Implementing Semiring-Based Constraints Using Mozart

Although Constraint Programming (CP) is considered a useful tool for tackling combinatorial problems, its lack of flexibility when dealing with uncertainties and preferences is still a matter of research. Several formal frameworks for soft constraints have been proposed within the CP community: all of them seem to be theoretically solid, but few practical implementations exist. In this paper we present an implementation for Mozart of one of these frameworks, which is based on a semiring structure. We explain how the soft constraints constructs were adapted to the propagation process that Mozart performs, and show how they can be transparently integrated with current Mozart hard propagators. Additionally, we show how overconstrained problems can be successfully relaxed and solved, and how preferences can be added to a problem, while keeping the formal model as a direct reference.