Lagrangian Based Global Search for Sat

Satissability is a class of NP-complete problems that model a wide range of real-world applications. These problems are diicult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method for solving satis-ability problems. We derive new approachesfor applyingLagrangianmethods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Instead of restarting from a new starting point when a search reaches a local trap, the Lagrange multipliers in our method provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. One of the major advantages of our method is that it has very few algorithmic parameters to be tuned by users, and the search procedure can be made deterministic and the results, reproducible. We demonstrate our method by applying it to solve an extensive set of benchmark problems archived in DIMACS of Rutgers University. Our method generally performs better than the best existing methods and can achieve an order-of-magnitude speedup for some problems. Moreover, our method can solve some new benchmark problems that cannot be solved by other local-search methods.