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

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Principles and Practice of Constraint Programming (CP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,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.

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  3. Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Global constraint catalogue: Past, present and future. Constraints 12(1), 21–62 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: Filtering Algorithms for the NValue Constraint. Constraints 11(4), 271–293 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  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. Carter, M.W., Tovey, C.A.: When is the classroom assignment problem hard? Operations Research 40(1), 28–39 (1992)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Article  Google Scholar 

  10. Dowling, D., Krishnamoorthy, M., Mackenzie, H., Sier, D.: Staff rostering at a large international airport. Annals of Operations Research 72, 125–147 (1997)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fischetti, M., Martello, S., Toth, P.: The fixed job schedule problem with spread-time constraints. Operations Research 35(6), 849–858 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fischetti, M., Martello, S., Toth, P.: The fixed job schedule problem with working-time constraints. Operations Research 37(3), 395–403 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  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. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, 2nd edn. Annals of Discrete Mathematics, vol. 57. Elsevier (2004)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  17. Halldórsson, M.M., Radhakrishnan, J.: Greed is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica 18(1), 145–163 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Krishnamoorthy, M., Ernst, A.T.: The personnel task scheduling problem. In: Optimization Methods and Applications, pp. 343–368. Springer, US (2001)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Lecoutre, C., Sais, L., Tabary, S., Vidal, V.: Reasoning from last conflict(s) in constraint programming. Artif. Intell. 173(18), 1592–1614 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Schulte, C., Stuckey, P.J.: Efficient constraint propagation engines. CoRR abs/cs/0611009 (2006)

    Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. École des Mines de Nantes, LINA (UMR CNRS 6241), LUNAM Université, France

    Jean-Guillaume Fages

  2. École des Mines de Nantes, IRCCyN (UMR CNRS 6597), LUNAM Université, 4 rue Alfred Kastler, La Chantrerie, BP20722, 44307, Nantes Cedex 3, France

    Tanguy Lapègue

Authors
  1. Jean-Guillaume Fages
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  2. Tanguy Lapègue
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Editors and Affiliations

  1. School of Information and Communication Technology, KTH Royal Institute of Technology, P.O. Box Forum 120, 16440, Kista, Sweden

    Christian Schulte

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Fages, JG., Lapègue, T. (2013). Filtering AtMostNValue with Difference Constraints: Application to the Shift Minimisation Personnel Task Scheduling Problem. In: Schulte, C. (eds) Principles and Practice of Constraint Programming. CP 2013. Lecture Notes in Computer Science, vol 8124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40627-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-40627-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40626-3

  • Online ISBN: 978-3-642-40627-0

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