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Heuristic solutions for the vehicle routing problem with time windows and synchronized visits

Abstract

We present a simulated annealing based algorithm for a variant of the vehicle routing problem (VRP), in which a time window is associated with each client service and some services require simultaneous visits from different vehicles to be accomplished. The problem is called the VRP with time windows and synchronized visits. The algorithm features a set of local improvement methods to deal with various objectives of the problem. Experiments conducted on the benchmark instances from the literature clearly show that our method is fast and outperforms the existing approaches. It produces all known optimal solutions of the benchmark in very short computational times, and improves the best results for the rest of the instances.

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References

  1. Afifi, S., Dang, D.C., Moukrim, A.: A simulated annealing algorithm for the vehicle routing problem with time windows and synchronization constraints. In: Proceedings of LION-7, Lecture Notes in Computer Science, vol. 7997, pp. 259–265 (2013)

  2. Aho, A.V., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM J. Comput. 1(2), 131–137 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baños, R., Ortega, J., Gil, C., Márquez, A.L., De Toro, F.: A hybrid meta-heuristic for multi-objective vehicle routing problems with time windows. Comput. Ind. Eng. 65(2), 286–296 (2013)

    Article  Google Scholar 

  4. Baños, R., Ortega, J., Gil, C., Fernandez, A., De Toro, F.: A simulated annealing-based parallel multi-objective approach to vehicle routing problems with time windows. Expert Syst. Appl. 40(5), 1696–1707 (2013)

    Article  Google Scholar 

  5. Bouly, H., Dang, D.C., Moukrim, A.: A memetic algorithm for the team orienteering problem. 4OR 8(1), 49–70 (2009)

    Article  Google Scholar 

  6. Bredström, D., Rönnqvist, M.: A branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. NHH Dept of Finance and Management Science Discussion Paper (2007)

  7. Bredström, D., Rönnqvist, M.: Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. Eur. J. Oper. Res. 191(1), 19–31 (2008)

    Article  MATH  Google Scholar 

  8. Chiang, W.C., Russell, R.A.: Simulated annealing metaheuristics for the vehicle routing problem with time windows. Ann. Oper. Res. 63(1), 3–27 (1996)

    Article  MATH  Google Scholar 

  9. Czech, Z., Czarnas, P.: Parallel simulated annealing for the vehicle routing problem with time windows. In: Proceedings of 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing (2002)

  10. Dang, D.C., Guibadj, R.N., Moukrim, A.: An effective PSO-inspired algorithm for the team orienteering problem. Eur. J. Oper. Res. 229(2), 332–344 (2013)

    Article  Google Scholar 

  11. Dohn, A., Rasmussen, M.S., Larsen, J.: The Vehicle Routing Problem with Time Windows and Temporal Dependencies. Networks 58(4), 273–289 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Drexl, M.: Synchronization in vehicle routing a survey of VRPs with multiple synchronization constraints. Transp. Sci. 46(3), 297–316 (2012)

    Article  Google Scholar 

  13. El Hachemi, N., Gendreau, M., Rousseau, L.M.: A heuristic to solve the synchronized log-truck scheduling problem. Comput. Oper. Res. 40(3), 666–673 (2013)

    Article  Google Scholar 

  14. Fischetti, M., Lodi, A.: Local branching. Math. Program. 98(1–3), 23–47 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ioachim, I., Desrosiers, J., Soumis, F., Bélanger, N.: Fleet assignment and routing with schedule synchronization constraints. Eur. J. Oper. Res. 119(1), 75–90 (1999)

    Article  MATH  Google Scholar 

  16. Kirkpatrick, S., Vecchi, M., et al.: Optimization by simmulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lenstra, J.K., Kan, A.: Complexity of vehicle routing and scheduling problems. Networks 11(2), 221–227 (1981)

    Article  Google Scholar 

  18. Li, Y., Lim, A., Rodrigues, B.: Manpower allocation with time windows and job-teaming constraints. Nav. Res. Logist. (NRL) 52(4), 302–311 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Potvin, J.Y., Kervahut, T., Garcia, B.L., Rousseau, J.M.: The vehicle routing problem with time windows part I: tabu search. INFORMS J. Comput. 8(2), 158–164 (1996)

    Article  MATH  Google Scholar 

  20. Rasmussen, M.S., Justesen, T., Dohn, A., Larsen, J.: The home care crew scheduling problem: Preference-based visit clustering and temporal dependencies. Eur. J. Oper. Res. 219(3), 598–610 (2012)

    Article  MATH  Google Scholar 

  21. Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  22. Solomon, M.M., Desrosiers, J.: Time window constrained routing and scheduling problems. Transp. Sci. 22, 1–13 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tavakkoli-Moghaddam, R., Gazanfari, M., Alinaghian, M., Salamatbakhsh, A., Norouzi, N.: A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing. J. Manuf. Syst. 30(2), 83–92 (2011)

    Article  Google Scholar 

  24. Toth, P., Vigo, D.: An overview of vehicle routing problems. Veh. Routing Probl. 9, 1–26 (2002)

    Article  Google Scholar 

  25. Van Breedam, A.: Improvement heuristics for the vehicle routing problem based on simulated annealing. Eur. J. Oper. Res. 86(3), 480–490 (1995)

    Article  MATH  Google Scholar 

  26. Wen, M., Larsen, J., Clausen, J., Cordeau, J.F., Laporte, G.: Vehicle routing with cross-docking. J. Oper. Res. Soc. 60(12), 1708–1718 (2009)

    Article  MATH  Google Scholar 

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Acknowledgments

This work was partially supported by the Regional Council of Picardy and the European Regional Development Fund (ERDF), under PRIMA project. It was also partially supported by the National Agency for Research, under ATHENA project, reference ANR-13-BS02-0006-01. This work was carried out in the framework of the Labex MS2T, which was funded by the French Government, through the program “Investments for the future” managed by the National Agency for Research (Reference ANR-11-IDEX-0004-02). We would also like to thank the referees for their insightful comments that helped us improve the quality of this paper.

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Correspondence to Sohaib Afifi.

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A preliminary version [1] of this paper was presented at the conference Learning and Intelligent OptimizatioN (LION 7), 2013.

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Afifi, S., Dang, DC. & Moukrim, A. Heuristic solutions for the vehicle routing problem with time windows and synchronized visits. Optim Lett 10, 511–525 (2016). https://doi.org/10.1007/s11590-015-0878-3

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  • DOI: https://doi.org/10.1007/s11590-015-0878-3

Keywords

  • Vehicle routing
  • Synchronization
  • Destruction/repair
  • Local search
  • Simulated annealing