SATLIB is an online resource for SAT-related research established in June 1998. Its core components, a benchmark suite of SAT instances and a collection of SAT solvers, aim to facilitate empirical research on SAT by providing a uniform test-bed for SAT solvers along with freely available implementations of high-performing SAT algorithms. In this article, we give an overview of SATLIB; in particular, we describe its current set of benchmark problems. Currently, the main SATLIB web site

Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly well-known families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SAT-encoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithm-dependent and problem-dependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the best-performing algorithms and shows how this can be overcome.

Stochastic local search algorithms based on the WalkSAT architecture are among the best known methods for solving hard and large instances of the propositional satisfiability problem (SAT). The performance and behaviour of these algorithms critically depends on the setting of the noise parameter, which controls the greediness of the search process. The optimal setting for the noise parameter varies considerably between different types and sizes of problem instances; consequently, considerable manual tuning is typically required to obtain peak performance. In this paper, we characterise the impact of the noise setting on the behaviour of WalkSAT and introduce a simple adaptive noise mechanism for WalkSAT that does not require manual adjustment for different problem instances. We present experimental results indicating that by using this selftuning noise mechanism, various WalkSAT variants (including WalkSAT/SKC and Novelty ) achieve performance levels close to their peak performance for instance-specific, manually tuned noise settings.

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.

The university course timetabling problem is an optimisation problem in which a set of events has to be scheduled in timeslots and located in suitable rooms. Recently, a set of benchmark instances was introduced and used for an ‘International Timetabling Competition’ to which 24 algorithms were submitted by various research groups active in the field of timetabling. We describe and analyse a hybrid metaheuristic algorithm which was developed under the very same rules and deadlines imposed by the competition and outperformed the official winner. It combines various construction heuristics, tabu search, variable neighbourhood descent and simulated annealing. Due to the complexity of developing hybrid metaheuristics, we strongly relied on an experimental methodology for configuring the algorithms as well as for choosing proper parameter settings. In particular, we used racing procedures that allow an automatic or semi-automatic configuration of algorithms with a good save in time. Our successful example shows that the systematic design of hybrid algorithms through an experimental methodology leads to high performing algorithms for hard combinatorial optimisation problems.

Is it possible to predict how long an algorithm will take to solve a previously-unseen instance of an NP-complete problem? If so, what uses can be found for models that make such predictions? This paper provides answers to these questions and evaluates the answers experimentally. We propose the use of supervised machine learning to build models that predict an algorithm’s runtime given a problem instance. We discuss the construction of these models and describe techniques for interpreting them to gain understanding of the characteristics that cause instances to be hard or easy. We also present two applications of our models: building algorithm portfolios that outperform their constituent algorithms, and generating test distributions that emphasize hard problems. We demonstrate the effectiveness of our techniques in a case study of the combinatorial auction winner determination problem. Our experimental results show that we can build very accurate models of an algorithm’s running time, interpret our models, build an algorithm portfolio that strongly outperforms the best single algorithm, and tune a standard benchmark suite to generate much harder problem instances.

Abstract. Parallel implementationsof metaheuristicsappear quite naturally asan effective alternative to speed up the search for approximate solutions of combinatorial optimization problems. They not only allow solving larger problems or finding improved solutions with respect to their sequential counterparts, but they also lead to more robust algorithms. We review some trends in parallel computing and report recent results about linear speedups that can be obtained with parallel implementations using multiple independent processors. Parallel implementations of tabu search, GRASP, genetic algorithms, simulated annealing, and ant colonies are reviewed and discussed to illustrate the main strategies used in the parallelization of different metaheuristics and their hybrids. 1. Introduction. Although

We introduce the dynamic SAT problem, a generalisation of the satisfiability problem in propositional logic which allows changes of a problem over time. DynSAT can be seen as a particular form of a dynamic CSP, but considering results and recent success in solving conventional SAT problems, we believe that the conceptual simplicity of SAT will allow us to more easily devise and investigate high-performing algorithms for DynSAT than for dynamic CSPs. In this article, we motivate the DynSAT problem, discuss various formalisations of it, and investigate stochastic local search (SLS) algorithms for solving it. In particular, we apply SLS algorithms which perform well on conventional SAT problems to dynamic problems and we analyse and characterise their performance empirically; this initial investigation indicates that the performance differences between various algorithms of the well-known WalkSAT family of SAT algorithms generally carry over when applied to DynSAT. We also study different generic approaches of solving DynSAT problems using SLS algorithms and investigate their performance differences when applied to different types of DynSAT problems.

Abstract. Graph coloring is a well known problem from graph theory that, when attacldng it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k one has to find a feasible coloring: once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local Search on the graph coloring problem. Iterated Local Search is a simple and powerful metaheuristic that has shown very good results for a variety of optimization problems. In our research we investigated several perturbation schemes and present computational results on a widely used set of benchmarks problems, a sub-set of those available from the DIMACS benchmark suite. Our results suggest that Iterated Local Search is particularly promising on hard, structured graphs.

Stochastic Local Search (SLS) algorithms are amongst the most effective approaches for solving hard and large propositional satisfiability (SAT) problems. Prominent and successful SLS algorithms for SAT, including many members of the WalkSAT and GSAT families of algorithms, tend to show highly regular behaviour when applied to hard SAT instances: The run-time distributions (RTDs) of these algorithms are closely approximated by exponential distributions.