Adrian Balint

Improving stochastic local search for SAT with a new probability distribution

This paper introduces a new SLS-solver for the satisfiability problem. It is based on the solver gNovelty+. In contrast to gNovelty+, when our solver reaches a local minimum, it computes a probability distribution on the variables from an unsatisfied clause. It then flips a variable picked according to this distribution. Compared with other state-of-the-art SLS-solvers this distribution needs neither noise nor a random walk to escape efficiently from cycles. We compared this algorithm which we called Sparrow to the winners of the SAT 2009 competition on a broad range of 3-SAT instances. Our results show that Sparrow is significantly outperforming all of its competitors on the random 3-SAT problem.

Choosing probability distributions for stochastic local search and the role of make versus break

Stochastic local search solvers for SAT made a large progress with the introduction of probability distributions like the ones used by the SAT Competition 2011 winners Sparrow2010 and EagleUp. These solvers though used a relatively complex decision heuristic, where probability distributions played a marginal role. In this paper we analyze a pure and simple probability distribution based solver probSAT, which is probably one of the simplest SLS solvers ever presented. We analyze different functions for the probability distribution for selecting the next flip variable with respect to the performance of the solver. Further we also analyze the role of make and break within the definition of these probability distributions and show that the general definition of the score improvement by flipping a variable, as make minus break is questionable. By empirical evaluations we show that the performance of our new algorithm exceeds that of the SAT Competition winners by orders of magnitude.

EDACC - an advanced platform for the experiment design, administration and analysis of empirical algorithms

The design, execution and analysis of experiments using heuristic algorithms can be a very time consuming task in the development of an algorithm. There are a lot of problems that have to be solved throughout this process. To speed up this process we have designed and implemented a framework called EDACC, which supports all the tasks that arise throughout the experimentation with algorithms. A graphical user interface together with a database facilitates archiving and management of solvers and problem instances. It also enables the creation of complex experiments and the generation of the computation jobs needed to perform the experiment. The task of running the jobs on an arbitrary computer system (or computer cluster or grid) is taken by a compute client, which is designed to increase computation throughput to a maximum. Real-time monitoring of running jobs can be done with the GUI or with a web frontend, both of which provide a wide variety of descriptive statistics and statistic testing to analyze the results. The web frontend also provides all the tools needed for the organization and execution of solver competitions.

Overview and analysis of the SAT Challenge 2012 solver competition

Programs for the Boolean satisfiability problem (SAT), i.e., SAT solvers, are nowadays used as core decision procedures for a wide range of combinatorial problems. Advances in SAT solving during the last 10-15 years have been spurred by yearly solver competitions. In this article, we report on the main SAT solver competition held in 2012, SAT Challenge 2012. Besides providing an overview of how SAT Challenge 2012 was organized, we present an in-depth analysis of key aspects of the results obtained during the competition.

A Novel Approach to Combine a SLS- and a DPLL-Solver for the Satisfiability Problem

The paper at hand presents a novel and generic approach on how to combine a SLS and a DPLL solver to create an incomplete hybrid SAT solver. In our approach, the SLS solver gets supported by a DPLL solver to boost its performance. In order to develop the idea behind our approach, we first define the term of a search space partition (SSP) and explain its construction and use. For testing our new approach, which utilizes SSPs, we implemented it in the solver hybridGM , using gNovelty+ and March_ks . After explaining the implementation details, we perform an empirical study on several publicly available benchmarks in order to test the performance of the new hybrid SAT solver. The results indicate a superior performance of hybridGM over gNovelty+ , proving our new approach to be worthwhile.

Improving Implementation of SLS Solvers for SAT and New Heuristics for k-SAT with Long Clauses

Stochastic Local Search (SLS) solvers are considered one of the best solving technique for randomly generated problems and more recently also have shown great promise for several types of hard combinatorial problems. Within this work, we provide a thorough analysis of different implementation variants of SLS solvers on random and on hard combinatorial problems. By analyzing existing SLS implementations, we are able to discover new improvements inspired by CDCL solvers, which can speed up the search of all types of SLS solvers. Further, our analysis reveals that the multilevel break values of variables can be easily computed and used within the decision heuristic. By augmenting the probSAT solver with the new heuristic, we are able to reach new state-of-the-art performance on several types of SAT problems, especially on those with long clauses. We further provide a detailed analysis of the clause selection policy used in focused search SLS solvers.

Engineering a Lightweight and Efficient Local Search SAT Solver

One important category of SAT solver implementations use stochastic local search (SLS, for short). These solvers try to find a satisfying assignment for the input Boolean formula (mostly, required to be in CNF) by modifying the (mostly randomly chosen) initial assignment by bit flips until a satisfying assignment is possibly reached. Usually such SLS type algorithms proceed in a greedy fashion by increasing the number of satisfied clauses until some local optimum is reached. Trying to find its way out of such local optima typically requires the use of randomness. We present an easy, straightforward SLS type SAT solver, called probSAT, which uses just one simple strategy being based on biased probabilistic flips. Within an extensive empirical study we evaluate the current state-of-the-art solvers on a wide range of SAT problems, and show that our approach is able to exceed the performance of other solving techniques.