Practical problems often combine real-world hard constraints with soft constraints involving preferences, uncertainties or flexible requirements. A probability distribution over the models that meet the hard constraints is an answer to such problems that is in the spirit of incorporating soft constraints. We propose a method using SAT-based reasoning, probabilistic reasoning and linear programming that computes such a distribution when soft constraints are interpreted as constraints whose violation is bound by a given probability. The method, called Optimized Probabilistic Satisfiability (oPSAT), consists of a two-phase computation of a probability distribution over the set of valuations of a SAT formula. Algorithms for both phases are presented and their complexity is discussed. We also describe an application of the oPSAT technique to the problem of combinatorial materials discovery. © 2013 Springer-Verlag.
CITATION STYLE
Finger, M., Le Bras, R., Gomes, C. P., & Selman, B. (2013). Solutions for hard and soft constraints using optimized probabilistic satisfiability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7962 LNCS, pp. 233–249). Springer Verlag. https://doi.org/10.1007/978-3-642-39071-5_18
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