The Configurable SAT Solver Challenge (CSSC)

It is well known that different solution strategies work well for different types of instances of hard combinatorial problems. As a consequence, most solvers for the propositional satisfiability problem (SAT) expose parameters that allow them to be customized to a particular family of instances. In the international SAT competition series, these parameters are ignored: solvers are run using a single default parameter setting (supplied by the authors) for all benchmark instances in a given track. While this competition format rewards solvers with robust default settings, it does not reflect the situation faced by a practitioner who only cares about performance on one particular application and can invest some time into tuning solver parameters for this application. The new Configurable SAT Solver Competition (CSSC) compares solvers in this latter setting, scoring each solver by the performance it achieved after a fully automated configuration step. This article describes the CSSC in more detail, and reports the results obtained in its two instantiations so far, CSSC 2013 and 2014

Improving WalkSAT for Random 3-SAT Problems

Stochastic local search (SLS) algorithms are well known for their ability to efficiently find models of random instances of the Boolean satisfiability (SAT) problems. One of the most famous SLS algorithms for SAT is called WalkSAT, which has wide influence and performs well on most of random 3-SAT instances. However, the performance of WalkSAT lags far behind on random 3-SAT instances equal to or greater than the phase transition ratio. Motivated by this limitation, in the present work, firstly an allocation strategy is introduced and utilized in WalkSAT to determine the initial assignment, leading to a new algorithm called WalkSATvav. The experimental results show that WalkSATvav significantly outperforms the state-of-the-art SLS solvers on random 3-SAT instances at the phase transition for SAT Competition 2017. However, WalkSATvav cannot rival its competitors on random 3-SAT instances greater than the phase transition ratio. Accordingly, WalkSATvav is further improved for such instances by utilizing a combination of an improved genetic algorithm and an improved ant colony algorithm, which complement each other in guiding the search direction. The resulting algorithm, called WalkSATga, is far better than WalkSAT and significantly outperforms some previous known SLS solvers on random 3-SAT instances greater than the phase transition ratio from SAT Competition 2017. Finally, a new SAT solver called WalkSATlg, which combines WalkSATvav and WalkSATga, is proposed, which is competitive with the winner of random satisfiable category of SAT competition 2017 on random 3-SAT problem

Improving probability selection based weights for satisfiability problems

Boolean Satisfiability problem (SAT) plays a prominent role in many domains of computer science and artificial intelligence due to its significant importance in both theory and applications. Algorithms for solving SAT problems can be categorized into two main classes: complete algorithms and incomplete algorithms (typically stochastic local search (SLS) algorithms). SLS algorithms are among the most effective for solving uniform random SAT problems, while hybrid algorithms achieved great breakthroughs for solving hard random SAT (HRS) problem recently. However, there is a lack of algorithms that can effectively solve both uniform random SAT and HRS problems. In this paper, a new SLS algorithm named SelectNTS is proposed aiming at solving both uniform random SAT and HRS problem effectively. SelectNTS is essentially an improved probability selection based local search algorithm, the core of which includes new clause and variable selection heuristics: a new clause weighting scheme and a biased random walk strategy are utilized to select a clause, while a new probability selection strategy with the variation of configuration checking strategy is used to select a variable. Extensive experimental results show that SelectNTS outperforms the state-of-the-art random SAT algorithms and hybrid algorithms in solving both uniform random SAT and HRS problems effectively

Preprocessing and Stochastic Local Search in Maximum Satisfiability

Problems which ask to compute an optimal solution to its instances are called optimization problems. The maximum satisfiability (MaxSAT) problem is a well-studied combinatorial optimization problem with many applications in domains such as cancer therapy design, electronic markets, hardware debugging and routing. Many problems, including the aforementioned ones, can be encoded in MaxSAT. Thus MaxSAT serves as a general optimization paradigm and therefore advances in MaxSAT algorithms translate to advances in solving other problems. In this thesis, we analyze the effects of MaxSAT preprocessing, the process of reformulating the input instance prior to solving, on the perceived costs of solutions during search. We show that after preprocessing most MaxSAT solvers may misinterpret the costs of non-optimal solutions. Many MaxSAT algorithms use the found non-optimal solutions in guiding the search for solutions and so the misinterpretation of costs may misguide the search. Towards remedying this issue, we introduce and study the concept of locally minimal solutions. We show that for some of the central preprocessing techniques for MaxSAT, the perceived cost of a locally minimal solution to a preprocessed instance equals the cost of the corresponding reconstructed solution to the original instance. We develop a stochastic local search algorithm for MaxSAT, called LMS-SLS, that is prepended with a preprocessor and that searches over locally minimal solutions. We implement LMS-SLS and analyze the performance of its different components, particularly the effects of preprocessing and computing locally minimal solutions, and also compare LMS-SLS with the state-of-the-art SLS solver SATLike for MaxSAT.

Effect of Initial Assignment on Local Search Performance for Max Sat

In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics - Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows