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

We have proposed the discrete Lagrange-multiplier method (DLM) to solve satisfiability 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. 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 satisfiability benchmark instances, and show the importance of dynamic scaling of Lagrange multipliers and the flat-move strategy. We show that DLM can perform better than competing local-search methods when its parameters are selected properly.