It has been widely observed that there is no single “dominant ” SAT solver; instead, different solvers perform best on different instances. Rather than following the traditional approach of choosing the best solver for a given class of instances, we advocate making this decision online on a per-instance basis. Building on previous work, we describe SATzilla, an automated approach for constructing per-instance algorithm portfolios for SAT that use so-called empirical hardness models to choose among their constituent solvers. This approach takes as input a distribution of problem instances and a set of component solvers, and constructs a portfolio optimizing a given objective function (such as mean runtime, percent of instances solved, or score in a competition). The excellent performance of our SATzilla portfolios has been independently verified in the 2007 SAT Competition, where our SATzilla-07 solvers won three gold, one silver and one bronze medal. In this article, we go well beyond SATzilla-07 by making the portfolio construction scalable and completely automated, and improving it by integrating local search solvers as candidate solvers, by predicting performance score instead of runtime, and by using hierarchical hardness models that take into account different types of SAT instances. We demonstrate the effectiveness of these new techniques in extensive experimental results on data sets including instances from the most recent SAT competition. 1.

It is well known that the ratio of the number of clauses to the number of variables in a random k-SAT instance is highly correlated with the instance's empirical hardness. We consider the problem of identifying such features of random SAT instances automatically with machine learning. We describe and analyze models for three SAT solvers---kcnfs, oksolver and satz---and for two different distributions of instances: uniform random 3-SAT with varying ratio of clauses-to-variables, and uniform random 3-SAT with fixed ratio of clauses-tovariables.

Abstract. In this paper we introduce MINIMAXSAT, a new Max-SAT solver that incorporates the best SAT and Max-SAT techniques. It can handle hard clauses (clauses of mandatory satisfaction as in SAT), soft clauses (clauses whose falsification is penalized by a cost as in Max-SAT) as well as pseudo-boolean objective functions and constraints. Its main features are: learning and backjumping on hard clauses; resolution-based and subtraction-based lower bounding; and lazy propagation with the two-watched literals scheme. Our empirical evaluation on a wide set of optimization benchmarks indicates that its performance is usually close to the best specialized alternative and, in some cases, even better. 1

Designing high-performance algorithms for computationally hard problems is a difficult and often time-consuming task. In this work, we demonstrate that this task can be automated in the context of stochastic local search (SLS) solvers for the propositional satisfiability problem (SAT). We first introduce a generalised, highly parameterised solver framework, dubbed SATenstein, that includes components gleaned from or inspired by existing high-performance SLS algorithms for SAT. The parameters of SATenstein control the selection of components used in any specific instantiation and the behaviour of these components. SATenstein can be configured to instantiate a broad range of existing high-performance SLSbased SAT solvers, and also billions of novel algorithms. We used an automated algorithm configuration procedure to find instantiations of SATenstein that perform well on several well-known, challenging distributions of SAT instances. Overall, we consistently obtained significant improvements over the previously best-performing SLS algorithms, despite expending minimal manual effort. 1 1

Abstract. The adaptive noise mechanism was introduced in Novelty+toautomatically adapt noise settings during the search [4]. The local search algorithm G 2 WSAT deterministically exploits promising decreasing variables to reduce randomness and consequently the dependence on noise parameters. In this paper, we first integrate the adaptive noise mechanism in G 2 WSAT to obtain an algorithm adaptG 2 WSAT, whose performance suggests that the deterministic exploitation of promising decreasing variables cooperates well with this mechanism. Then, we propose an approach that uses look-ahead for promising decreasing variables to further reinforce this cooperation. We implement this approach in adaptG 2 WSAT, resulting in a new local search algorithm called adaptG 2 WSATP. Without any manual noise or other parameter tuning, adaptG 2 WSATP shows generally good performance, compared with G 2 WSAT with approximately optimal static noise settings, or is sometimes even better than G 2 WSAT. In addition, adaptG 2 WSATP is favorably compared with state-of-the-art local search algorithms such as R+adaptNovelty+ and VW. 1

In this paper we introduce MINIMAXSAT, a new Max-SAT solver that is built on top of MIN-ISAT+. It incorporates the best current SAT and Max-SAT techniques. It can handle hard clauses (clauses of mandatory satisfaction as in SAT), soft clauses (clauses whose falsification is penalized by a cost as in Max-SAT) as well as pseudo-boolean objective functions and constraints. Its main features are: learning and backjumping on hard clauses; resolution-based and substractionbased lower bounding; and lazy propagation with the two-watched literal scheme. Our empirical evaluation comparing a wide set of solving alternatives on a broad set of optimization benchmarks indicates that the performance of MINIMAXSAT is usually close to the best specialized alternative and, in some cases, even better. 1.

Abstract. The effects of combining search and modelling techniques can be complex and unpredictable, so guidelines are very important for the design and development of effective and robust solvers and models. A recently observed phenomenon is the negative effect of symmetry breaking constraints on local search performance. The reasons for this are poorly understood, and we attempt to shed light on the phenomenon by testing three conjectures: that the constraints create deep new local optima; that they can reduce the relative size of the basins of attraction of global optima; and that complex local search heuristics reduce their negative effects. 1

Local search procedures for solving satisfiability problems have attracted considerable attention since the development of GSAT in 1992. However, recent work indicates that for many real-world problems, complete search methods have the advantage, because modern heuristics are able to effectively exploit problem structure. Indeed, to develop a local search technique that can effectively deal with variable dependencies has been an open challenge since1997. In this paper we show that local search techniques can effectively exploit information about problem structure producing significant improvements in performance on structured problem instances. Building on the earlier work of Ostrowski et al. we describe how information about variable dependencies can be built into a local search, so that only independent variables are considered for flipping. The cost effect of a flip is then dynamically calculated using a dependency lattice that models dependent variables using gates (specifically and, or and equivalence gates). The experimental study on hard structured benchmark problems demonstrates that our new approach significantly outperforms the previously reported best local search techniques. 1

Systematic search and local search paradigms for combinatorial problems are generally believed to have complementary strengths. Nevertheless, attempts to combine the power of the two paradigms have had limited success, due in part to the expensive information communication overhead involved. We propose a hybrid strategy based on shared memory, ideally suited for multi-core processor architectures. This method enables continuous information exchange between two solvers without slowing down either of the two. Such a hybrid search strategy is surprisingly effective, leading to substantially better quality solutions to many challenging Maximum Satisfiability (MaxSAT) instances than what the current best exact or heuristic methods yield, and it often achieves this within seconds. This hybrid approach is naturally best suited to MaxSAT instances for which proving unsatisfiability is already hard; otherwise the method falls back to pure local search. 1

Abstract. The optimization of algorithm performance by automatically identifying good parameter settings is an important problem that has recently attracted much attention in the discrete optimization community. One promising approach constructs predictive performance models and uses them to focus attention on promising regions of a design space. Such methods have become quite sophisticated and have achieved significant successes on other problems, particularly in experimental design applications. However, they have typically been designed to achieve good performance only under a budget expressed as a number of function evaluations (e.g., target algorithm runs). In this work, we show how to extend the Sequential Parameter Optimization framework [SPO; see 5] to operate effectively under time bounds. Our methods take into account both the varying amount of time required for different algorithm runs and the complexity of model building and evaluation; they are particularly useful for minimizing target algorithm runtime. Specifically, we introduce a novel intensification mechanism, and show how to reduce the overhead incurred by constructing and using models. Overall, we show that our method represents a new state of the art in model-based optimization of algorithms with continuous parameters on single problem instances. 1