Constraint satisfaction as global optimization

  • Authors:
  • Pedro Meseguer;Javier Larrosa

  • Affiliations:
  • Universitat Politecnica de Catalunya, Dep. Llenguatges i Sistemes Informatics, Barcelona, Spain;Universitat Politecnica de Catalunya, Dep. Llenguatges i Sistemes Informatics, Barcelona, Spain

  • Venue:
  • IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
  • Year:
  • 1995

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Abstract

We present a optimization formulation for discrete binary CSP, based on the construction of a continuous function A(P) whose global maximum represents the best possible solution for that problem. By the best possible solution we mean either (i) a solution of the problem, if it is solvable, or (ii) a partial solution violating a minimal number of constraints, if the problem is unsolvable. This approach is based on relaxation labeling techniques used to enforce consistency in image interpretation. We have used a projected gradient ascent algorithm to maximize A(P) on the n-queens problem obtaining good results but with a high computational cost. To elude this problem, we have developed a heuristic for variable and value selection inspired in the direction in which A(P) is maximized. We have tested this heuristic with forward checking on several classes of CSP.