Improving Constraint Satisfaction Algorithm Efficiency for the AllDifferent Constraint

Solving finite-domain linear constraints in presence of the $\texttt{alldifferent}$

In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evalu…

数独中的组合探索

Combinatorial Explorations in Su-Doku

Su-Doku是一个流行的组合谜题，它为启发式探索提供了一个很好的测试平台。从它看似简单的一套规则中产生了几个有趣的问题。有多少个不同的数独网格？如何找到一个解决Su-Doku难题？是否有一个唯一的解决方案，以给定的数独难题？什么是一个好的估计一个难题的难度？最小的谜题尺寸是多少（“givens”的数量）？本文探讨了这些问题是如何与众所周知的alldifferent约束，出现在各种各样的约束满足问题（CSP），并比较各种算法的基础上不同配方的苏独。

动态全局约束：第一个视图

Dynamic Global Constraints: A First View

全局约束被证明是一个有效的工具，用于建模和解决大规模的现实生活中的组合问题。它们封装了一组二进制约束，并使用全局推理这一组，他们过滤所涉及的变量的域比弧一致性之间的一组二进制约束。此外，全局约束利用语义信息，实现更有效的过滤比广义一致性算法的n元约束。随着约束规划（CP）应用领域的不断扩展，对全局约束的设计提出了新的挑战。特别是，应用CP先进的计划与调度（APS），需要动态添加新的变量和约束的过程中的约束满足，因此，这将是有益的，如果全局约束可以采用新的变量。在本文中，我们给出了这样的动态全局约束的动机，我们描述了一个动态版本的著名alldifferent约束。

Consistency Techniques for Flow-Based Projection-Safe Global Cost Functions in Weighted Constraint Satisfaction

Many combinatorial problems deal with preferences and violations, the goal of which is to find solutions with the minimum cost. Weighted constraint satisfaction is a framework for modeling such problems, which consists of a set of cost functions to measure the degree of violation or preferences of different combinations of variable assignments. Typical solution methods for weighted constraint satisfaction problems (WCSPs) are based on branch-and-bound search, which are made practical through the use of powerful consistency techniques such as AC*, FDAC*, EDAC* to deduce hidden cost information …

Planning Graph as a (Dynamic) CSP: Exploiting EBL, DDB and other CSP Search Techniques in Graphplan

This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation based learning, dependency directed backtracking, dynamic variable ordering, forward checking, sticky values and random-restart search strategies can be adapted to Graphplan. Empirical results are provided to demonstrate that these augmentations improve Graphplan's performance significantly (up to 1000x speedups) on several benchmark problems. Special attentio…

改进连接主义能量最小化

Improving Connectionist Energy Minimization

为能量最小化而设计的对称网络，如玻尔兹曼机和Hopfield网，经常被研究用于优化、约束满足和NP难问题的近似。然而，找到一个全球解决方案（即，能量函数的全局最小值）不能得到保证，并且甚至局部解也可能需要指数数量的步骤。我们提出了一个改进的标准本地激活函数用于这样的网络。改进的算法保证了树形子网络在线性时间内找到全局最小值。该算法称为activate，是统一的，并且不假设网络是树状的。它可以识别树状子网络，即使在循环拓扑结构（任意网络），并避免局部极小值沿这些树。对于无环网络，该算法保证从系统的任何初始状态收敛到全局最小值（自稳定），并在各种类型的控制器下保持正确。在消极的一面，我们表明，在存在的周期，没有统一的算法存在，保证最优性，即使在顺序异步调度。异步调度程序一次只能激活一个单元，而同步调度程序可以在单个时间步长中激活任意数量的单元。此外，没有统一的算法存在优化，甚至非循环网络时，调度器是同步的。最后，我们展示了如何使用循环割集计划的算法可以得到改进。一般的算法称为带割集激活算法，改进了激活算法，并有一定的性能保证，这与网络的环割集的大小有关。