A Framework for Decision-based Consistencies

International audienceConsistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (general- ized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S∆φ, E∆φ, B∆φ and D∆φ, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this gen- eral framework provides us with a better insight into decision-based con- sistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones

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

Local consistency for extended CSPs

AbstractWe extend the framework of Constraint Satisfaction Problems to make it more suitable for/applicable to modern constraint programming languages where both constraint satisfaction and constraint solving have a role. Some rough principles for local consistency conditions in the extended framework are developed, appropriate notions of local consistency are formulated, and relationships between the various consistency conditions are established

Consistance duale conservative

Les consistances sont des propriétés de réseaux de contraintes qui peuvent être exploitées afin de générer des inférences. Lorsqu'un nombre important d'inférences peut être effectué, il devient alors plus facile de résoudre les réseaux à l'aide par exemple d'une recherche systématique. Dans ce papier, nous nous intéressons aux consistances de relation, i.e. aux consistances qui permettent d'identifier des couples de valeurs inconsistantes. Nous proposons une nouvelle consistance, appelée consistance duale (DC pour Dual Consistency), et nous la comparons à la consistance de chemin (PC pour Path Consistency). Nous montrons que la DC conservative (CDC), i.e. DC telle que seules les relations associées aux contraintes du réseau soient filtrées, est plus forte, en terme de filtrage, que la PC conservative (CPC). En suivant l'approche de Mac Gregor, nous introduisons un algorithme pour établir la CDC (forte) avec une complexité spatiale très faible dans le pire des cas. Bien que l'efficacité relative de l'algorithme introduit dépend en partie de la densité du graphe de contraintes, l'expérimentation que nous avons conduite montre que, sur de nombreuses séries d'instances, établir CDC à l'aide de cet algorithme est largement plus rapide qu'établir CPC à l'aide d'algorithmes directement adaptés de PC-8 ou PC-2001. Par ailleurs, nous avons observé qu'établir CDC lors d'une phase de pré-traitement permet une accélération significative de la résolution de certaines instances structurées difficiles

Cohérences basées sur les valeurs en échec

International audienceNon disponibl

Aiding design with constraints: an extension of quad trees in order to deal with piecewise functions

Issu de : IESM'05 - International Conference on Industrial Engineering and Systems Management, Marrakech, MOROCCO, May 16-19, 2005International audienceThis paper deals with aiding preliminary design when considered as a constraint satisfaction problem (CSP). In this case, constraint filtering techniques provide some kind of interactive assistance to the designer. However, some kinds of numerical constraints corresponding with numerical relations cannot be filtered precisely with classical analytical filtering techniques such as interval arithmetic or box-consistency; it is therefore necessary to discretize them in order to include them in the CSP. To this end, quad trees (QT) have been proposed for binary constraints, or 2k trees when more than two variables are considered; but QT assume that a constraint must be defined by a single numerical function. The aim of this paper is to show that QT techniques can be extended when a constraint is defined by a piecewise function or by a set of numerical functions defined on intervals. The first section recalls some basics relevant to the preliminary design problem and the interests of the CSP assistance. The second section presents the principles of the QT. The last section describes our contributions relevant to QT extensions dealing with piecewise functions

Global Inverse Consistency for Interactive Constraint Satisfaction

International audienceSome applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples

A Microstructure-based Family of Tractable Classes for CSPs

International audienceThe study of tractable classes is an important issue in Artificial Intelligence, especially in Constraint Satisfaction Problems. In this context, the Broken Triangle Property (BTP) is a state-of-the-art microstructure-based tractable class which generalizes well-known and previously-defined tractable classes, notably the set of instances whose constraint graph is a tree. In this paper, we propose to extend and to generalize this class using a more general approach based on a parameter k which is a given constant. To this end, we introduce the k-BTP property (and the class of instances satisfying this property) such that we have 2-BTP = BTP, and for k > 2, k-BTP is a relaxation of BTP in the sense that k-BTP is a subset of (k + 1)-BTP. Moreover, we show that if k-TW is the class of instances having tree-width bounded by a constant k, then k-TW is a subset of (k + 1)-BTP. Concerning tractability, we show that instances satisfying k-BTP and which are strong k-consistent are tractable, that is, can be recognized and solved in polynomial time. We also study the relationship between k-BTP and the approach of Naanaa who proposed a set-theoretical tool, known as the directional rank, to extend tractable classes in a parameterized way. Finally we propose an experimental study of 3-BTP which shows the practical interest of this class, particularly w.r.t. the practical solving of instances satisfying 3-BTP and for other instances, w.r.t. to backdoors based on this tractable class