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arXiv 1306.4418cs.AI
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基于结构的约束规划扩展归结

Structure Based Extended Resolution for Constraint Programming

Geoffrey Chu, Peter J. Stuckey

摘要:

Nogood学习是减少约束编程(CP)求解器中搜索的一种强大方法。目前的技术水平,称为懒惰条款生成(LCG),使用决议来获得nogoods表达的原因,每个搜索失败。这些无用的东西可以修剪搜索树的其他部分,在各种各样的问题上产生指数级的加速。Nogood学习求解器可以被视为解决证明系统。证明系统越强,解决CP问题的速度就越快。最近的研究表明,LCG中使用的证明系统至少与一般归结一样强大。然而,存在更强的证明系统,例如\emph{extended resolution}。扩展解析允许在现有变量上引入表示任意逻辑概念的文字,并且可以允许比一般解析指数更小的证明。使用扩展解析的主要问题是准确地找出引入哪些文字是有用的。在本文中,我们表明,我们可以使用CP模型中包含的结构信息,以引入有用的文字,这可以转化为显着的加速一系列的问题。

英文摘要:

Nogood learning is a powerful approach to reducing search in Constraint Programming (CP) solvers. The current state of the art, called Lazy Clause Generation (LCG), uses resolution to derive nogoods expressing the reasons for each search failure. Such nogoods can prune other parts of the search tree, producing exponential speedups on a wide variety of problems. Nogood learning solvers can be seen as resolution proof systems. The stronger the proof system, the faster it can solve a CP problem. It has recently been shown that the proof system used in LCG is at least as strong as general resolution. However, stronger proof systems such as \emph{extended resolution} exist. Extended resolution allows for literals expressing arbitrary logical concepts over existing variables to be introduced and can allow exponentially smaller proofs than general resolution. The primary problem in using extended resolution is to figure out exactly which literals are useful to introduce. In this paper, we show that we can use the structural information contained in a CP model in order to introduce useful literals, and that this can translate into significant speedups on a range of problems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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