A 0–1 quadratic knapsack problem for modelizing and solving the constraint satisfaction problems

  • Mohamed Ettaouil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1323)


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.


Constraint Satisfaction Problem 0–1 quadratic Knapsack problem duality heuristics Branch-and-bound 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mohamed Ettaouil
    • 1
  1. 1.Département de Mathématiques et Informatique de Fès-Saïss et Laboratoire d'Informatique de Paris-Nord, LIPN, URA CNRS n° 1507 Université Sidi Mohammed Ben AbdellahFaculté des Sciences et Techniques Fès SaïssFès, Maroc

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