A Time-Dependent No-Overlap Constraint: Application to Urban Delivery Problems

  • Penélope Aguiar Melgarejo
  • Philippe Laborie
  • Christine Solnon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9075)

Abstract

The Time-Dependent Traveling Salesman Problem (TDTSP) is the extended version of the TSP where arc costs depend on the time when the arc is traveled. When we consider urban deliveries, travel times vary considerably during the day and optimizing a delivery tour comes down to solving an instance of the TDTSP. In this paper we propose a set of benchmarks for the TDTSP based on real traffic data and show the interest of handling time dependency in the problem. We then present a new global constraint (an extension of no-overlap) that integrates time-dependent transition times and show that this new constraint outperforms the classical CP approach.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Optimod’Lyon website, (21 July 2014). http://www.optimodlyon.com/
  2. 2.
    Abeledo, H., Fukasawa, R., Pessoa, A., Uchoa, E.: The time dependent traveling salesman problem: polyhedra and algorithm. Mathematical Programming Computation 5(1), 27–55 (2013)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Aguiar Melgarejo, P., Baudel, T., Solnon, C.: Global and reactive routing in urban context: first experiments and difficulty assessment. In: CP-2012 Workshop on Optimization and Smart Cities, October 2012Google Scholar
  4. 4.
    Baptiste, P., Laborie, P., Le Pape, C., Nuijten, W.: Constraint-based scheduling and planning. In: F. Rossi, P. van Beek, T.W. (eds.) Handbook of Constraint Programming, chap. 22, pp. 759–798. Elsevier (2006)Google Scholar
  5. 5.
    Baptiste, P., Le Pape, C.: Disjunctive constraints for manufacturing scheduling: principles and extensions. In: Proc. 3rd International Conference on Computer Integrated Manufacturing (1995)Google Scholar
  6. 6.
    Benchimol, P., van Hoeve, W.J., Regin, J.C., Rousseau, L.M., Rueher, M.: Improved filtering for weighted circuit constraints. Constraints, pp. 205–233 (2012)Google Scholar
  7. 7.
    Bentner, J., Bauer, G., Obermair, G.M., Morgenstern, I., Schneider, J.: Optimization of the time-dependent traveling salesman problem with Monte Carlo methods. Physical Review E 64(3), August 2001Google Scholar
  8. 8.
    Bront, J.: Integer Programming approaches to the Time Dependent Travelling Salesman Problem. Ph.D. thesis, Universidad de Buenos Aires (2012)Google Scholar
  9. 9.
    Cordeau, J.F., Ghiani, G., Guerriero, E.: Properties and Branch-and-Cut Algorithm for the Time-Dependent Traveling Salesman ProblemGoogle Scholar
  10. 10.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, McGraw-Hill edn. (1990)Google Scholar
  11. 11.
    Donati, A.V., Montemanni, R., Casagrande, N., Rizzoli, A.E., Gambardella, L.M.: Time dependent vehicle routing problem with a multi ant colony system. European Journal of Operational Research 185(3), 1174–1191 (2008)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Fages, J.G., Lorca, X.: Improving the asymmetric tsp by considering graph structure. arxiv preprint arxiv:1206.3437 (2012)Google Scholar
  13. 13.
    Figliozzi, M.A.: The time dependent vehicle routing problem with time windows: Benchmark problems, an efficient solution algorithm, and solution characteristics. Transportation Research Part E Logistics and Transportation Review 48, 616–636 (2012)CrossRefGoogle Scholar
  14. 14.
    Fleischmann, B., Gietz, M., Gnutzmann, S.: Time-Varying Travel Times in Vehicle Routing. Transportation Science 38(2), 160–173 (2004)CrossRefGoogle Scholar
  15. 15.
    Focacci, F., Laborie, P., Nuijten, W.: Solving Scheduling Problems with Setup Times and Alternative Resources. AIPS Proceedings (2000)Google Scholar
  16. 16.
    Fox, K.R., Gavish, B., Graves, S.C.: An n-Constraint Formulation of the (Time- Dependent) Traveling Salesman Problem. Operations Research 28(4), 1018–1021 (1980)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Gouveia, L., Voss, S.: A classification of formulations for the (time-dependent) traveling salesman problem. European Journal of Operational Research 83(1), 69–82 (1995)CrossRefMATHGoogle Scholar
  18. 18.
    Hashimoto, H., Yagiura, M., Ibaraki, T.: An iterated local search algorithm for the time-dependent vehicle routing problem with time windows. Discrete Optimization 5(2), 434–456 (2008)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Ichoua, S., Gendreau, M., Potvin, J.Y.: Vehicle Dispatching With Time-Dependent Travel Times. European Journal of Operations Research (2003)Google Scholar
  20. 20.
    Kelareva, E., Tierney, K., Kilby, P.: CP Methods for Scheduling and Routing with Time-Dependent Task Costs. EURO Journal on Computational Optimization 2, 147–194 (2014)CrossRefMATHGoogle Scholar
  21. 21.
    Laborie, P., Godard, D.: Self-adapting large neighborhood search: application to single-mode scheduling problems. In: Proceedings of the 3rd Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA), pp. 276–284 (2007)Google Scholar
  22. 22.
    Laborie, P., Rogerie, J.: Reasoning with conditional time-intervals. In: FLAIRS Conference, pp. 555–560 (2008)Google Scholar
  23. 23.
    Laborie, P., Rogerie, J., Shaw, P., Vilím, P.: Reasoning with conditional time-intervals. Part II: an algebraical model for resources. In: FLAIRS Conference (2009)Google Scholar
  24. 24.
    Li, F., Golden, B., Wasil, E.: Solving the time dependent traveling salesman problem. In: Golden, B., Raghavan, S., Wasil, E. (eds.) The Next Wave in Computing, Optimization, and Decision Technologies, Operations Research/Computer Science Interfaces Series, vol. 29, pp. 163–182. Springer, US (2005)CrossRefGoogle Scholar
  25. 25.
    Maden, W., Eglese, R., Black, D.: Vehicle Routing and Scheduling with Time Varying Data: A Case Study. Journal of the Operational Research Society 61, 515–522 (2009)CrossRefGoogle Scholar
  26. 26.
    Malandraki, C., Daskin, M.S.: Time Dependent Vehicle Routing Problems: Formulations. Properties and Heuristic Algorithms. Transportation Science 26, 185–200 (1992)MATHGoogle Scholar
  27. 27.
    Nannicini, G.: Point-to-Point Shortest Paths on Dynamic Time-Dependent Road Networks. Ph.D. thesis, Ecole Polytechnique, Palaiseau (2009)Google Scholar
  28. 28.
    Picard, J.C., Queyranne, M.: The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling (1978)Google Scholar
  29. 29.
    Schneider, J.: The time-dependent traveling salesman problem. Physica A: Statistical Mechanics and its Applications 314(1–4), 151–155 (2002)CrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Stecco, G., Cordeau, J.F., Moretti, E.: A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times. Computers & Operations Research 35(8), 2635–2655 (2007)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Penélope Aguiar Melgarejo
    • 1
    • 2
    • 3
  • Philippe Laborie
    • 3
  • Christine Solnon
    • 1
    • 2
  1. 1.Université de Lyon, CNRSLyonFrance
  2. 2.INSA-Lyon, LIRIS, UMR5205LyonFrance
  3. 3.France LabIBMGentillyFrance

Personalised recommendations