Computing All Optimal Solutions in Satisfiability Problems with Preferences

The problem of finding an optimal solution in a constraint satisfaction problem with preferences has attracted a lot of researchers in Artificial Intelligence in general, and in the constraint programming community in particular. As a consequence, several approaches for expressing and reasoning about satisfiability problems with preferences have been proposed, and viable solutions exist for finding one optimal Solution. However, in many cases, it is not desirable to find just one solution. Indeed, it might be desirable to he able to compute more, and possibly all, optimal solutions, e.g.. for comparatively evaluate them on the basis of other criteria not captured by the preferences. In this paper we present a procedure for computing all optimal solutions of a satisfiability problem with preferences. The procedure is guaranteed to compute all and only the optimal solutions, i.e., models which are not optimal are not even computed.