Research on incomplete algorithms for satisfiability testing lead to some of the first scalable SAT solvers in the early 1990's. Unlike systematic solvers often based on an exhaustive branching and backtracking search, incomplete methods are generally based on stochastic local search. On problems from a variety of domains, such incomplete methods for SAT can significantly outperform DPLL-based methods. While the early greedy algorithms already showed promise, especially on random instances, the introduction of randomization and so-called uphill moves during the search significantly extended the reach of incomplete algorithms for SAT. This chapter discusses such algorithms, along with a few key techniques that helped boost their performance such as focusing on variables appearing in currently unsatisfied clauses, devising methods to efficiently pull the search out of local minima through clause re-weighting, and adaptive noise mechanisms. The chapter also briefly discusses a formal foundation for some of the techniques based on the discrete Lagrangian method.
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