar
  6. Gendreau, M., A. Hertz, and G. Laporte. (1994). “A Tabu Search Heuristic for the Vehicle Routing Problem.” Management Science 40(10), 1276–1290.Google Scholar
  7. Glover, F. (1989). “Tabu Search, part I.” ORSA Journal on Computing 1(3), 190–206.Google Scholar
  8. Glover, F. (1990). “Tabu Search, part II.” ORSA Journal on Computing 2(1), 4–32.Google Scholar
  9. Glover, F. and M. Laguna. (1995). “Tabu Search.” In Modern Heuristic Techniques for Combinatorial Problems. McGraw-Hill, pp. 70–150.Google Scholar
  10. Glover, F.W. and M. Laguna. (1997). Tabu Search. Kluwer Academic.Google Scholar
  11. ILOG S.A. (1998). 9, Rue de Verdun, Gentilly, France. ILOG Dispatcher Reference Manual, Version 1.2.Google Scholar
  12. ILOG S.A. (1998). 9, Rue de Verdun, Gentilly, France. ILOG Solver Reference Manual, Version 4.3.Google Scholar
  13. Kilby, P., P. Prosser, and P. Shaw. (1997). “Guided Local Search for the Vehicle Routing Problem.” In Proceedings of the 2nd International Conference on Meta-heuristics.Google Scholar
  14. Laporte, G. and I.H. Osman. (1995). “Routing Problems: A Bibliography.” Annals of Operations Research 61, 227–262.Google Scholar
  15. Lin, S. (1965). “Computer Solutions of the Traveling Salesman Problem.” Bell Systems Technology Journal 44, 2245–2269.Google Scholar
  16. Or, I. (1976). “Travelling Salesman-Type Combinatorial Problems and their Relation to the Logistics of Blood-Banking.” Ph.D. Thesis, Department of Industrial Engineering and Management Sciences, Northwest University, Evanston, IL.Google Scholar
  17. Osman, I.H. (1993). “Metastrategy Simulated Annealing and Tabu Search Algorithms for the Vehicle Routing Problem.” Annals of Operations Research 41, 421–451.Google Scholar
  18. Pesant, G. and M. Gendreau. (1996). “A View of Local Search in Constraint Programming.” In E.C. Freuder (ed.), Second International Conference on Principles and Practice of Constraint Programming-CP96. Springer-Verlag, pp. 353–366.Google Scholar
  19. Pesant, G., M. Gendreau, J.-Y. Potvin, and J.-M. Rousseau. (1998). “An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows.” Transportation Science 32, 12–29.Google Scholar
  20. Potvin, J.-Y. and S. Bengio. (1994). “A Genetic Approach to the Vehicle Routing Problem with Time Windows.” Technical Report CRT-953, Centre de Recherche sur les Transports, University of Montreal.Google Scholar
  21. Potvin, J.-Y., T. Kervahut, B.-L. Garcia, and J.-M. Rousseau. (1993). “A Tabu Search Heuristic for the Vehicle Routing Problem with Time Windows.” Technical Report CRT-855, Centre de Recherche sur les Transports. University of Montreal.Google Scholar
  22. Rochat, Y. and E.D. Taillard. (1995). “Probabilistic Diversification and Intensification in Local Search for Vehicle Routing.” Journal of Heuristics 1(1), 147–167.Google Scholar
  23. Savelsbergh, M.W.P. (1988). Amsterdam: Centrum voor Wiskunde en Informatica.Google Scholar
  24. Savelsbergh, M.W.P. (1992). “The Vehicle Routing Problem with Time Windows: Minimizing Route Duration.” ORSA Journal on Computing 4(2), 146–154.Google Scholar
  25. Shaw, P. (1998). “Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems.” In M. Maher and J.-F. Puget (eds.), Fourth International Conference on Principles and Practice of Constraint Programming-CP98, Springer-Verlag, pp. 417–431.Google Scholar
  26. Solomon, M.M. (1987). “Algorithms for the Vehicle Routing and Scheduling Problem with Time Window Constraints.” Operations Research 35, 254–265.Google Scholar
  27. Taillard, E., P. Badeau, M. Gendreau, F. Guertain, and J.-Y. Potvin. (1997). “A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows.” Transportation Science 32(2).Google Scholar
  28. Thangiah, S.R., I.H. Osman, and T. Sun. (1994). “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.Google Scholar
  29. Tsang, E. and C. Voudouris. (1997). “Fast Local Search and Guided Local Search and Their Application to British Telecom's Workforce Scheduling Problem.” Operations Research Letters 20(3), 119–127.Google Scholar
  30. Voudouris, C. (1997). “Guided Local Search for Combinatorial Problems.” Ph.D. Thesis, University of Essex, Colchester, UK.Google Scholar
  31. Voudouris, C. and E. Tsang. (1995). “Function Optimization Using Guided Local Search.” Technical Report CSM-249, Department of Computer Science, University of Essex.Google Scholar
  32. Voudouris, C. and E.P.K. Tsang. (1996). “Partial Constraint Satisfaction Problems and Guided Local Search.” In Proceedings of Practical Applications of Constraint Technology (PACT '96).Google Scholar
  33. Voudouris, C. and E.P.K. Tsang. (1998). “Guided Local Search.” European Journal of Operational Research 113(2), 80–110.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Bruno De Backer
    • 1
  • Vincent Furnon
    • 2
  • Paul Shaw
    • 3
  • Philip Kilby
    • 4
  • Patrick Prosser
    • 5
  1. 1.ILOG S.A.GentillyFrance
  2. 2.ILOG S.A.GentillyFrance
  3. 3.ILOG S.A.GentillyFrance
  4. 4.CSIRO Mathematical and Information SciencesCanberraAustralia
  5. 5.Department of Computer ScienceUniversity of StrathclydeGlasgowScotland

Personalised recommendations