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A parallel algorithm for the vehicle routing problem with time window constraints

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Abstract

In this paper, we describe a new parallel tabu search heuristic for the vehicle routingproblem with time window constraints (VRPTW). The neighborhood structure we proposeis based on simple customer shifts and allows us to consider infeasible interim‐solutions.Similarly to the column generation approach used in exact algorithms, all routes generatedby the tabu search heuristic are collected in a pool. To obtain a new initial solution forthe tabu search heuristic, a fast set covering heuristic is periodically applied to the routes inthe pool. The parallel heuristic has been implemented on a Multiple‐Instruction Multiple‐Datacomputer architecture with eight nodes. Computational results for Solomon's benchmarkproblems demonstrate that our parallel heuristic can produce high‐quality solutions.

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References

  1. A. Bachem, W. Hochstättler and M. Malich, The simulated trading heuristic for solving vehicle routing problems, Discrete Applied Mathematics 65(1996)47-72.

    Google Scholar 

  2. P. Badeau, M. Gendreau, F. Guertin, J.-Y. Potvin and E. Taillard, A parallel tabu search heuristic for the vehicle routing problem with time windows, Technical Report CRT-95-84, Université de Montréal, 1995.

  3. J.E. Beasley, A Lagrangian heuristic for set covering problems, Naval Research Logistics 37(1990)151-164.

    Google Scholar 

  4. J.E. Beasley, Lagrangian relaxation, in: Modern Heuristic Techniques for Combinatorial Problems, ed. C.R. Reeves, Wiley, 1993, pp. 243-303.

  5. W.C. Chiang and R.A. Russell, Simulated annealing metaheuristics for the vehicle routing problem with time windows, Annals of Operations Research 63(1996)3-27.

    Google Scholar 

  6. M. Desrochers, J. Desrosiers and M.M. Solomon, A new optimization algorithm for the vehicle routing problem with time windows, Operations Research 40(1992)342-354.

    Google Scholar 

  7. J. Desrosiers, Y. Dumas, M.M. Solomon and F. Soumis, Time constrained routing and scheduling, in: Network Routing, Handbooks on Operations Research and Management Science 8, ed. M.O. Ball, T.L. Magnanti, C.L. Monma and G.L. Nemhauser, North-Holland, Amsterdam, 1995, pp. 35-139.

    Google Scholar 

  8. M.L. Fisher, Vehicle routing, in: Network Routing, Handbooks on Operations Research and Management Science 8, eds. M.O. Ball, T.L. Magnanti, C.L. Monma and G.L. Nemhauser, North-Holland, Amsterdam, 1995, pp. 1-33.

    Google Scholar 

  9. M.L. Fisher, K.O. Jörnsten and O.B.G. Madsen, Vehicle routing with time windows: Two optimization algorithms, Operations Research 45(1997)488-492.

    Google Scholar 

  10. B.-L. Garcia, J.-Y. Potvin and J.-M. Rousseau, A parallel implementation of the tabu search heuristic for vehicle routing problems with time window constraints, Computers Oper. Res. 21(1994)1025-1033.

    Google Scholar 

  11. A. Geist, A. Beguelin, J. Dongarra, W. Jaing, R. Mancheck and V. Sunderam, PVM 3.0 user's guide and reference manual, Oak Ridge National Laboratory, Tennessee.

  12. S. Gélinas, M. Desrochers, J. Desrosiers and M.M. Solomon, A new branching strategy for time constrained routing problems with application to backhauling, Annals of Operations Research 61(1995)91-109.

    Google Scholar 

  13. M. Gendreau, A. Hertz and G. Laporte, A tabu search heuristic for the vehicle routing problem, Management Science 40(1994)1276-1290.

    Google Scholar 

  14. M. Gendreau, G. Laporte and J.-Y. Potvin, Vehicle routing: Modern heuristics, in: Local Search in Combinatorial Optimization, eds. E.H.L. Aarts and J.K. Lenstra, Wiley, Chichester, 1997, pp. 311-336

    Google Scholar 

  15. F. Glover, Tabu search, part I, ORSA J. Computing 1(1989)190-206.

    Google Scholar 

  16. F. Glover, Tabu search, part II, ORSA J. Computing 2(1990)4-32.

    Google Scholar 

  17. F. Glover, E. Taillard and D. de Werra, A user's guide to tabu search, Annals of Operations Research 41(1993)3-28.

    Google Scholar 

  18. G.A.P. Kindervater and M.W.P. Savelsbergh, Vehicle routing: Handling edge exchanges, in: Local Search in Combinatorial Optimization, eds. E.H.L. Aarts and J.K. Lenstra, Wiley, Chichester, 1997, pp. 337-360.

    Google Scholar 

  19. N. Kohl and O.B.G. Madsen, An optimization algorithm for the vehicle routing problem with time windows based on Lagrangian relaxation, Operations Research 45(1997)395-406.

    Google Scholar 

  20. G. Laporte, The vehicle routing problem: An overview of exact and approximate algorithms, European J. Operational Research 59(1992)345-358.

    Google Scholar 

  21. G. Laporte and I.H. Osman, Routing problems: A bibliography, Annals of Operations Research 61(1995)227-262.

    Google Scholar 

  22. J.K. Lenstra and A.H.G. Rinnooy Kan, Complexity of vehicle routing and scheduling problems, Networks 11(1981)221-227.

    Google Scholar 

  23. S. Lin, Computer solutions of the traveling salesman problem, Bell Systems Technical Journal 44(1965)2245-2269.

    Google Scholar 

  24. S. Lin and B.W. Kernighan, An effective heuristic algorithm for the traveling salesman problem, Operations Research 21(1973)498-516.

    Google Scholar 

  25. I.H. Osman and G. Laporte, Metaheuristics: A bibliography, Annals of Operations Research 63(1996)513-628.

    Google Scholar 

  26. I. Or, Traveling salesman-type combinatorial problems and their relation to the logistics of blood banking, Ph.D. Thesis, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, 1976.

    Google Scholar 

  27. J.-Y. Potvin, T. Kervahut, B.-L Garcia and J.-M. Rousseau, The vehicle routing problem with time windows — Part 1: Tabu search, INFORMS J. Computing 8(1996)158-164.

    Google Scholar 

  28. J.-Y. Potvin and J.-M. Rousseau, A parallel route building algorithm for the vehicle routing and scheduling problem with time windows, European J. Operational Research 66(1993)331-340.

    Google Scholar 

  29. J.-Y. Potvin and J.-M. Rousseau, An exchange heuristic for routeing problems with time windows, Journal of the Operational Research Society 46(195)1433-1446.

  30. Y. Rochat and E.D. Taillard, Probabilistic diversification and intensification in local search for vehicle routing, J. of Heuristics 1(1995)147-167.

    Google Scholar 

  31. C. Rego and C. Roucairol, A parallel tabu search algorithm using ejection chains for the vehicle routing problem, in: Meta-Heuristics: Theory and Applications, eds. I.H. Osman and J.P. Kelly, Kluwer Academic, 1996, pp. 661-675.

  32. R.A. Russell, Hybrid heuristics for the vehicle routing problem with time windows, Transportation Science 29(1995)156-166.

    Google Scholar 

  33. M.W.P. Savelsbergh, An efficient implementation of local search algorithms for constrained routing problems, European J. of Operational Research 47(1990)75-85.

    Google Scholar 

  34. M.M. Solomon, Algorithms for the vehicle routing and scheduling problem with time window constraints, Operations Research 35(1987)254-265.

    Google Scholar 

  35. E. Taillard, Parallel iterative search methods for vehicle routing problems, Networks 23(1993)661-673.

    Google Scholar 

  36. E. Taillard, P. Badeau, M. Gendreau, F. Guertin and J.-Y. Potvin, A new neighborhood structure for the vehicle routing problem with time windows, Technical Report CRT-95-66, Université de Montréal, 1995.

  37. S.R. Thangiah, I.H. Osman and T. Sun, Metaheuristics for vehicle routing problems with time windows, Research Report UKC/IMS/OR94/8, Institute of Mathematics and Statistics, University of Kent, 1995.

  38. M. Toulouse, T.G. Crainic and M. Gendreau, Communication issues in designing cooperative multi-thread parallel searches, in: Meta-Heuristics: Theory and Applications, eds. I.H. Osman and J.P. Kelly, Kluwer Academic, 1996, pp. 503-522.

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Authors
  1. J. Schulze
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  2. T. Fahle
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Schulze, J., Fahle, T. A parallel algorithm for the vehicle routing problem with time window constraints. Annals of Operations Research 86, 585–607 (1999). https://doi.org/10.1023/A:1018948011707

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