An Arc-Consistency Algorithm for Dynamic and Distributed Constraint Satisfaction Problems

This paper presents the new DDAC4 algorithm for dynamic arc consistency enforcement in distributed constraint satisfaction problems (CSP). The algorithm is an adaptation of the well-known AC-4 algorithm to system settings where constraints can be added and deleted in concurrent processes. It is the first algorithm for arc-consistency enforcement in this system setting. Arc-consistency is achieved whenever the overall system reaches quiescence after a constraint is added or deleted.     

On the arc consistency problem

In this paper,we propose a new arc consistency algorithm,AC-8,which requires less computation time and space than AC-6 and AC-7.The main idea of the optimization is the divide-and-conquer strategy,thereby decomposing an arc consistency problem into a series of smaller ones and trying to solve them in sequence. In this way,not only the space complexity but also the time complexity can be reduced.The reason for this is that due to the ahead of time performed inconsistency propagation(in the semse that some of them are executed before the entire inconsistency checking has been finished),each constraint subnetwork will be searched with a gradually shrunk domain.In addition,the technique of AC-6 can be integrated into our algorithm,leading to a further decrease in computational complexity.     

一种维持约束网络相容性的双向传播策略

约束满足问题是经典NP-hard问题,其基本算法是递归形式的回溯算法和弧一致性算法.将弧相容与回溯搜索结合,可以有效降低解空间大小.针对弧相容的维持问题,提出一种新的基于时序计数的传播方案,用于增量更新约束子网.将accumulateRevision和pushRevison作为双向修订的主要方法,以减少修订次数和域过滤变量的数量.实验结果表明,与经典的基于关系的方案和基于变量的传播方案相比,该方案的整体求解速度明显提高,且具有较少的修订时间.     

Parallel consistent labeling algorithms

Mackworth and Freuder have analyzed the time complexity of several constraint satisfaction algorithms.⁽¹⁾ Mohr and Henderson have given new algorithms, AC-4 and PC-3, for arc and path consistency, respectively, and have shown that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms.⁽²⁾ In this paper, we give parallel algorithms for solving node and arc consistency. We show that any parallel algorithm for enforcing are consistency in the worst case must have O(na) sequential steps, wheren is number of nodes, anda is the number of labels per node. We give several parallel algorithms to do arc consistency. It is also shown that they all have optimal time complexity. The results of running the parallel algorithms on a BBN Butterfly multiprocessor are also presented.This work was partially supported by NSF Grants MCS-8221750, DCR-8506393, and DMC-8502115.     

Robust design based on constraint networks

This paper describes a robust design method using constraint networks. As opposed to the traditional statistical robust methodology, the proposed method gives a valid model to analyze parameter uncertainties so as to predict conflicts in concurrent design. The mathematical model, which reflects the requirements of robust design, is given in the paper. A general consistency algorithm is designed using interval arithmetic to refine the intervals. This paper also proves that the consistency algorithm is arc consistent if the constraint network is integrated. The constraint network uses the consistency algorithm to verify the design process early in the process and to assist the designers in determining design variables to reduce the multidisciplinary iterations in concurrent design. The quantitative effect of downstream constraints can be analyzed before determining design parameters and potential conflicts can be predicted. A layout design example shows the validity of the method.     

An optimal coarse-grained arc consistency algorithm

The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: fine-grained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarse-grained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarse-grained algorithms, like AC-3, over fine-grained algorithms, like AC-4, is the ease of integration when implementing an algorithm in a constraint solver. However, fine-grained algorithms usually have optimal worst case time complexity while coarse-grained algorithms do not. For example, AC-3 is an algorithm with non-optimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarse-grained algorithm, AC2001/3.1, that is worst case optimal and preserves as much as possible the ease of its integration into a solver (no heavy data structure to be maintained during search). Experimental results show that AC2001/3.1 is competitive with the best fine-grained algorithms such as AC-6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the best-known time and space complexity. The same idea is then extended to non-binary constraints.     

Peek arc consistency

This paper studies peek arc consistency, a reasoning technique that extends the well-known arc consistency technique for constraint satisfaction. In contrast to other more costly extensions of arc consistency that have been studied in the literature, peek arc consistency requires only linear space and quadratic time and can be parallelized in a straightforward way such that it runs in linear time with a linear number of processors. We demonstrate that for various constraint languages, peek arc consistency gives a polynomial-time decision procedure for the constraint satisfaction problem. We also present an algebraic characterization of those constraint languages that can be solved by peek arc consistency, and study the robustness of the algorithm.     

一种高效的FDE并行传播算法

约束规划(constraint programming, CP)是表示和求解组合问题的经典范式之一.扩展约束(extensional constraint)或称表约束(table constraint)是约束规划中最为常见的约束类型.绝大多数约束规划问题都可以用表约束表达.在问题求解时,相容性算法用于缩减搜索空间.目前,最为高效的表约束相容性算法是简单表约缩减(simple table reduction, STR)算法簇,如Compact-Table (CT)和STRbit算法.它们在搜索过程中维持广义弧相容(generalized arc consistency, GAC).此外,完全成对相容性(full pairwise consistency, fPWC)是一种比GAC剪枝能力更强的相容性.最为高效的维持fPWC算法是PW-CT算法.多年来,人们提出了多种表约束相容性算法来提高剪枝能力和执行效率.因子分解编码(factor-decomposition encoding, FDE)通过对平凡问题重新编码.它一定程度地扩大了问题模型,使在新的问题上维持相对较弱的GAC等价于在原问题...     

Extending GENET with lazy arc consistency

Many important applications, such as graph coloring, scheduling and production planning, can be solved by GENET, a local search method which is used to solve binary constraint satisfaction problems (CSPs). Where complete search methods are typically augmented with consistency methods to reduce the search, local search methods are not. We propose a consistency technique, lazy arc consistency, which is suitable for use within GENET. We show it can improve the efficiency of the GENET search on some instances of binary CSPs, and does not suffer the overhead of full arc consistency     

Experimental Analysis of Numeric and Symbolic Constraint Satisfaction Techniques for Temporal Reasoning

Many temporal applications like planning and scheduling can be viewed as special cases of the numeric and symbolic temporal constraint satisfaction problem. Thus we have developed a temporal model, TemPro, based on the interval Algebra, to express such applications in term of qualitative and quantitative temporal constraints. TemPro extends the interval algebra relations of Allen to handle numeric information. To solve a constraint satisfaction problem, different approaches have been developed. These approaches generally use constraint propagation to simplify the original problem and backtracking to directly search for possible solutions. The constraint propagation can also be used during the backtracking to improve the performance of the search. The objective of this paper is to assess different policies for finding if a TemPro network is consistent. The main question we want to answer here is how much constraint propagation is useful for finding a single solution for a TemPro constraint graph. For this purpose, we have experimented by randomly generating large consistent networks for which either arc and/or path consistency algorithms (AC-3, AC-7 and PC-2) were applied. The main result of this study is an optimal policy combining these algorithms either at the symbolic (Allen relation propagation) or at the numerical level.     

基于静态前提的谓词知识树分解策略

智能规划问题实质是一种搜索问题,通常需采用某种策略来缩小搜索空间,提高规划效率。在“以谓词为主体”的规划求解方法中,规划树的生成效率将直接影响规划求解效率。为此,提出了基于静态前提的谓词知识树分解策略,并给出了相应的分解算法。对任意一个规划领域,利用该分解算法可将知识树分解成若干个较小规模的知识子树。在规划求解的过程中,利用知识子树可有效地减少搜索空间,从而快速生成规划树,提高规划效率。同时,利用知识子树还可提取出隐含在动作描述中的领域知识。实验结果表明该分解算法是有效的。     

Domain filtering consistencies for non-binary constraints

In non-binary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering consistencies have been proposed. In this paper we present a detailed theoretical, algorithmic and empirical study of domain filtering consistencies for non-binary problems. We study three domain filtering consistencies that are inspired by corresponding variable based domain filtering consistencies for binary problems. These consistencies are stronger than generalized arc consistency, but weaker than pairwise consistency, which is a strong consistency that removes tuples from constraint relations. Among other theoretical results, and contrary to expectations, we prove that these new consistencies do not reduce to the variable based definitions of their counterparts on binary constraints. We propose a number of algorithms to achieve the three consistencies. One of these algorithms has a time complexity comparable to that for generalized arc consistency despite performing more pruning. Experiments demonstrate that our new consistencies are promising as they can be more efficient than generalized arc consistency on certain non-binary problems.     

加权约束满足问题的符号ADD求解算法

加权约束满足问题(WCSP)是一类软约束满足问题。给出WCSP的代数决策图(ADD)描述,以及基于ADD的两种符号求解算法。首先,通过对变量和变量域值的二进制编码,给出软约束图的ADD表示。其次,将分支定界搜索算法与桶消元算法及符号ADD技术相结合,在静态变量序下,利用结点一致性预处理技术,对WCSP问题进行符号ADD求解。通过引入有向弧一致性计数技术提高符号ADD算法的搜索下界,对符号ADD求解算法作了改进。最后,对大量随机生成的测试用例进行实验分析。结果表明,文中算法在性能上明显优于带有存在有向弧一致性或结点一致性预处理技术的具有前向检查功能的深度优先分支定界搜索算法。     

A novel discrete relaxation architecture

The discrete relaxation algorithm (DRA) is a computational technique that enforces arc consistency (AC) in a constraint satisfaction problem (CSP). The original sequential AC-1 algorithm suffers from O(n³m³) time complexity, and even the optimal sequential AC-4 algorithm is O (n²m²) for an n-object and m-label DRA problem. Sample problem runs show that these algorithms are all too slow to meet the need for any useful, real-time CSP applications. A parallel DRA5 algorithm that reaches a lower bound of O(nm) (where the number of processors is polynomial in the problem size) is given. A fine-grained, massively parallel hardware computer architecture has been designed for the DRA5 algorithm. For practical problems, many orders of magnitude of efficiency improvement can be reached on such a hardware architecture     

改进的电弧弧长自适应T-S模糊观测器

通常基于Lyapunov方法设计自适应观测器时,要求系统满足Kalman—Yakubovitch—Popov（KYP）定理的约束．因此,通过增加辅助变量放宽了约束条件,对未知参数的一类非线性系统,提出了一种模糊自适应观测器,用来观测熔化极气体保护焊的弧长．在焊枪到工件的距离未知的情况下,可以有效地获得弧长变化信息．仿真结果验证了该方法的有效性．     

Efficient algorithms for singleton arc consistency

In this paper, we propose two original and efficient approaches for enforcing singleton arc consistency. In the first one, the data structures used to enforce arc consistency are shared between all subproblems where a domain is reduced to a singleton. This new algorithm is not optimal but it requires far less space and is often more efficient in practice than the optimal algorithm SAC-Opt. In the second approach, we perform several runs of a greedy search (where at each step, arc consistency is maintained), possibly detecting the singleton arc consistency of several values in one run. It is an original illustration of applying inference (i.e., establishing singleton arc consistency) by search. Using a greedy search allows benefiting from the incrementality of arc consistency, learning relevant information from conflicts and, potentially finding solution(s) during the inference process. We present extensive experiments that show the benefit of our two approaches.     

基于约束满足的热轧批量计划模型与算法

将热轧批量计划问题作为一个约束满足问题处理，建立不确定计划数的VRPSTw约束满足模型．在求解过程中．先用约束满足的一致性技术过滤变量的值域，收缩搜索空间；然后用变量选择和值选择构造轧制计划的解．为变量赋值之后，实施约束传播，保证每块板坯只被访问一次并动态禁止子回路．在已有的解的基础上，应用基于禁忌的k-opt互换改进解的质量．数据实验证明模型和算法是有效的．     

工艺设计知识库的建造与维护

文中根据工艺设计知识的特点,构造了层次化的知识表达、组织与知识库模型,分析了工艺知识库不一致的表现形式,并给出了相应的一致性验证算法,提出了基于广义决策表的知识库完备性检查方法。     

HIERARCHICAL ARC CONSISTENCY FOR DISJOINT REAL INTERVALS IN CONSTRAINT LOGIC PROGRAMMING

There have been many proposals for adding sound implementations of numeric processing to Prolog. This paper describes an approach to numeric constraint processing which has been implemented in Echidna, a new constraint logic programming (CLP) language. Echidna uses consistency algorithms which can actively process a wider variety of numeric constraints than most other CLP systems, including constraints containing some common nonlinear functions. A unique feature of Echidna is that it implements domains for real-valued variables with hierarchical data structures and exploits this structure using a hierarchical arc consistency algorithm specialized for numeric constraints. This gives Echidna two advantages over other systems. First, the union of disjoint intervals can be represented directly. Other approaches require trying each disjoint interval in turn during backtrack search. Second, the hierarchical structure facilitates varying the precision of constraint processing. Consequently, it is possible to implement more effective constraint processing control algorithms which avoid unnecessary detailed domain analysis. These advantages distinguish Echidna from other CLP systems for numeric constraint processing.     

Brightness-Based Selection and Edge Detection-Based Enhancement Separation Algorithm for Low-Resolution Metal Transfer Images

Next-generation gas metal arc welding (GMAW) machines require the rapid metal transfer process be accurately monitored using a high-speed vision system and be feedback controlled. However, the necessity for high frame rate reduces the resolution achievable and bright welding arc makes it difficult to clearly image the metal transfer process. Processing of images for real-time monitoring of metal transfer process is thus challenging. To address this challenge, the authors analyzed the characteristics of metal transfer images in a novel modification of GMAW, referred to as double-electrode GMAW, and proposed an algorithm consisting of a system of effective steps to extract the needed droplet feedback information from high frame rate low-resolution metal transfer images. Experimental results verified the effectiveness of the proposed algorithm in automatically locating the droplet and computing the droplet size with an adequate accuracy.