A Linear Weight Transfer Rule for Local Search

The Divide and Distribute Fixed Weights algorithm (ddfw) is a dynamic local search SAT-solving algorithm that transfers weight from satisfied to falsified clauses in local minima. ddfw is remarkably effective on several hard combinatorial instances. Yet, despite its success, it has received little study since its debut in 2005. In this paper, we propose three modifications to the base algorithm: a linear weight transfer method that moves a dynamic amount of weight between clauses in local minima, an adjustment to how satisfied clauses are chosen in local minima to give weight, and a weighted-random method of selecting variables to flip. We implemented our modifications to ddfw on top of the solver yalsat. Our experiments show that our modifications boost the performance compared to the original ddfw algorithm on multiple benchmarks, including those from the past three years of SAT competitions. Moreover, our improved solver exclusively solves hard combinatorial instances that refute a conjecture on the lower bound of two Van der Waerden numbers set forth by Ahmed et al. (2014), and it performs well on a hard graph-coloring instance that has been open for over three decades

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.

Engineering stochastic local search for the satisfiability problem

This thesis describes new algorithms for the Propositional Satisfiability Problem (SAT), a fundamental problem in theoretical and practical computer science. Besides the theoretical relevance of the SAT problem, many practical applications corroborate the importance of the SAT problem. Within this thesis, we provide different improvements for SLS solvers, and also propose new SLS solving techniques for the SAT problem. By means of empirical evaluations, we compare our solving methods with available state-of-the-art methods and show the superiority of the former. The results of our solvers within different SAT competitions further confirm their state-of-the-art performance. First, we propose a new technique to analyze the search behavior of an SLS solver. We show that this approach can be used to construct hybrid solvers that are able to exceed the performance of the SLS component. We present a new type of heuristic for SLS solvers based on the concept of probability distributions, which we implement in the solver Sparrow that reaches state-of-the-art performance on a wide range of randomly generated SAT problems. To improve the applicability of SLS solvers on structured problems, we analyze different preprocessing techniques in combination with the solver Sparrow. We are able to show that the performance of SLS solvers can be significantly improved on structured problems. Within our final study, we propose and analyze a solver based solely on probability distributions. Our new solver, named probSAT, allows a detailed analysis of the role of make and break for SLS solvers. Within comprehensive evaluations, we analyze probSAT on different SAT problems, and show that it establishes new state-of-the-art standards. Finally we present an advanced framework for the empirical evaluation of algorithms, named EDACC, which provides a plethora of functionalities for the design, execution and analysis of experiments with all kind of algorithms