Full arc consistency in WCSP and in constraint hierarchies with finite domains

Abstract

Consistency techniques proved to be an efficient method for reducing the search space of CSP and hence they were modified for soft constraint frameworks too. Several algorithms for local consistency in Weighted CSP, where costs are assigned to tuples, were introduced in [2,3]. The strongest form among them is Full Star Directional Arc Consistency (FDAC*). The algorithm for enforcing FDAC* is based on sending costs from one constraint to another in one direction with respect to the fixed order of variables. We consider the fixed order of variables to be rather limiting so we propose Full Star Arc Consistency (FAC*) which extends the cost sending process by allowing to send the costs in any direction. Because it may not be always possible to send the cost along a directed edge, the proposed extension enables the costs to be sent along other paths. The hope is that by combining more costs we can prune more values from variables' domains. When enforcing FAC*, we choose a variable and move the costs towards the chosen variable. The costs of values of that variable can be used by a value-ordering heuristics during Branch & Bound search. Constraint hierarchies [1] are another popular soft constraint framework, which provides a very simple way for a user to specify preferences over constraints. It is possible to use the above-mentioned WCSP consistency algorithms for constraint hierarchies too. We show how constraint hierarchies with finite domains using the unsatisfied-count-better comparator [1] can be transformed to WCSP. We believe that constraint hierarchies with other comparators can also be transformed to a generalization of WCSP that still allows to use the algorithms for enforcing FDAC* and FAC*. © Springer-Verlag Berlin Heidelberg 2005.