Maintaining Alternative Values in Constraint-Based Configuration

Abstract

Constraint programming techniques are widely used to model and solve interactive decision problems, and especially configuration problems. In this type of application, the configurable product is described by means of a set of constraints bearing on the configuration variables. The user interactively solves the CSP by assigning the variables according to her preferences. The system then has to keep the domains of the other variables consistent with these choices. Since maintaining the global inverse consistency of the domains is not tractable, the domains are instead filtered according to some level of local consistency, e.g. arc-consistency. The present paper aims at offering a more convenient interaction by providing the user with possible alternative values for the already assigned variables, i.e. values that could replace the current ones without leading to a constraint violation. We thus present the new concept of alternative domains in a (possibly) partially assigned CSP. We propose a propagation algorithm that computes all the alternative domains in a single step. Its worst case complexity is comparable to the one of the naive algorithm that would run a full propagation for each variable, but its experimental efficiency is better.