Results 1 - 10 of 89

Solving Combinatorial Auctions using Stochastic Local Search

by Holger H. Hoos, Craig Boutilier , 2000
"... Combinatorial auctions (CAs) have emerged as an important model in economics and show promise as a useful tool for tackling resource allocation in AI. Unfortunately, winner determination for CAs is NP-hard and recent algorithms have difficulty with problems involving goods and bids beyond the hundre ..."
Abstract - Cited by 106 (2 self) - Add to MetaCart
Combinatorial auctions (CAs) have emerged as an important model in economics and show promise as a useful tool for tackling resource allocation in AI. Unfortunately, winner determination for CAs is NP-hard and recent algorithms have difficulty with problems involving goods and bids beyond the hundreds. We apply a new stochastic local search algorithm, Casanova, to this problem, and demonstrate that it finds high quality (even optimal) solutions much faster than recently proposed methods (up to several orders of magnitude), particularly for large problems. We also propose a logical language for naturally expressing combinatorial bids in which a single logical bid corresponds to a large (often exponential) number of explicit bids. We show that Casanova performs much better than systematic methods on such problems.

Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT

by Frank Hutter, Dave A. D. Tompkins, Holger H. Hoos , 2002
"... In this paper, we study the approach of dynamic local search for the SAT problem. We focus on the recent and promising Exponentiated Sub-Gradient (ESG) algorithm, and examine the factors determining the time complexity of its search steps. Based on the insights gained from our analysis, we developed ..."
Abstract - Cited by 94 (21 self) - Add to MetaCart
In this paper, we study the approach of dynamic local search for the SAT problem. We focus on the recent and promising Exponentiated Sub-Gradient (ESG) algorithm, and examine the factors determining the time complexity of its search steps. Based on the insights gained from our analysis, we developed Scaling and Probabilistic Smoothing (SAPS), an efficient SAT algorithm that is conceptually closely related to ESG. We also introduce a reactive version of SAPS (RSAPS) that adaptively tunes one of the algorithm's important parameters. We show that for a broad range of standard benchmark problems for SAT, SAPS and RSAPS achieve significantly better performance than both ESG and the state-of-the-art WalkSAT variant, Novelty.
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SATLIB: An Online Resource for Research on SAT

by Holger H. Hoos, Thomas Stützle , 2000
"... 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 implementat ..."
Abstract - Cited by 92 (5 self) - Add to MetaCart
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

An Adaptive Noise Mechanism for WalkSAT

by Holger Hoos , 2002
"... 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 ..."
Abstract - Cited by 75 (13 self) - Add to MetaCart
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.
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Local search algorithms for SAT: An empirical evaluation

by Holger H. Hoos, Thomas Stützle - JOURNAL OF AUTOMATED REASONING , 2000
"... 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 num ..."
Abstract - Cited by 69 (18 self) - Add to MetaCart
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.

UnitWalk: A new SAT solver that uses local search guided by unit clause elimination

by Edward A. Hirsch, Arist Kojevnikov , 2002
"... In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification. ..."
Abstract - Cited by 69 (1 self) - Add to MetaCart
In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification.

UBCSAT: An implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT

by Dave A. D. Tompkins, Holger H. Hoos - In SAT , 2004
"... Abstract. In this paper we introduce UBCSAT, a new implementation and experimentation environment for Stochastic Local Search (SLS) algorithms for SAT and MAX-SAT. Based on a novel triggered procedure architecture, UBCSAT provides implementations of numerous well-known and widely used SLS algorithms ..."
Abstract - Cited by 64 (15 self) - Add to MetaCart
Abstract. In this paper we introduce UBCSAT, a new implementation and experimentation environment for Stochastic Local Search (SLS) algorithms for SAT and MAX-SAT. Based on a novel triggered procedure architecture, UBCSAT provides implementations of numerous well-known and widely used SLS algorithms for SAT and MAX-SAT, including GSAT, WalkSAT, and SAPS; these implementations generally match or exceed the efficiency of the respective original reference implementations. Through numerous reporting and statistical features, including the measurement of run-time distributions, UBCSAT facilitates the advanced empirical analysis of these algorithms. New algorithm variants, SLS algorithms, and reporting features can be added to UBCSAT in a straightforward and efficient way. UBCSAT is implemented in C and runs on numerous platforms and operating systems; it is publicly and freely available at
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Performance prediction and automated tuning of randomized and parametric algorithms: An initial investigation

by Frank Hutter, Youssef Hamadi, et al. , 2006
"... Machine learning can be utilized to build models that predict the run-time of search algorithms for hard combinatorial problems. Such empirical hardness models have previously been studied for complete, deterministic search algorithms. In this work, we demonstrate that such models can also make surp ..."
Abstract - Cited by 61 (23 self) - Add to MetaCart
Machine learning can be utilized to build models that predict the run-time of search algorithms for hard combinatorial problems. Such empirical hardness models have previously been studied for complete, deterministic search algorithms. In this work, we demonstrate that such models can also make surprisingly accurate run-time predictions for incomplete, randomized search methods, such as stochastic local search algorithms. We also show for the first time how information about an algorithm’s parameter settings can be incorporated into a model, and how such models can be used to automatically adjust the algorithm’s parameters on a perinstance basis in order to optimize its performance. Empirical results for Novelty + and SAPS on random and structured SAT instances show good predictive performance and significant speedups using our automatically determined parameter settings when compared to the default and best fixed parameter settings.
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Towards a characterisation of the behaviour of stochastic local search algorithms for SAT

by Holger H. Hoos, Thomas Stützle - ARTIFICIAL INTELLIGENCE , 1999
"... Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the run-time behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the run-time distribution provi ..."
Abstract - Cited by 55 (16 self) - Add to MetaCart
Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the run-time behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the run-time distribution provides important information about the behaviour of SLS algorithms. In this paper we investigate the empirical run-time distributions for Walksat, one of the most powerful SLS algorithms for the Propositional Satisfiability Problem (SAT). Using statistical analysis techniques, we show that on hard Random-3-SAT problems, Walksat's run-time behaviour can be characterised by exponential distributions. This characterisation can be generalised to various SLS algorithms for SAT and to encoded problems from other domains. This result also has a number of consequences which are of theoretical as well as practical interest. One of these is the fact that these algorithms can be easily parallelised such that optimal speed-up is achieved for hard problem instances.

Satisfiability Solvers

by Carla P. Gomes, Henry Kautz, Ashish Sabharwal, Bart Selman , 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
Abstract - Cited by 50 (0 self) - Add to MetaCart
The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,