On Solving Optimization Problems Using Boolean Satisfiability

The last few years have seen significant advances in Boolean satisfiability (SAT) solving. This has lead to the successful deployment of SAT solvers in a wide range of problems in Engineering and Computer Science. In general, most SAT solvers are applied to Boolean decision problems that are expressed in conjunctive normal form (CNF). While this input format is applicable to some engineering tasks, it poses a significant obstacle to others. One of the main advances in SAT is generalizing SAT solvers to handle stronger representation of constraints. Specifically, pseudo-Boolean (PB) constraints which are efficient in representing counting constraints and can replace an exponential number of CNF constraints. Another significant advantage of PB constraints is its ability to express Boolean optimization problems. This allows for new applications that were never handled by SAT solvers before. In this paper, we describe two methods to solve Boolean optimization problems using SAT solvers. Both methods are implemented and evaluated using the SAT solver PBS. We develop an adaptive flow that analyzes a given Boolean optimization problem and selects the solving method that best fits the problem characteristics. Empirical evidence on a variety of benchmarks shows that both methods are competitive. The results also show that SAT-based methods tend to outperform generic integer linear programming (ILP) solvers.