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42
A New Method for Solving Hard Satisfiability Problems
 AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
Abstract

Cited by 734 (21 self)
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We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, Nqueens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a modelfinding procedure. Its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theoremproving problems as modelfinding tasks.
Local Search Strategies for Satisfiability Testing
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1995
"... It has recently been shown that local search is surprisingly good at finding satisfying assignments for certain classes of CNF formulas [24]. In this paper we demonstrate that the power of local search for satisfiability testing can be further enhanced by employinga new strategy, called "mixed ..."
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Cited by 313 (27 self)
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It has recently been shown that local search is surprisingly good at finding satisfying assignments for certain classes of CNF formulas [24]. In this paper we demonstrate that the power of local search for satisfiability testing can be further enhanced by employinga new strategy, called "mixed random walk", for escaping from local minima. We present experimental results showing how this strategy allows us to handle formulas that are substantially larger than those that can be solved with basic local search. We also present a detailed comparison of our random walk strategy with simulated annealing. Our results show that mixed random walk is the superior strategy on several classes of computationally difficult problem instances. Finally, we present results demonstrating the effectiveness of local search with walk for solving circuit synthesis and diagnosis problems.
DomainIndependent Extensions to GSAT: Solving Large Structured Satisfiability Problems
 PROC. IJCAI93
, 1993
"... GSAT is a randomized local search procedure for solving propositional satisfiability problems (Selman et al. 1992). GSAT can solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam proc ..."
Abstract

Cited by 231 (10 self)
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GSAT is a randomized local search procedure for solving propositional satisfiability problems (Selman et al. 1992). GSAT can solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the DavisPutnam procedure. GSAT also efficiently solves encodings of graph coloring problems, Nqueens, and Boolean induction. However, GSAT does not perform as well on handcrafted encodings of blocksworld planning problems and formulas with a high degree of asymmetry. We present three strategies that dramatically improve GSAT's performance on such formulas. These strategies, in effect, manage to uncover hidden structure in the formula under considerations, thereby significantly extending the applicability of the GSAT algorithm.
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 144 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Local search algorithms for SAT: An empirical evaluation
 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 ..."
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Cited by 72 (18 self)
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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 wellknown 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 SATencoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithmdependent and problemdependent 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 bestperforming algorithms and shows how this can be overcome.
UnitWalk: A new SAT solver that uses local search guided by unit clause elimination
, 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. ..."
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Cited by 69 (1 self)
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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.
A Discrete LagrangianBased GlobalSearch Method for Solving Satisfiability Problems
 Journal of Global Optimization
, 1998
"... Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a n ..."
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Cited by 66 (7 self)
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Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrangemultiplierbased globalsearch method for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Instead of restarting from a new starting point when a search reaches a local trap, the Lagrange multipliers in our method provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. One of the major advantages of our method is that it has very few algorithmic parameters to be tuned by users, and the se...
Iterated Robust Tabu Search for MAXSAT
 In Proc. of the 16th Conf. of the Canadian Society for Computational Studies of Intelligence
, 2003
"... MAXSAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for M ..."
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Cited by 25 (6 self)
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MAXSAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAXSAT that combines Iterated Local Search and Tabu Search, two wellknown SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current stateoftheart MAXSAT algorithms on various widely studied classes of unweighted and weighted MAXSAT instances, particularly for Random3SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAXSAT instances.
A Minsat approach for learning in logic domains
 INFORMS Journal on computing
, 2002
"... This paper describes a method for learning logic relationships that correctlyclassifya given data set. The method derives from given logic data certain minimum cost satisfiabilityproblems, solves these problems, and deduces from the solutions the desired logic relationships. Uses of the method inclu ..."
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Cited by 21 (16 self)
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This paper describes a method for learning logic relationships that correctlyclassifya given data set. The method derives from given logic data certain minimum cost satisfiabilityproblems, solves these problems, and deduces from the solutions the desired logic relationships. Uses of the method include data mining, learning logic in expert systems, and identification of critical characteristics for recognition systems. Computational tests have proved that the method is fast and effective.
TraceBased Methods for Solving Nonlinear Global Optimization and Satisfiability Problems
 J. of Global Optimization
, 1996
"... . In this paper we present a method called NOVEL (Nonlinear Optimization via External Lead) for solving continuous and discrete global optimization problems. NOVEL addresses the balance between global search and local search, using a trace to aid in identifying promising regions before committing to ..."
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Cited by 19 (5 self)
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. In this paper we present a method called NOVEL (Nonlinear Optimization via External Lead) for solving continuous and discrete global optimization problems. NOVEL addresses the balance between global search and local search, using a trace to aid in identifying promising regions before committing to local searches. We discuss NOVEL for solving continuous constrained optimization problems and show how it can be extended to solve constrained satisfaction and discrete satisfiability problems. We first transform the problem using Lagrange multipliers into an unconstrained version. Since a stable solution in a Lagrangian formulation only guarantees a local optimum satisfying the constraints, we propose a global search phase in which an aperiodic and bounded trace function is added to the search to first identify promising regions for local search. The trace generates an informationbearing trajectory from which good starting points are identified for further local searches. Taking only a sm...