Solving hard satisfiability problems: a unified algorithm based on discrete Lagrange multipliers

Abstract

Presents improved strategies in DLM-99-SAT (Discrete Lagrange Multipliers 1999, Satisfiability) to escape from traps and to select proper parameter sets to use when applied to solve some difficult but satisfiable SAT problems. One of the main issues in DLM-99-SAT is that it has a large number of tunable parameters, making it difficult to determine the best parameters to use when given a new instance. To this end, we propose a set of performance metrics and a set of rules using these metrics that determine at run-time the best parameters to use for a specific instance. Our experimental results show that these rules are able to select the most suitable parameter set for each instance with very little overhead. Finally, we verify the performance of DLM-99-SAT by solving some benchmarks in SATLIB (SATisfiability problems LIBrary) and some of the most difficult but satisfiable DIMACS SAT benchmark problems, including par32-1-c to par32-4-c and hanoi4-simple.