Advertisement

Improving the Computational Efficiency in Symmetrical Numeric Constraint Satisfaction Problems

  • R. M. Gasca
  • C. Del Valle
  • V. Cejudo
  • I. Barba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4177)

Abstract

Models are used in science and engineering for experimentation, analysis, diagnosis or design. In some cases, they can be considered as numeric constraint satisfaction problems (NCSP). Many models are symmetrical NCSP. The consideration of symmetries ensures that NCSP-solver will find solutions if they exist on a smaller search space. Our work proposes a strategy to perform it. We transform the symmetrical NCSP into a new NCSP by means of addition of symmetry-breaking constraints before the search begins. The specification of a library of possible symmetries for numeric constraints allows an easy choice of these new constraints. The summarized results of the studied cases show the suitability of the symmetry-breaking constraints to improve the solving process of certain types of symmetrical NCSP. Their possible speed-up facilitates the application of modelling and solving larger and more realistic problems.

Keywords

Search Space Interval Arithmetic Symmetry Analysis Balance Incomplete Block Design Cold Stream 
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.
    Benhamou, F., Sais, L.: Theoretical study of symmetries in propositional calculus and applications. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, Springer, Heidelberg (1992)Google Scholar
  2. 2.
    Benhamou, F., Older, W.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints. The Journal of Logic Programming, 1–24 (1997)Google Scholar
  3. 3.
    Collavizza, H., Delobel, F., Rueher, M.: Extending consistent domains of numeric CSP. In: Proceedings of Sixteenth IJCAI 1999, Stockholm, pp. 406–411 (1999)Google Scholar
  4. 4.
    Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking Predicates for search problems. In: Proc. of KR 1996, pp. 148–159 (1996)Google Scholar
  5. 5.
    Dague, P.: Numeric Reasoning with relative orders of magnitude. In: Proc. of the Thirteenth IJCAI, Cambery, pp. 541–547 (1993)Google Scholar
  6. 6.
    Fox, M., Long, D.: The Detection and Explotation of Symmetry in Planning Problems. In: Proceedings IJCAI’99, pp. 956–961 (1999)Google Scholar
  7. 7.
    Gent, I.P., Smith, B.M.: Symmetry Breaking During Search in Constraint Programming. In: Report 99.02 University of Leeds (1999)Google Scholar
  8. 8.
    Gent, I.P., Smith, B.M.: Symmetry Breaking in Constraint Programming. In: Proc. ECAI 2000 (2000)Google Scholar
  9. 9.
    Hyvönen, E.: Constraint reasoning based on interval arithmetic: the tolerance propagation. Artificial Intelligence 58, 1–112 (1992)CrossRefGoogle Scholar
  10. 10.
    Jussien, N., Lhomme, O.: Dynamic domain splitting for numeric CSPs. In: Proceedings ECAI 1998, pp. 224–228 (1998)Google Scholar
  11. 11.
    Lhomme, O.: Contribution à la résolution de constraintes sur les réels par propagation d’intervalles. Ph. D. Nice-Sophia University. Antipolis (1994)Google Scholar
  12. 12.
    Mavovrouniotis, M.L., Stephanopoulos, G.: Formal Order of Magnitude Reasoning in process engineering. Comput. Chem Engineering 12(9-10), 67–880 (1988)Google Scholar
  13. 13.
    Meseguer, P., Torras, C.: Solving Strategies for Highly Symmetric CSPs. In: Proceedings IJCAI 1999, pp. 400–411 (1999)Google Scholar
  14. 14.
    Puget, J.F.: On the satisfiability of symmetrical constrained satisfaction problems. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 350–361. Springer, Heidelberg (1993)Google Scholar
  15. 15.
    Puget, J.F.: Symmetry Breaking using stabilizers. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 585–589. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Van Hentenryck, P., Michel, L., Numerica, D.Y.: A modeling language for global optimization. The MIT Press, Cambridge (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. M. Gasca
    • 1
  • C. Del Valle
    • 1
  • V. Cejudo
    • 1
  • I. Barba
    • 1
  1. 1.Departmento de Lenguajes y Sistemas InformáticosUniversidad de SevillaSpain

Personalised recommendations