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A filtering algorithm for global sequencing constraints

  • Jean-Charles Régin
  • Jean-François Puget
Session 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1330)

Abstract

Sequencing constraints have proved very useful in many real-life problems such as rostering or car sequencing problems. They are used to express constraints such as: every sequence of 7 days of work must contain at least 2 days off. More precisely, a global sequencing constraint (gsc) C is specified in terms of an ordered set of variables X (C) = {x1,..., xp} which take their values in D(C) = {v1,..., vd}, some integers q, min and max and a given subset V of D(C). On one hand, a gsc constrains the number of variables in X(C) instantiated to a value vi ε D(C) be in an interval [1i, ui]. On the other hand, a gsc constrains for each sequence Si of q consecutive variables of X(C), that at least min and at most max variables of Si are instantiated to a value of V. In this paper, we propose an automatic reformulation of a gsc in terms of global cardinality constraints. This is equivalent to defining a powerful filtering algorithm for a gsc which deals with a part of the globality of the constraint. We illustrate the power of our approach on a set of difficult car sequencing problems.

Keywords

Assembly Line Constraint Satisfaction Problem Constraint Network Implied Constraint Backtrack Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [BC94]
    N. Beldiceanu and E. Contejean. Introducing global constraints in chip. Journal of Mathematical and Computer Modelling, 20(12):97–123, 1994.Google Scholar
  2. [DSV88]
    M. Dincbas, H. Simonis, and P. Van Hentenryck. Solving the car-sequencing problem in constraint logic programming. In ECAI'88, proceedings of the European Conference on Artificial Intelligence, pages 290–295, 1988.Google Scholar
  3. [Mac77]
    A.K. Mackworth. Consistency in networks of relations. Artificial Intelligence, 8:99–118, 1977.Google Scholar
  4. [Nui94]
    W.P. Nuijten. Time and Resource Constrained Scheduling: A Constraint Satisfaction Approach. PhD thesis, Eindhoven University of Technology, 1994.Google Scholar
  5. [PL95]
    J-F. Puget and M. Leconte. Beyong the glass box: Constraints as objects. In John Lloyd, editor, Logic Programming, Proceedings of the 1995 International Symposium, pages 513–527. The MIT Press, Portland, Oregon, 1995.Google Scholar
  6. [Rég94]
    J-C. Régin. A filtering algorithm for constraints of difference in CSPs. In AAAI-94, proceedings of the Twelth National Conference on Artificial Intelligence, pages 362–367, Seattle, Washington, 1994.Google Scholar
  7. [Rég96]
    J-C. Régin. Generalized arc consistency for global cardinality constraint. In AAAI-96, proceedings of the Thirteenth National Conference on Artificial Intelligence, pages 209–215, Portland, Oregon, 1996.Google Scholar
  8. [Sim96]
    H. Simonis. Problem classification scheme for finite domain constraint solving. In CP96, Workshop on Constraint Programming Applications: An Inventory and Taxonomy, pages 1–26, Cambridge, MA, USA, 1996.Google Scholar
  9. [Smi96]
    B.M. Smith. Succeed-first or fail-first: A case study in variable and value ordering. In proceedings ILOG Solver and ILOG Scheduler Second International Users' Conference, Paris, France, 1996.Google Scholar
  10. [VDT92]
    P. Van Hentenryck, Y. Deville, and C.M. Teng. A generic arc-consistency algorithm and its specializations. Artificial Intelligence, 57:291–321, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jean-Charles Régin
    • 1
  • Jean-François Puget
    • 1
  1. 1.ILOG S.A.Gentilly CedexFrance

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