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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Benhamou, F., Older, W.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints. The Journal of Logic Programming, 1–24 (1997)
Collavizza, H., Delobel, F., Rueher, M.: Extending consistent domains of numeric CSP. In: Proceedings of Sixteenth IJCAI 1999, Stockholm, pp. 406–411 (1999)
Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking Predicates for search problems. In: Proc. of KR 1996, pp. 148–159 (1996)
Dague, P.: Numeric Reasoning with relative orders of magnitude. In: Proc. of the Thirteenth IJCAI, Cambery, pp. 541–547 (1993)
Fox, M., Long, D.: The Detection and Explotation of Symmetry in Planning Problems. In: Proceedings IJCAI’99, pp. 956–961 (1999)
Gent, I.P., Smith, B.M.: Symmetry Breaking During Search in Constraint Programming. In: Report 99.02 University of Leeds (1999)
Gent, I.P., Smith, B.M.: Symmetry Breaking in Constraint Programming. In: Proc. ECAI 2000 (2000)
Hyvönen, E.: Constraint reasoning based on interval arithmetic: the tolerance propagation. Artificial Intelligence 58, 1–112 (1992)
Jussien, N., Lhomme, O.: Dynamic domain splitting for numeric CSPs. In: Proceedings ECAI 1998, pp. 224–228 (1998)
Lhomme, O.: Contribution à la résolution de constraintes sur les réels par propagation d’intervalles. Ph. D. Nice-Sophia University. Antipolis (1994)
Mavovrouniotis, M.L., Stephanopoulos, G.: Formal Order of Magnitude Reasoning in process engineering. Comput. Chem Engineering 12(9-10), 67–880 (1988)
Meseguer, P., Torras, C.: Solving Strategies for Highly Symmetric CSPs. In: Proceedings IJCAI 1999, pp. 400–411 (1999)
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)
Puget, J.F.: Symmetry Breaking using stabilizers. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 585–589. Springer, Heidelberg (2003)
Van Hentenryck, P., Michel, L., Numerica, D.Y.: A modeling language for global optimization. The MIT Press, Cambridge (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gasca, R.M., Del Valle, C., Cejudo, V., Barba, I. (2006). Improving the Computational Efficiency in Symmetrical Numeric Constraint Satisfaction Problems. In: Marín, R., Onaindía, E., Bugarín, A., Santos, J. (eds) Current Topics in Artificial Intelligence. CAEPIA 2005. Lecture Notes in Computer Science(), vol 4177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881216_29
Download citation
DOI: https://doi.org/10.1007/11881216_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45914-9
Online ISBN: 978-3-540-45915-6
eBook Packages: Computer ScienceComputer Science (R0)