Abstract
In this paper, we propose a new way for representing and solving constraintsatisfaction problems (CSPs). We first show that a CSP can be modelized by a single pseudo-Boolean function. Then some theoretical results establishing the links between a CSP and its associated pseudo-Boolean function are described. We propose a Branch and Bound method exploiting this representation for solving CSPs. This method follows the same scheme developed by the Forward-Checking procedure. The main difference between the Branch and bound method and the Forward-Checking method lies in the computation performed at every node of the search tree. The Branch and Bound method uses the constraints in an active way to infer a knowledge about the problem. Then a solution or failure may be detected quickly.
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References
B. Aspvall, M.F. Plass and R.E. Tarjan, “A linear algorithm for testing the truth of certain quantified Boolean formulas”, Information Processing Letters 8, 121–123, (1979).
F. Barahona, M. Jüngler and G. Reinelt, “Experiments in quadratic 0-1 programming”, Mathematical Programming 44, 127–137 (1989).
H. Bennaceur, “Partial consistency for constraint-satisfaction problems”, Proceedings of the 11th European Conference on Artificial Intelligence, 120–125, (1994).
C. Bessière, “Arc-consistency and arc-consistency again”, Research Note, Vol. 65, 1, 179–190, (1994).
Y. Crama, “Recognition problems for special classes of polynomials in 0-1 variables”, Mathematical Programming 44, 127–137, (1989).
E.C. Freuder, “A sufficient condition for backtrack-free search”, Journal of the ACM, vol. 29 nℴ 1, 24–32, (1982).
V.P. Gulti, S.K. Gupta and A.K. Mittal, “Unconstrained quadratic bivalent programming problem”, European Journal of Operational Research 15, 121–125, (1994).
P.L. Hammer and P. Hansen, “Logical relations in quadratic 0-1 optimization”, Revue roumaine de mathématiques pures et appliqués, tome XXVI, nℴ 3, 421–429, (1981).
P.L. Hammer, P. Hansen and B. Simeoné, “Roof Duality, complementation and persistency in quadratic 0-1 optimization”, Mathematical programming, 28, 121–155, (1984).
R. Mohr and T.C. Hendeson, “Arc and path consistency revisited”, Artificial Intelligence 28–2, (1986).
U. Montanari, “Networks of constraints: Fundamental properties and applications to picture processing”, Information Sciences, vol. 7 nℴ2, 95–132, (1974).
B. Nadel, “Constraint satisfaction algorithms”, Computational Intelligence, 5, 188–224, (1986).
P. Jegou, “Contribution à l'étude des problèmes de satisfaction de contraintes”, Thèse de Doctorat, Montpellier II, France, (1991).
A. Sutter, “Programmation non linéaire en variables 0-1”, Thèse de doctorat du CNAM (Paris), (1989).
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© 1995 Springer-Verlag Berlin Heidelberg
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Bennaceur, H. (1995). Boolean approach for representing and solving constraint-satisfaction problems. In: Gori, M., Soda, G. (eds) Topics in Artificial Intelligence. AI*IA 1995. Lecture Notes in Computer Science, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60437-5_16
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DOI: https://doi.org/10.1007/3-540-60437-5_16
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