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413
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 683 (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.
Planning as satisfiability
 IN ECAI92
, 1992
"... We develop a formal model of planning based on satisfiability rather than deduction. The satis ability approach not only provides a more flexible framework for stating di erent kinds of constraints on plans, but also more accurately reflects the theory behind modern constraintbased planning systems ..."
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Cited by 431 (26 self)
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We develop a formal model of planning based on satisfiability rather than deduction. The satis ability approach not only provides a more flexible framework for stating di erent kinds of constraints on plans, but also more accurately reflects the theory behind modern constraintbased planning systems. Finally, we consider the computational characteristics of the resulting formulas, by solving them with two very different satisfiability testing procedures.
Minimizing Conflicts: A Heuristic Repair Method for ConstraintSatisfaction and Scheduling Problems
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 1993
"... This paper describes a simple heuristic approach to solving largescale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a valueorder ..."
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Cited by 398 (6 self)
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This paper describes a simple heuristic approach to solving largescale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a valueordering heuristic, the minconflicts heuristic, that attempts to minimize the number of constraint violations after each step. The heuristic can be used with a variety of different search strategies. We demonstrate empirically that on the nqueens problem, a technique based on this approach performs orders of magnitude better than traditional backtracking techniques. We also describe a scheduling application where the approach has been used successfully. A theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective.
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 rando ..."
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Cited by 270 (25 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.
The Markov Chain Monte Carlo method: an approach to approximate counting and integration
, 1996
"... In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends crucially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stocha ..."
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Cited by 234 (13 self)
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In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends crucially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stochastic processes hardly touches on the sort of nonasymptotic analysis required in this application. As a consequence, it had previously not been possible to make useful, mathematically rigorous statements about the quality of the estimates obtained. Within the last ten years, analytical tools have been devised with the aim of correcting this deficiency. As well as permitting the analysis of Monte Carlo algorithms for classical problems in statistical physics, the introduction of these tools has spurred the development of new approximation algorithms for a wider class of problems in combinatorial enumeration and optimization. The “Markov chain Monte Carlo ” method has been applied to a variety of such problems, and often provides the only known efficient (i.e., polynomial time) solution technique.
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 216 (12 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.
Evidence for Invariants in Local Search
 IN PROCEEDINGS OF AAAI97
, 1997
"... It is well known that the performance of a stochastic local search procedure depends upon the setting of its noise parameter, and that the optimal setting varies with the problem distribution. It is therefore desirable to develop general priniciples for tuning the procedures. We present two statisti ..."
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Cited by 183 (11 self)
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It is well known that the performance of a stochastic local search procedure depends upon the setting of its noise parameter, and that the optimal setting varies with the problem distribution. It is therefore desirable to develop general priniciples for tuning the procedures. We present two statistical measures of the local search process that allow one to quickly find the optimal noise settings. These properties are independent of the fine details of the local search strategies, and appear to be relatively independent of the structure of the problem domains. We applied these principles to the problem of evaluating new search heuristics, and discovered two promising new strategies.
Drawing Graphs Nicely Using Simulated Annealing
, 1996
"... The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general graphs with straighline edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the crite ..."
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Cited by 174 (11 self)
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The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general graphs with straighline edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the "spring method" and its variants.
Simulated annealing: Practice versus theory
 Mathl. Comput. Modelling
, 1993
"... this paper "ergodic" is used in a very weak sense, as it is not proposed, theoretically or practically, that all states of the system are actually to be visited ..."
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Cited by 156 (20 self)
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this paper "ergodic" is used in a very weak sense, as it is not proposed, theoretically or practically, that all states of the system are actually to be visited