A new Approach for Solving Satisfiability Problems with Qualitative Preferences

The problem of expressing and solving satisfiability problems (SAT) with qualitative preferences is central in many areas of Computer Science and Artificial Intelligence. In previous papers, it has been shown that qualitative preferences on literals allow for capturing qualitative/quantitative preferences on literals/formulas; and that an optimal model for a satisfiability problems with qualitative preferences on literals can be computed via a simple modification of the Davis-Logemann-Loveland procedure (DLL): Given a SAT formula, an optimal solution is computed by simply imposing that DLL branches according to the partial order on the preferences. Unfortunately, it is well known that introducing an ordering on the branching heuristic of DLL may cause an exponential degradation in its performances. The experimental analysis reported in these papers hightlights that such degradation can indeed show up in the presence of a significant number of preferences. In this paper we propose an alternative solution which does not require any modification of the DLL heuristic: Once a solution is computed, a constraint is added to the input formula imposing that the new solution (if any) has to be better than the last computed. We implemented this idea, and the resulting system can lead to significant improvements wrt the original proposal when dealing with MINONE/MAX-SAT problems corresponding to qualitative preferences on structured instances.