Tunneling between plateaus

Abstract

There are two important challenges for local search algorithms when applied to Maximal Satisfiability (MAXSAT). 1) Local search spends a great deal of time blindly exploring plateaus in the search space and 2) local search is less effective on application instances. This second problem may be related to local search's inability to exploit problem structure. We propose a genetic recombination operator to address both of these issues. On problems with well defined local optima, partition crossover is able to tunnel between local optima to discover new local optima in O(n) time. The PXSAT algorithm combines partition crossover and local search to produce a new way to escape plateaus. Partition crossover locally decomposes the evaluation function for a given instance into independent components, and is guaranteed to find the best solution among an exponential number of candidate solutions in O(n) time. Empirical results on an extensive set of application instances show that the proposed framework substantially improves two of best local search solvers, AdaptG2WSAT and Sparrow, on many application instances. PXSAT combined with AdaptG2WSAT is also able to outperform CCLS, winner of several recent MAXSAT competitions.