Finite Domain Bounds Consistency Revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency. In this paper we clarify the differences and similarities among the three commonly used notions of bounds consistency.Comment: 12 page

2-D scene analysis using split-level relaxation

technical reportWe present a new method for applying multiple semantic constraints based on discrete relaxation. A separate graph is maintained for each constraint relation and used in parallel to achieve a consistent labeling. This permits both local and global analysis without recourse to complete graphs. Here local means with respect to a paricular constraint graph, and thus actually includes global spatial relations on the features; e.g., parallel edges on an object will be neighbors in the parallel constraint graph even though they are far apart in Euclidean space. Another major result is a technique for handling occlusion by incorporating the use of spatially local feature sets in the relaxation-type updating method

Maintaining Soft Arc Consistency in BnB-ADOPT+ During Search

Gutierrez and Meseguer show how to enforce consistency in BnB-ADOPT + for distributed constraint optimization, but they consider unconditional deletions only. However, during search, more values can be pruned conditionally according to variable instantiations that define subproblems. Enforcing consistency in these subproblems can cause further search space reduction. We introduce efficient methods to maintain soft arc consistencies in every subproblem during search, a non trivial task due to asynchronicity and induced overheads. Experimental results show substantial benefits on three different benchmarks. © 2013 Springer-Verlag.The work of Gutierrez and Meseguer was partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya 2009-SGR-1434.Peer Reviewe

Reasoning from Last Conflict(s) in Constraint Programming

International audienceConstraint programming is a popular paradigm to deal with combinatorial problems in arti cial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but su er from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classi ed into look-ahead (constraint propagation and search heuristics) and look-back (intelligent backtracking and learning) approaches. In this paper, we present an original look-ahead approach that allows to guide backtrack search toward sources of conicts and, as a side e ect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conict, the last assigned variable is selected in priority, so long as the constraint network cannot be made consistent. This allows us to find, following the current partial instantiation from the leaf to the root of the search tree, the culprit decision that prevents the last variable from being assigned. This way of reasoning can easily be grafted to many variations of backtracking algorithms and represents an original mechanism to reduce thrashing. Moreover, we show that this approach can be generalized so as to collect a (small) set of incompatible variables that are together responsible for the last conict. Experiments over a wide range of benchmarks demonstrate the e ectiveness of this approach in both constraint satisfaction and automated arti cial intelligence planning

Tractable projection-safe soft global constraints in weighted constraint satisfaction.

Wu, Yi.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 74-80).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction Problems --- p.1Chapter 1.2 --- Weighted Constraint Satisfaction Problems --- p.3Chapter 1.3 --- Motivation and Goal --- p.4Chapter 1.4 --- Outline of the Thesis --- p.5Chapter 2 --- Background --- p.7Chapter 2.1 --- Constraint Satisfaction Problems --- p.7Chapter 2.1.1 --- Backtracking Tree search --- p.8Chapter 2.1.2 --- Local consistencies in CSP --- p.11Chapter 2.2 --- Weighted Constraint Satisfaction Problems --- p.18Chapter 2.2.1 --- Branch and Bound Search --- p.20Chapter 2.2.2 --- Local Consistencies in WCSP --- p.21Chapter 2.3 --- Global Constraints --- p.31Chapter 3 --- Tractable Projection-Safety --- p.36Chapter 3.1 --- Tractable Projection-Safety: Definition and Analysis --- p.37Chapter 3.2 --- Polynomially Decomposable Soft Constraints --- p.42Chapter 4 --- Examples of Polynomially Decomposable Soft Global Constraints --- p.48Chapter 4.1 --- Soft Among Constraint --- p.49Chapter 4.2 --- Soft Regular Constraint --- p.51Chapter 4.3 --- Soft Grammar Constraint --- p.54Chapter 4.4 --- Max_Weight/Min Weight Constraint --- p.57Chapter 5 --- Experiments --- p.61Chapter 5.1 --- The car Sequencing Problem --- p.61Chapter 5.2 --- The nonogram problem --- p.62Chapter 5.3 --- Well-Formed Parenthesis --- p.64Chapter 5.4 --- Minimum Energy Broadcasting Problem --- p.64Chapter 6 --- Related Work --- p.67Chapter 6.1 --- WCSP Consistencies --- p.67Chapter 6.2 --- Global Constraints . --- p.68Chapter 7 --- Conclusion --- p.71Chapter 7.1 --- Contributions --- p.71Chapter 7.2 --- Future Work --- p.72Bibliography --- p.7

Preprocessing versus search processing for constraint satisfaction problems

A perennial problem in hybrid backtrack CSP search is how much local consistency processing should be done to achieve the best efficiency. This can be divided into two separate questions: (1) how much work should be done before the actual search begins, i.e. during preprocessing? and (2) how much of the same processing should be interleaved with search? At present there are two leading approaches to establishing stronger consistencies than the basic arc consistency maintenance that is done in most solvers. On the one hand there are various kinds singleton arc consistency that can be used; on the other there are several variants of restricted path consistency. To date these have not been compared directly. The present work attempts to do this for a variety of problems, and in so doing, it also provides an empirical evaluation of the preprocessing versus search processing issue. Comparisons are made using the domain/degree and domain/weighted degree variable ordering heuristics. In general, it appears that preprocessing with higher levels of consistency followed by hybrid-AC processing (i.e. MAC) gives the best results, especially when the weighted degree heuristic is used. For problems with n-ary constraints, this difference seems to be even more pronounced. In some cases, higher levels of consistency maintenance established during preprocessing leads to performance gains over MAC of several orders of magnitude