Abstract
A constraint satisfaction problem CSP consists of assigning values to variables which are subject to a set of constraints. This problem can be modelized as a 0–1 quadratic knapsack problem. We show that a CSP has a solution if and only if the value of the optimization problem is null. A branch-and-bound method exploiting this representation is presented. At each node, a lower bound given naturally by the value of dual problem may be improved by a new Lagrangean heuristic. An upper bound is computed by satisfying the quadratic constraint. The theoritical results presented are used for filtring the associated subproblem and for detecting quickly a solution or a failure. The simulation results assess the effectiveness of the theoretical results shown in this paper.
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© 1997 Springer-Verlag Berlin Heidelberg
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Ettaouil, M. (1997). A 0–1 quadratic knapsack problem for modelizing and solving the constraint satisfaction problems. In: Coasta, E., Cardoso, A. (eds) Progress in Artificial Intelligence. EPIA 1997. Lecture Notes in Computer Science, vol 1323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023911
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DOI: https://doi.org/10.1007/BFb0023911
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