Using Cost Distributions to Guide Weight Decay in Local Search for SAT

Abstract

Abstract. Although clause weighting local search algorithms have produced some of the best results on a range of challenging satisfiability (SAT) benchmarks, this performance is dependent on the careful handtuning of sensitive parameters. When such hand-tuning is not possible, clause weighting algorithms are generally outperformed by self-tuning WalkSAT-based algorithms such as AdaptNovelty + and AdaptG 2 WSAT. In this paper we investigate tuning the weight decay parameter of two clause weighting algorithms using the statistical properties of cost distributions that are dynamically accumulated as the search progresses. This method selects a parameter setting both according to the speed of descent in the cost space and according to the shape of the accumulated cost distribution, where we take the shape to be a predictor of future performance. In a wide ranging empirical study we show that this automated approach to parameter tuning can outperform the default settings for two state-of-the-art algorithms that employ clause weighting (PAWS and gNovelty + ). We also show that these self-tuning algorithms are competitive with three of the best-known self-tuning SAT local search techniques: RSAPS, AdaptNovelty + and AdaptG 2 WSAT.

Ai@nicta

“…Other work on SAT includes both empirical and theoretical investigations into the power and efficiency of SAT algorithms, particularly concerning the use of restarts (Huang 2010), the interplay between components of SAT algorithms (Huang 2007), and estimating the cost of SAT solving in terms of the search tree size (Kilby et al 2006) and run time (Haim and Walsh 2008). Significant progress was made on one challenging problem in dynamic local search algorithms, namely parameter tuning (Thornton and Pham 2008). NICTA also played a key role in the preparation of the Handbook of Satisfiability, which provides a comprehensive account of theoretical and empirical studies of SAT algorithms and applications (Biere et al 2009).…”

Captain Jack: New Variable Selection Heuristics in Local Search for SAT

“…GNOVELTY + combines a clause penalty-based scheme similar to PAWS [15] . 1 The definition and notation we use differs slightly from the published version of SPARROW [3], but accurately reflects the source code implementation.…”

“…The value of a property can depend on the specific context in which the variable is selected and additional state information of the algorithm. For example, algorithms with dynamic clause penalties, such as PAWS [15] and GNOVELTY + [13], use a penalized property penScore, whose value depends on the full variable assignment and on the clause penalties (weights).…”