Discovering and harnessing structures in solving application satisfiability instances
Date
2018
Authors
Chen, Wenxiang, author
Whitley, L. Darrell, advisor
Draper, Bruce A., committee member
Böhm, A. P. Wim, committee member
Chong, Edwin K. P., committee member
Journal Title
Journal ISSN
Volume Title
Abstract
Boolean satisfiability (SAT) is the first problem proven to be NP-Complete. It has become a fundamental problem for computational complexity theory, and many real-world problems can be encoded as SAT instances. Two major search paradigms have been proposed for SAT solving: Systematic Search (SS) and Stochastic Local Search (SLS). SLS solvers have been shown to be very effective at uniform random instances; SLS solvers are consistently the top winning entries for random tracks at SAT competitions. However, SS solvers dominate hard combinatorial tracks and industrial tracks at SAT competitions, with SLS entries being at the very bottom of the ranking. In this work, we classify both hard combinatorial instances and industrial instances as Application Instances. As application instances are more interesting from a practical perspective, it is critical to analyze the structures in application instances as well as to improve SLS on application instances. We focus on two structural properties of SAT instances in this work: variable interaction topology and subproblem constrainedness. Decomposability focuses on how well the variable interaction of an application instance can be decomposed. We first show that many application instances are indeed highly decomposable. The decomposability of a SAT instance have been extensively exploited with success by SS solvers. Meanwhile, SLS solvers direct the variables to flip using only the objective function, and are completely oblivious of the decomposability of application instances that is inherent to the original problem domain. We propose a new method to decompose variable interactions within SLS solvers, leveraging numerous visited local optima. Our empirical study suggests that the proposed method can vastly simplify SAT instances, which further results in decomposing the instances into thousands of connected components. Furthermore, we demonstrate the utility of the decomposition, in improving SLS solvers. We propose a new framework called PXSAT, based on the recombination operator Partition Crossover (PX). Given q components, PX is able to find the best of 2q possible candidate solutions in linear time. Empirical results on an extensive set of application instances show PXSAT can yield statistically significantly better results. We improve two of best local search solvers, AdaptG2WSAT and Sparrow. PXSAT combined with AdaptG2WSAT is also able to outperform CCLS, winners of several recent MAXSAT competitions. The other structural property we study is subproblem constrainedness. We observe that, on some application SAT instance classes, the original problem can be partitioned into several subproblems, where each subproblems is highly constrained. While subproblem constrainedness has been exploited in SS solvers before, we propose to exploit it in SLS solvers using two alternative representations that can be obtained efficiently based on the canonical CNF representation. Our empirical results show that the new alternative representative enables a simple SLS solver to outperform several sophisticated and highly optimized SLS solvers on the SAT encoding of semiprime factoring problem.
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Subject
MAXSAT
SAT
optimization
local search