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.