Using Hard Constraints for Representing Soft Constraints

Most of the current algorithms dedicated to the resolution of over-constrained problems, as PFC-MRDAC, are based on the search for a support for each value of each variable taken independently. The structure of soft constraints is only used to speed-up such a search, but not to globally deduce the existence or the absence of support. These algorithms do not use the filtering algorithms associated with the soft constraints. In this paper we present a new schema where a soft constraint is represented by a hard constraint in order to automatically benefit from the pruning performance of the filtering algorithm associated with this constraint and from the incremental aspect of these filtering algorithms. In other words, thanks to this schema every filtering algorithm associated with a constraint can still be used when the constraint is soft. The PFC-MRDAC (via the Satisfiability Sum constraint) algorithm and the search for disjoint conflict sets are then adapted to this new schema.