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 adaptG2WSAT+ selects a variable to flip, as heuristic adaptG2WSAT+, the way in which clause weighting algorithm RSAPSselects a variable to flip, as heuristic RSAPS, and the way in which variable weighting algorithm VWselects 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 adaptG2WSAT+, 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 NCVWis generally effective on a wide range of instances while adaptG2WSAT+, RSAPS, VW, and gNovelty+ and adaptG2WSAT0, which won the gold and silver medals in the satisfiable random category in the SAT 2007 competition, respectively, are not.