Local search strategies for satisfiability testing

Abstract

It has recently been shown that local search is surprisingly good at nding satisfying assignments for certain classes of CNF formulas 24]. In this paper we demonstrate that the power of local search for satis ability testing can be further enhanced by employing a new strategy, called \mixed random walk", for escaping from local minima. We present experimental results showing how this strategy allows us to handle formulas that are substantially larger than those that can be solved with basic local search. We also present a detailed comparison of our random walk strategy with simulated annealing. Our results show that mixed random walk is the superior strategy on several classes of computationally di cult problem instances. Finally, we present results demonstrating the e ectiveness of local search with walk for solving circuit synthesis and diagnosis problems.

Efficiently Calculating Evolutionary Tree Measures Using SAT

“…On the other hand, we use Walksat [24,25], adaptg2wsat [8], novelty+p [8] for the upper bounds of both measures. We use the UBCSAT implementation [27] for the latter two since it was significantly faster than the stand-alone versions.…”

“…In this case we do a comparison among several solvers. They are walksat [24,25], adaptg2wsat [8], novelty+p [8], minisat [10,11], SATzilla [29] and March KS [15]. Notice that we compare all kinds of different solvers: local search algorithms (the first three), DPLL with learning (minisat), SAT solver portfolio (SATzilla) and solver specialized on random instances (March KS).…”

Zchaff2004: An Efficient SAT Solver

“…Consequently, there are many practical algorithms based on various principles such as Resolution [7], Systematic Search [8], Stochastic Local Search [9], Binary Decision Diagrams [10], Stålmarck's [11] algorithm, and others. Gu et al [12] provide a review of many of the algorithms.…”

An Empirical Study of Optimal Noise and Runtime Distributions in Local Search

“…For SAT, techniques such as greedy local search, tabu search, solution guided search, focused random walk, and reactive or adaptive search have led to much success. Specifically, Walksat [7] stands out as one of the initial solvers that introduced many of the key ideas in use today and, is still competitive with the state of the art.While many attempts have been made to understand the behavior of local search methods in terms of local minima, exploring "plateaus", the exploration vs. exploitation tradeoff, etc., our formal understanding is limited mostly to relatively simple variants of local search, such as a pure greedy search, a pure random walk, or a combination of the two. This is not surprising as the techniques employed by Walksat and other state-of-the-art local search solvers are too complex to allow a formal analysis in terms of, for example, a traditional Markov Chain.…”

“…For SAT, techniques such as greedy local search, tabu search, solution guided search, focused random walk, and reactive or adaptive search have led to much success. Specifically, Walksat [7] stands out as one of the initial solvers that introduced many of the key ideas in use today and, is still competitive with the state of the art.…”