Constraint optimization problem

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The general aim for constraint optimization problem is to find an optimal solution to a set of constraints subject to some objective function obj. For example, consider a CSP LaTeX:  P = \{ C, x_1 \in D_1, \dots, x_n \in D_n\} together with a function LaTeX:  obj : Sol \to \mathbb{R} . LaTeX: obj is a mapping from solutions to LaTeX: P (i.e., all elements the set LaTeX: Sol) to the set of real numbers, LaTeX: \mathbb{R}.

A solution, LaTeX: d, to a constraint optimization problem is a complete assignment of variables that satisfies all constraints LaTeX: C \in P and for which the value LaTeX: obj(d) is optimal (either minimal or maximal, depending on the sense of the optimization).

See also constraint satisfaction problem.

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