Solving a quantified constraint satisfaction problem (QCSP) is usually a hard task due to its computational complexity. Exact algorithms play an important role in solving this problem, among which backtrack algorithms are effective. In a backtrack algorithm, an important step is assigning a variable by a chosen value when exploiting a branch, and thus a good value selection rule may speed up greatly. In this paper, we propose two value selection rules for existentially and universally quantified variables, respectively, to avoid unnecessary searching. The rule for universally quantified variables is prior to trying failure values in previous branches, and the rule for existentially quantified variables selects the promising values first. Two rules are integrated into the state-of-the-art QCSP solver, i.e., QCSP-Solve, which is an exact solver based on backtracking. We perform a number of experiments to evaluate improvements brought by our rules. From computational results, we can conclude that the new value selection rules speed up the solver by 5 times on average and 30 times at most. We also show both rules perform well particularly on instances with existentially and universally quantified variables occurring alternatively.

中文翻译：

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使用值选择规则解决量化的约束满足问题

由于其计算复杂性，解决量化约束满足问题（QCSP）通常是一项艰巨的任务。精确算法在解决此问题中起着重要作用，其中回溯算法是有效的。在回溯算法中，重要的一步是在利用分支时通过选择的值分配变量，因此好的值选择规则可能会大大加快速度。在本文中，我们针对存在和普遍量化的变量分别提出了两个值选择规则，以避免不必要的搜索。普遍量化变量的规则在尝试先前分支中的失败值之前，而生存量化变量的规则首先选择有希望的值。最新的QCSP求解器集成了两个规则，即QCSP-Solve，这是基于回溯的精确求解器。我们进行了许多实验，以评估规则带来的改进。从计算结果可以得出结论，新的值选择规则平均将求解器速度提高了5倍，最多将速度提高了30倍。我们还显示，这两个规则特别适用于存在交替存在的存在性和普遍性量化变量的实例。