Adaptive Clause Weight Redistribution

Abstract

Abstract. In recent years, dynamic local search (DLS) clause weighting algorithms have emerged as the local search state-of-the-art for solving propositional satisfiability problems. However, most DLS algorithms require the tuning of domain dependent parameters before their performance becomes competitive. If manual parameter tuning is impractical then various mechanisms have been developed that can automatically adjust a parameter value during the search. To date, the most effective adaptive clause weighting algorithm is RSAPS. However, RSAPS is unable to convincingly outperform the best non-weighting adaptive algorithm AdaptNovelty + , even though manually tuned clause weighting algorithms can routinely outperform the Novelty + heuristic on which AdaptNovelty + is based. In this study we introduce R+DDFW + , an enhanced version of the DDFW clause weighting algorithm developed in 2005, that not only adapts the total amount of weight according to the degree of stagnation in the search, but also incorporates the latest resolution-based preprocessing approach used by the winner of the 2005 SAT competition (R+AdaptNovelty + ). In an empirical study we show R+DDFW + improves on DDFW and outperforms the other leading adaptive (R+Adapt-Novelty + , R+RSAPS) and non-adaptive (R+G 2 WSAT) local search solvers over a range of random and structured benchmark problems.

Weight Redistribution for Unweighted MAX-SAT

“…DDFW's closest rivals are AdaptNovelty + and DDFW + , with AdaptNovelty + defeating DDFW + on the uuf problems, equalling it on the jnh problems and being defeated by DDFW + on the bor-2 and bor-3 problems. These results partly confirm the initial evaluation of DDFW and DDFW + in the SAT domain [8]. There, both algorithms were shown to have better performance in comparison to several other state-of-the-art SAT algorithms (including AdaptNovelty + and RSAPS) on a range of SAT competition benchmark problems.…”

“…More recently, a new approach to clause weighting has been proposed, termed divide and distribute fixed weight (DDFW) [8]. DDFW introduces two ideas into the area of clause weighting algorithms for SAT.…”

“…Firstly, it evenly distributes a fixed quantity of weight across all clauses at the start of the search, and escapes local minima by transferring weight from satisfied to unsatisfied clauses in a single step (rather than using the two phase approach of SAPS and PAWS). Secondly, DDFW exploits neighbourhood relationships between clauses when deciding which pairs of clauses will exchange weight (see [8] for details). For the current MAX-SAT study we additionally changed DDFW so that it keeps track of the current best cost and the current best solution (see lines 3-5 and 9-12 in Algorithm 1).…”

“…Initial empirical evaluations of DDFW and DDFW + on a range of structured and unstructured SAT problems have shown both algorithms can outperform AdaptNovelty + and RSAPS, and that DDFW + has a better average performance than DDFW [8]. However, a similar study has yet to be attempted in the MAX-SAT domain.…”

“…The search then continues to follow each increase with a reset and each reset with an increase. In this way a long period of stagnation will produce oscillating phases of weight increase and reduction, such that the total weight can never exceed 3× the total number of clauses plus the total number of false clauses (for more detail see [8]). …”