Soft constraints for lexicographic orders

Abstract

While classical Constraint Satisfaction Problems (CSPs) concern the search for the boolean assignment of a set of variables that has to satisfy some given requirements, their soft variant considers ordered domains for assignments, thus modeling preferences: the aim is to provide an environment where suitable algorithms (e.g. on constraint propagation) can be stated and proved, and inherited by its instances. Besides their flexibility, these formalisms have been advocated for their modularity: suitable operators can be defined, in order to manipulate such structures and build new ones. However, some intuitive constructions were given less attention, such as lexicographic orders. Our works explores such orders in three instances of the soft CSP framework. Our results allow for a wider application of the formalism, and it is going to be pivotal for the use of constraints in modeling scenarios where the features to be satisfied are equipped with a fixed order of importance. © Springer-Verlag 2013.