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In [[artificial intelligence]] and [[operations research]], a '''Weighted Constraint Satisfaction Problem''' ('''WCSP''') is a generalization of a [[constraint satisfaction problem]] (CSP) where some of the [[constraint (mathematics)|constraint]]s can be violated (according to a violation degree) and in which [[preference]]s among solutions can be expressed. This generalization makes it possible to represent more real-world problems, in particular those that are over-constrained (no solution can be found without violating at least one constraint), or those where we want to find a minimal-cost solution (according to a [[
==Formal definition==
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