Whereas all constraints in a Constraint[[constraint Satisfactionsatisfaction Problemproblem]] must be satisfied, a '''Weighted Constraint Satisfaction Problem''' (WCSP) is a constraint satisfaction problem where constraints can be violated (according a violation degree) and in which preferences among solutions can be expressed. Many real problems can be represented as Constraint Satisfaction Problem. However, a wide range of problems are over-constrained (no solution can be found without violate a least one constraint) or have multiple solutions and the goal is to find the best solution according to an objective function. This kind of Constraint Satisfaction Problem are called Weighted Constraint Satisfaction Problem (WCSP).
