Consistency restoration and explanations in dynamic CSPs—Application to configuration

Abstract

Most of the algorithms developed within the Constraint Satisfaction Problem (CSP) framework cannot be used as such to solve interactive decision support problems, like product configuration. Indeed, in such problems, the user is in charge of assigning values to variables. Global consistency maintaining is only one among several functionalities that should be offered by a CSP-based platform in order to help the user in her task; other important functionalities include providing explanations for some user's choices and ways to restore consistency. This paper presents an extension of the CSP framework in this direction. The key idea consists in considering and handling the user's choices as assumptions. From a theoretical point of view, the complexity issues of various computational tasks involved in interactive decision support problems are investigated. The results cohere with what is known when Boolean constraints are considered and show all the tasks intractable in the worst case. Since interactivity requires short response times, intractability must be circumvented some way. To this end, we present a new method for compiling configuration problems, that can be generalized to valued CSPs. Specifically, an automaton representing the set of solutions of the CSP is first computed off-line, then this data structure is exploited so as to ensure both consistency maintenance and computation of maximal consistent subsets of user's choices in an efficient way.

Reformulating Positive Table Constraints Using Functional Dependencies

“…We considered two cases with respect to size: measuring the sum of the sizes of each table constraint in the reformulation, as well as the sum of the sizes of a REGULAR-based compilation of each table. We considered positive table constraints from the following five datasets: the Renault Megane Car Configuration Problem (we used the two largest table constraints, R80 and R140) [2]; a dataset of digital cameras [18]; a dataset of laptops [18]; the AI-CBR travel case-base [14]; and a dataset based on the crossword puzzle CSP benchmark [1]. We used a well-known library, called TANE [11], to compute the set of minimal functional dependencies for each table.…”

Compacité pratique des diagrammes de décision valués. Normalisation, heuristiques et expérimentations

“…Les diagrammes de décision -automates, diagrammes de décision binaires ordonnés (OBDD), diagrammes de décision multivalués (MDD) -sont particulièrement intéressants pour la compilation de problèmes de satisfaction de contraintes, et spécialement pour le type d'application qui nous intéresse,à savoir la compilation de problèmes de configuration de produit [3,10,12]. Cela dit, ces diagrammes ne permettent pas tels quels de représenter des fonctions de coût, ou plus généralement des fonctions associant une valuation (coût, degré de satisfaction, probabilité, etc.)…”

“…aux affectations de variables -ils ne permettent pas la compilation de problèmes de satisfaction de contraintes valuées (VCSPs). Dans un tel cadre, les diagrammes de décision valués (VDDs) -diagrammes de décision algébriques (ADDs) [4], diagrammes de dé-cisionà arcs valués (EVBDDs) [15,14,3], Semiring Labeled Decision Diagrams (SLDDs) [20], diagrammes de décision algébriques affines (AADDs) [18][17] sont alors des langages cibles pertinents. Les ADDs par exemple ontété utilisés pour la compilation de problèmes de planification [13] ; des travaux en configuration de produit [3,11] ont proposé d'utiliser les EVBDDs (ou de manièreéquivalente, les SLDDs additifs -SLDD + ) pour capturer des fonctions de coût ou de préférences fortement additives, c'est-à-dire des cas où la valuation associéeà une affectation des variables s'exprime directement par un VCSP dont toutes les contraintes souples sont unaires : l'idée est alors de compiler les contraintes dures qui définissent le produit configurable par un MDD, puis d'ajouter les valuations définies par les contraintes unaires directement sur les arcs.…”

Practically handling some configuration isomorphisms

“…The industrial need for configuration applications is ancient [10,4], and has triggered the development of many configuration programs and formalisms [13,20,1,14,19,21,22,9,15].…”