As many real-world problems involve user preferences, costs, or probabilities, constraint satisfaction has been extended to optimization by generalizing hard constraints to soft constraints. However, as techniques such as local consistency or conflict learning do not easily generalize to optimization, solving soft constraints appears more difficult than solving hard constraints. In this paper, we present an approach to solving soft constraints that exploits this disparity by re-formulating soft constraints into an optimization part (with unary objective functions), and a satisfiability part. This re-formulation is exploited by a search algorithm that enumerates subspaces with equal valuation, that is, plateaus in the search space, rather than individual elements of the space. Within the plateaus, familiar techniques for satisfiability can be exploited. Experimental results indicate that this hybrid approach is in some cases more efficient than other known methods for solving soft constraints.


Decision Variable Constraint Satisfaction Problem Soft Constraint Hard Constraint Tree Decomposition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Sachenbacher
    • 1
  • Brian C. Williams
    • 2
  1. 1.LMU MünchenMünchenGermany
  2. 2.MIT CSAILCambridgeUSA

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