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Soft-Regular with a Prefix-Size Violation Measure

  • Minh Thanh Khong
  • Christophe Lecoutre
  • Pierre Schaus
  • Yves Deville
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)

Abstract

In this paper, we propose a variant of the global constraint soft-regular by introducing a new violation measure that relates a cost variable to the size of the longest prefix of the assigned variables, which is consistent with the constraint automaton. This measure allows us to guarantee that first decisions (assigned variables) respect the rules imposed by the automaton. We present a simple algorithm, based on a Multi-valued Decision Diagram (MDD), that enforces Generalized Arc Consistency (GAC). We provide an illustrative case study on nurse rostering, which shows the practical interest of our approach.

Notes

Acknowledgments

The first author is supported by the FRIA-FNRS. The second author is supported by the project CPER Data from the “Hauts-de-France”.

References

  1. 1.
    Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of AAAI 1994, pp. 362–367 (1994)Google Scholar
  2. 2.
    Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Math. Comput. Modell. 20(12), 97–123 (1994)CrossRefGoogle Scholar
  3. 3.
    Van Hentenryck, P., Carillon, J.-P.: Generality versus specificity: an experience with AI and OR techniques. In: Proceedings of AAAI 1988, pp. 660–664 (1988)Google Scholar
  4. 4.
    Régin, J.-C.: Generalized arc consistency for global cardinality constraint. In: Proceedings of AAAI 1996, pp. 209–215 (1996)Google Scholar
  5. 5.
    Hooker, J.N.: Integrated Methods for Optimization. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-1-4614-1900-6CrossRefzbMATHGoogle Scholar
  6. 6.
    Aggoun, A., Beldiceanu, N.: Extending chip in order to solve complex scheduling and placement problems. Math. Comput. Modell. 17(7), 57–73 (1993)CrossRefGoogle Scholar
  7. 7.
    Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30201-8_36CrossRefzbMATHGoogle Scholar
  8. 8.
    Schaus, P.: Variable objective large neighborhood search: a practical approach to solve over-constrained problems. In: 2013 IEEE 25th International Conference on Tools with Artificial Intelligence (ICTAI), pp. 971–978. IEEE (2013)Google Scholar
  9. 9.
    van Hoeve, W.: Over-constrained problems. In: van Hentenryck, P., Milano, M. (eds.) Hybrid Optimization, pp. 191–225. Springer, New York (2011).  https://doi.org/10.1007/978-1-4419-1644-0_6CrossRefGoogle Scholar
  10. 10.
    Petit, T., Régin, J.-C., Bessière, C.: Specific filtering algorithms for over-constrained problems. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 451–463. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45578-7_31CrossRefGoogle Scholar
  11. 11.
    van Hoeve, W., Pesant, G., Rousseau, L.-M.: On global warming: flow-based soft global constraints. J. Heuristics 12(4–5), 347–373 (2006)CrossRefGoogle Scholar
  12. 12.
    He, J., Flener, P., Pearson, J.: Underestimating the cost of a soft constraint is dangerous: revisiting the edit-distance based soft regular constraint. J. Heuristics 19(5), 729–756 (2013)CrossRefGoogle Scholar
  13. 13.
    He, J., Flener, P., Pearson, J.: An automaton constraint for local search. Fundamenta Informaticae 107(2–3), 223–248 (2011)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Montanari, U.: Network of constraints: fundamental properties and applications to picture processing. Inf. Sci. 7, 95–132 (1974)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Dechter, R.: Constraint Processing. Morgan Kaufmann, Burlington (2003)zbMATHGoogle Scholar
  16. 16.
    Lecoutre, C.: Constraint Networks: Techniques and Algorithms. ISTE/Wiley, Hoboken (2009)CrossRefGoogle Scholar
  17. 17.
    Beldiceanu, N., Carlsson, M., Petit, T.: Deriving filtering algorithms from constraint checkers. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 107–122. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30201-8_11CrossRefzbMATHGoogle Scholar
  18. 18.
    Hadzic, T., Hansen, E.R., O’Sullivan, B.: On automata, MDDs and BDDs in constraint satisfaction. In: Proceedings of ECAI 2008 Workshop on Inference methods based on Graphical Structures of Knowledge (2008)Google Scholar
  19. 19.
    Cheng, K., Yap, R.: An MDD-based generalized arc consistency algorithm for positive and negative table constraints and some global constraints. Constraints 15(2), 265–304 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Perez, G., Régin, J.-C.: Improving GAC-4 for table and MDD constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 606–621. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10428-7_44CrossRefGoogle Scholar
  21. 21.
    Perez, G., Régin, J.-C.: Soft and cost MDD propagators. In: Proceedings of AAAI 2017, pp. 3922–3928 (2017)Google Scholar
  22. 22.
    Khong, M.T., Deville, Y., Schaus, P., Lecoutre, C.: Efficient reification of table constraints. In: 2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI). IEEE (2017)Google Scholar
  23. 23.
    Burke, E., De Causmaecker, P., Berghe, G.V., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7(6), 441–499 (2004)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Ernst, A., Jiang, H., Krishnamoorthy, M., Sier, D.: Staff scheduling and rostering: a review of applications, methods and models. Eur. J. Oper. Res. 153(1), 3–27 (2004)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Curtois, T., Qu, R.: Computational results on new staff scheduling benchmark instances. Technical report, ASAP Research Group, School of Computer Science, University of Nottingham, 06 October 2014Google Scholar
  26. 26.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998).  https://doi.org/10.1007/3-540-49481-2_30CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ICTEAMUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.CRIL-CNRS UMR 8188, Université d’ArtoisLensFrance

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