WhereasIn all[[artificial constraintsintelligence]] in aand [[constraintoperations satisfaction problemresearch]] (CSP) must be satisfied, a '''Weighted Constraint Satisfaction Problem''' ('''WCSP''') is a generalization of a [[constraint satisfaction problem]] (CSP) where constraintssome of the [[constraint (mathematics)|constraint]]s can be violated (according to a violation degree) and in which preferences[[preference]]s among solutions can be expressed. ManyThis realgeneralization problemsmakes canit bepossible representedto asrepresent Constraintmore Satisfactionreal-world Problem. Howeverproblems, ain wideparticular rangethose of problemsthat are over-constrained (no solution can be found without violating at least one constraint), or havethose multiplewhere solutionswe and the goal iswant to find the solution havinga minimal-cost solution (according to a [[oss function|cost function.]]) Thisamong kindmultiple ofpossible Constraint Satisfaction Problem are called Weighted Constraint Satisfaction Problem (WCSP)solutions.
