Abstract.Maxsat is an optimization version of Satisfiability aimed at finding a truth assignment that maximizes the satisfaction of the theory. The technique of solving a sequence of SAT decision problems has been quite successful for solving larger, more industrially focused Maxsat instances, particularly when only a small number of clauses need to be falsified. The SAT decision problems, however, become more and more complicated as the minimal number of clauses that must be falsified increases. This can significantly degrade the performance of the approach. This technique also has more difficulty with the important generalization where each clause is given a weight: the weights generate SAT decision problems that are harder for SAT solvers to solve. In this paper we introduce a new Maxsat algorithm that avoids these problems. Our algorithm also solves a sequence of SAT instances. However, these SAT instances are always simplifications of the initial Maxsat formula, and thus are relatively easy for modern SAT solvers. This is accomplished by moving all of the arithmetic reasoning into a separate hitting set problem which can then be solved with techniques better suited to numeric reasoning, e.g., techniques from mathematical programming. As a result the performance of our algorithm is unaffected by the addition of clause weights. Our algorithm can, however, require solving more SAT instances than previous approaches. Nevertheless, the approach is simpler than previous methods and displays superior performance on some benchmarks.

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Abstract. maxsat is an optimization version of satisfiability. Since many practical problems involve optimization, there are a wide range of potential applications for effective maxsat solvers. In this paper we present an extensive empirical evaluation of a number of maxsat solvers. In addition to traditional maxsat solvers, we also evaluate the use of a state-of-the-art Mixed Integer Program (mip) solver, cplex, for solving maxsat. mip solvers are the most popular technology for solving optimization problems and are also theoretically more powerful than sat solvers. In fact, we show that cplex is quite effective on a range of maxsat instances. Based on these observations we extend a previously developed hybrid approach for solving maxsat, that utilizes both a sat solver and a mip solver. Our extensions aim to take better advantage of the power of the mip solver. The resulting improved hybrid solver is shown to be quite effective.

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Abstract. maxsat is an optimization version of sat that can represent a wide variety of important optimization problems. A recent approach for solving maxsat is to exploit both a sat solver and a Mixed Integer Programming (mip) solver in a hybrid approach. Each solver generates information used by the other solver in a series of iterations that terminates when an optimal solution is found. Empirical results indicate that a bottleneck in this process is the time required by the mip solver, arising from the large number of times it is invoked. In this paper we present a modified approach that postpones the calls to the mip solver. This involves substituting non-optimal solutions for the optimal ones computed by the mip solver, whenever possible. We describe the new approach and some different instantiations of it. We perform an extensive empirical evaluation comparing the performance of the resulting solvers with other state-of-the-art maxsat solvers. We show that the best performing versions of our approach advance the state-of-the-art in maxsat solving.