Using Hard Constraints for Representing Soft Constraints

• Published in: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems Vol. 6697; pp. 176 - 189
• Main Author: Régin, Jean-Charles
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2011; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Choice Point; Constraint Network; Constraint Satisfaction Problem; Hard Constraint; Soft Constraint
• ISBN: 9783642213106; 3642213103
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-21311-3_17

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.