Improving the performance of discrete Lagrange-multiplier search for solving hard SAT problems

Recently, we have proposed the discrete Lagrange-multiplier method (DLM) to solve satissability problems. Instead of restarting from a new starting point when the search reaches a local minimum in the objective space, the Lagrange multipliers of violated constraints in DLM provide a force to lead the search out of the local minimum and move it in a direction provided by the multipliers. In this paper, we present the theoretical foundation of DLM for solving SAT problems and discuss some implementation issues. We study the performance of DLM on a set of hard sat-issability benchmark instances, and show the importance of dynamic scaling of Lagrange multipliers and the at-move strategy. We show that DLM can perform better than competing local-search methods when its parameters are selected properly.