Six Ways of Integrating Symmetries within Non-overlapping Constraints

  • Magnus Ågren
  • Nicolas Beldiceanu
  • Mats Carlsson
  • Mohamed Sbihi
  • Charlotte Truchet
  • Stéphane Zampelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5547)

Abstract

This paper introduces six ways for handling a chain of lexicographic ordering (lex-chain) constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a lex-chain constraint within a generic geometric constraint kernel, the four latter ways deal with the conjunction of a lex-chain constraint and a non-overlapping or a cumulative constraint. Experiments on academic two and three dimensional placement problems as well as on industrial problems show the benefit of such a strong integration of symmetry breaking constraints and non-overlapping ones.

Keywords

Early Start Placement Problem Sweep Algorithm Placement Space Symmetry Breaking Constraint 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Scheithauer, G.: Equivalence and dominance for problems of optimal packing of rectangles. Ricerca Operativa 27(83), 3–34 (1998)Google Scholar
  2. 2.
    Carlsson, M., Beldiceanu, N.: Arc-consistency for a chain of lexicographic ordering constraints. Technical Report T2002-18, Swedish Institute of Computer Science (2002)Google Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Poder, E., Sadek, R., Truchet, C.: A generic geometrical constraint kernel in space and time for handling polymorphic k-dimensional objects. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 180–194. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. Mathl. Comput. Modelling 17(7), 57–73 (1993)CrossRefGoogle Scholar
  5. 5.
    Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global constraint catalog. Technical Report T2005-08, Swedish Institute of Computer Science (2005), http://www.emn.fr/x-info/sdemasse/gccat/Clex_between.html
  6. 6.
    Beldiceanu, N., Carlsson, M.: Sweep as a generic pruning technique applied to the non-overlapping rectangles constraints. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 377–391. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Ågren, M., Beldiceanu, N., Carlsson, M., Sbihi, M., Truchet, C., Zampelli, S.: Six ways of integrating symmetries within non-overlapping constraints. SICS Technical Report T2009:01, Swedish Institute of Computer Science (2009)Google Scholar
  8. 8.
    Lahrichi, A.: Scheduling: the notions of hump, compulsory parts and their use in cumulative problems. C.R. Acad. Sci., Paris 294, 209–211 (1982)Google Scholar
  9. 9.
    Caseau, Y., Laburthe, F.: Cumulative scheduling with task intervals. In: Joint International Conference and Symposium on Logic Programming (JICSLP 1996). MIT Press, Cambridge (1996)Google Scholar
  10. 10.
    Simonis, H., O’Sullivan, B.: Search strategies for rectangle packing. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 52–66. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Magnus Ågren
    • 1
  • Nicolas Beldiceanu
    • 2
  • Mats Carlsson
    • 1
  • Mohamed Sbihi
    • 2
  • Charlotte Truchet
    • 3
  • Stéphane Zampelli
    • 2
  1. 1.SICSKistaSweden
  2. 2.École des Mines de Nantes, LINA UMR CNRS 6241NantesFrance
  3. 3.Université de Nantes, LINA UMR CNRS 6241NantesFrance

Personalised recommendations