Advertisement

Filtering AtMostNValue with Difference Constraints: Application to the Shift Minimisation Personnel Task Scheduling Problem

  • Jean-Guillaume Fages
  • Tanguy Lapègue
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)

Abstract

This paper introduces a propagator which filters a conjunction of difference constraints and an AtMostNValue constraint. This propagator is relevant in many applications such as the Shift Minimisation Personnel Task Scheduling Problem, which is used as a case study all along this paper. Extensive experiments show that it significantly improves a straightforward CP model, so that it competes with best known approaches from Operational Research.

Keywords

AtMostNValue Constraints Conjunction Global Constraints Shift Minimisation Personnel Task Scheduling Problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andreello, G., Caprara, A., Fischetti, M.: Embedding {0, 1/2}-cuts in a branch-and-cut framework: A computational study. INFORMS J. on Computing 19(2), 229–238 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Beldiceanu, N.: Pruning for the minimum constraint family and for the number of distinct values constraint family. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 211–224. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Global constraint catalogue: Past, present and future. Constraints 12(1), 21–62 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Filtering Algorithms for the NValue Constraint. Constraints 11(4), 271–293 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bessiere, C., Katsirelos, G., Narodytska, N., Quimper, C.G., Walsh, T.: Propagating conjunctions of alldifferent constraints. CoRR abs/1004.2626 (2010)Google Scholar
  6. 6.
    Carter, M.W., Tovey, C.A.: When is the classroom assignment problem hard? Operations Research 40(1), 28–39 (1992)CrossRefGoogle Scholar
  7. 7.
    Chabert, G., Jaulin, L., Lorca, X.: A constraint on the number of distinct vectors with application to localization. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 196–210. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    CHOCO Team: choco: an Open Source Java Constraint Programming Library. Tech. rep., Ecole des Mines de Nantes (2010), http://www.emn.fr/z-info/choco-solver/
  9. 9.
    Dijkstra, M.C., Kroon, L.G., Salomon, M., Van Nunen, J.A.E.E., van Wassenhove, L.N.: Planning the Size and Organization of KLM’s Aircraft Maintenance Personnel. Interfaces 24(6), 47–58 (1994)CrossRefGoogle Scholar
  10. 10.
    Dowling, D., Krishnamoorthy, M., Mackenzie, H., Sier, D.: Staff rostering at a large international airport. Annals of Operations Research 72, 125–147 (1997)CrossRefzbMATHGoogle Scholar
  11. 11.
    Ernst, A.T., Jiang, H., Krishnamoorthy, M., Sier, D.: Staff scheduling and rostering: A review of applications, methods and models. European Journal of Operational Research 153(1), 3–27 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Fischetti, M., Martello, S., Toth, P.: The fixed job schedule problem with spread-time constraints. Operations Research 35(6), 849–858 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Fischetti, M., Martello, S., Toth, P.: The fixed job schedule problem with working-time constraints. Operations Research 37(3), 395–403 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, 1st edn. W. H. Freeman (January 1979)Google Scholar
  15. 15.
    Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, 2nd edn. Annals of Discrete Mathematics, vol. 57. Elsevier (2004)Google Scholar
  16. 16.
    Gualandi, S., Malucelli, F.: Exact solution of graph coloring problems via constraint programming and column generation. INFORMS J. Comput. Sc. 24, 81–100 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Halldórsson, M.M., Radhakrishnan, J.: Greed is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica 18(1), 145–163 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Haralick, R.M., Elliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. In: Proceedings of the 6th International Joint Conference on Artificial Intelligence, IJCAI 1979, vol. 1, pp. 356–364. Morgan Kaufmann Publishers Inc. (1979)Google Scholar
  19. 19.
    Kadioglu, S., Malitsky, Y., Sellmann, M., Tierney, K.: Isac - instance-specific algorithm configuration. In: ECAI. Frontiers in Artificial Intelligence and Applications, vol. 215, pp. 751–756. IOS Press (2010)Google Scholar
  20. 20.
    Krishnamoorthy, M., Ernst, A.T.: The personnel task scheduling problem. In: Optimization Methods and Applications, pp. 343–368. Springer, US (2001)CrossRefGoogle Scholar
  21. 21.
    Krishnamoorthy, M., Ernst, A., Baatar, D.: Algorithms for large scale shift minimisation personnel task scheduling problems. European Journal of Operational Research 219, 34–48 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Kroon, L.G., Salomon, M., Wassenhove, L.N.V.: Exact and approximation algorithms for the tactical fixed interval scheduling problem. Operations Research 45(4) (1997)Google Scholar
  23. 23.
    Lapègue, T., Fages, J.G., Prot, D., Bellenguez-Morineau, O.: Personnel Task Scheduling Problem Library (2013), https://sites.google.com/site/ptsplib/smptsp/home
  24. 24.
    Lecoutre, C., Sais, L., Tabary, S., Vidal, V.: Reasoning from last conflict(s) in constraint programming. Artif. Intell. 173(18), 1592–1614 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Leone, R., Festa, P., Marchitto, E.: A Bus Driver Scheduling Problem: a new mathematical model and a GRASP approximate solution. Journal of Heuristics 17(4), 441–466 (2010)CrossRefGoogle Scholar
  26. 26.
    López-Ortiz, A., Quimper, C.G., Tromp, J., van Beek, P.: A fast and simple algorithm for bounds consistency of the alldifferent constraint. In: IJCAI, pp. 245–250. Morgan Kaufmann (2003)Google Scholar
  27. 27.
    Monette, J.N., Flener, P., Pearson, J.: Towards solver-independent propagators. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 544–560. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  28. 28.
    Pachet, F., Roy, P.: Automatic generation of music programs. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 331–345. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  29. 29.
    Régin, J.C.: A Filtering Algorithm for Constraints of Difference in CSPs. In: National Conference on Artificial Intelligence, pp. 362–367. AAAI (1994)Google Scholar
  30. 30.
    Schulte, C., Stuckey, P.J.: Efficient constraint propagation engines. CoRR abs/cs/0611009 (2006)Google Scholar
  31. 31.
    Smet, P., Wauters, T., Mihaylow, M., Vanden Berghe, G.: The shift minimisation personnel task scheduling problem: a new hybrid approach and computational insights. Technical report (2013)Google Scholar
  32. 32.
    Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., De Boeck, L.: Personnel scheduling: A literature review. European Journal of Operational Research 226(3), 367–385 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-Guillaume Fages
    • 1
  • Tanguy Lapègue
    • 2
  1. 1.École des Mines de Nantes, LINA (UMR CNRS 6241)LUNAM UniversitéFrance
  2. 2.École des Mines de Nantes, IRCCyN (UMR CNRS 6597)LUNAM UniversitéNantes Cedex 3France

Personalised recommendations