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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Weighted constraint satisfaction problem ： ウィキペディア英語版 Weighted constraint satisfaction problem Whereas all constraints in a constraint satisfaction problem (CSP) 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 violating at least one constraint) or have multiple solutions and the goal is to find the solution having minimal cost according to a cost function. This kind of Constraint Satisfaction Problem are called Weighted Constraint Satisfaction Problem (WCSP). ==Formal definition== A Weighted Constraint Network (WCN) is a triplet $\backslash langle\; X,C,k\; \backslash rangle$ where $X$ is a finite set of variables, $C$ is a finite set of soft constraints and $k>0$ is either a natural integer or $\backslash infty$. Each soft constraint $c\_S\; \backslash in\; C$ involves an ordered set $S$ of variables, called its scope, and is defined as a cost function from $l(S)$ to $\backslash langle\; 0,...,k\; \backslash rangle$ where $l(S)$ is the set of possible instantiations of $S$. When an instantiation $I\; \backslash in\; l(S)$ is given the cost $k$, i.e., $c\_S(I)=k$, it is said forbidden. Otherwise it is permitted with the corresponding cost (0 being completely satisfactory). In WCSP, specific subclass of Valued CSP (VCSP), costs are combined with the specific operator $\backslash oplus$ defined as: $\backslash forall\; \backslash alpha,\; \backslash beta\; \backslash in\; \backslash langle\; 0,...,k\; \backslash rangle,\; \backslash alpha\; \backslash oplus\; \backslash beta\; =\; min(k,\backslash alpha+\backslash beta)$. The partial inverse of $\backslash oplus$ is $\backslash ominus$ defined by: if , $\backslash alpha\; \backslash ominus\; \backslash beta\; =\; \backslash alpha\; -\; \backslash beta$ and if Without any loss of generality, the existence of a nullary constraint $c\_\backslash empty$ (a cost) as well as the presence of a unary constraint $c\_x$ for every variable $x$ is assumed. The total cost of an instantiation $I\; \backslash in\; l(S)$ on a soft constraint $c\_S$, includes the cost of $I$ on $c\_S$ as well as the nullary cost $c\_$ and the unary costs for $I$ of the variables in $S$. Considering a WCN, the usual (NP-hard) task of WCSP is to find a complete instantiation with a minimal cost. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Weighted constraint satisfaction problem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.