Switching among Non-Weighting, Clause Weighting, and Variable Weighting in Local Search for SAT

Abstract

One way to design a local search algorithm that is effective on many types of instances is allowing this algorithm to switch among heuristics. In this paper, we refer to the way in which non-weighting algorithm adaptG ² WSAT + selects a variable to flip, as heuristic adaptG ² WSAT +, the way in which clause weighting algorithm RSAPS selects a variable to flip, as heuristic RSAPS, and the way in which variable weighting algorithm VW selects a variable to flip, as heuristic VW. We propose a new switching criterion: the evenness or unevenness of the distribution of clause weights. We apply this criterion, along with another switching criterion previously proposed, to heuristic adaptG ² WSAT +, heuristic RSAPS, and heuristic VW. The resulting local search algorithm, which adaptively switches among these three heuristics in every search step according to these two criteria to intensify or diversify the search when necessary, is called NCVW (Non-, Clause, and Variable Weighting). Experimental results show that NCVW is generally effective on a wide range of instances while adaptG ² WSAT +, RSAPS, VW, and gNovelty + and adaptG ² WSAT0, which won the gold and silver medals in the satisfiable random category in the SAT 2007 competition, respectively, are not.

The work of the first author is partially supported by NSERC PGS-D (Natural Sciences and Engineering Research Council of Canada Post-Graduate Scholarships for Doctoral students).