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Learning Evaluation Functions to Improve Optimization by Local Search
 Journal of Machine Learning Research
, 2000
"... This paper describes algorithms that learn to improve search performance on largescale optimization tasks. The main algorithm, Stage, works by learning an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited durin ..."
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Cited by 56 (0 self)
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This paper describes algorithms that learn to improve search performance on largescale optimization tasks. The main algorithm, Stage, works by learning an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited during search. The learned evaluation function is then used to bias future search trajectories toward better optima on the same problem. Another algorithm, XStage, transfers previously learned evaluation functions to new, similar optimization problems. Empirical results are provided on seven largescale optimization domains: binpacking, channel routing, Bayesian network structurefinding, radiotherapy treatment planning, cartogram design, Boolean satisfiability, and Boggle board setup.
Restart Policies with Dependence among Runs: A Dynamic Programming Approach
, 2002
"... The time required for a backtracking search procedure to solve a problem can be reduced by employing randomized restart procedures. To date, ..."
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Cited by 31 (4 self)
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The time required for a backtracking search procedure to solve a problem can be reduced by employing randomized restart procedures. To date,
Efficient 2 and 3Flip Neighborhood Search Algorithms for the MAX SAT
 Journal of Heuristics
, 1998
"... . For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, w ..."
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Cited by 9 (2 self)
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. For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we consider rip neighborhoods for r 2, and propose, for r = 2; 3, new implementations that reduce the number of candidates in the neighborhood without sacricing the solution quality. For 2ip (resp., 3ip) neighborhood, we show that its expected size is O(n + m) (resp., O(m + t 2 n)), which is usually much smaller than the original size O(n 2 ) (resp., O(n 3 )), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance. These neighborhoods are then used under the framework of tabu search etc., and compa...
AutoWalksat: A SelfTuning Implementation of Walksat
 In Electronic Notes in Discrete Mathematics (ENDM
, 2001
"... Stochastic search algorithms have proven to be very fast at solving many satisfiability problems.The nature of their search requires careful parameter tuning to maximize performance, but depending on the problem and the details of the stochastic algorithm, the correct tuning may be difficult to asce ..."
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Cited by 9 (2 self)
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Stochastic search algorithms have proven to be very fast at solving many satisfiability problems.The nature of their search requires careful parameter tuning to maximize performance, but depending on the problem and the details of the stochastic algorithm, the correct tuning may be difficult to ascertain. In this paper we introduce AutoWalksat , a general algorithm which automatically tunes any variant of the Walksat family of stochastic satisfiability solvers. We demonstrate AutoWalksat's success in tuning WalksatSKC.
An Efficient Local Search Method for Random 3Satisfiability
, 2003
"... We report on some exceptionally good results in the solution of randomly generated 3satisfiability instances using the "recordtorecord travel (RRT)" local search method. When this simple, but lessstudied algorithm is applied to random onemillion variable instances from the problem's satisfiable ..."
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Cited by 7 (4 self)
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We report on some exceptionally good results in the solution of randomly generated 3satisfiability instances using the "recordtorecord travel (RRT)" local search method. When this simple, but lessstudied algorithm is applied to random onemillion variable instances from the problem's satisfiable phase, it seems to find satisfying truth assignments almost always in linear time, with the coefficient of linearity depending on the ratio α of clauses to variables in the generated instances. RRT has a parameter for tuning "greediness". By lessening greediness, the linear time phase can be extended up to very close to the satisfiability threshold α_c. Such linear time complexity is typical for randomwalk based local search methods for small values of α. Previously, however, it has been suspected that these methods necessarily lose their time linearity far below the satisfiability threshold. The only previously introduced algorithm reported to have nearly linear time complexity also close to the satisfiability threshold is the survey propagation (SP) algorithm. However, SP is not a local search method and is more complicated to implement than RRT. Comparative experiments with the WalkSAT local search algorithm show behavior somewhat similar to RRT, but with the linear time phase not extending quite as close to the satisfiability threshold.
Analysis of the Random Walk Algorithm on Random 3CNFs
, 2002
"... We analyze the efficiency of the random walk algorithm on random 3CNF instances, and prove the first polynomial time upper bound for small clause density, less than 1.63. We complement this by proving exponential lower bounds for the running time of this algorithm on the plantedSAT distribution wi ..."
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Cited by 4 (2 self)
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We analyze the efficiency of the random walk algorithm on random 3CNF instances, and prove the first polynomial time upper bound for small clause density, less than 1.63. We complement this by proving exponential lower bounds for the running time of this algorithm on the plantedSAT distribution with large constant clause density. This is the first polynomial upper bound on the running time of a local improvement algorithm on random instances, and conforms with the empirically observed efficiency of these algorithms on random CNFs.
Analyses on the 2 and 3Flip Neighborhoods for the MAX SAT
 Journal of Combinatorial Optimization
, 1999
"... For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we cons ..."
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Cited by 4 (2 self)
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For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most eective approaches. Most of the local search algorithms are based on the 1ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we consider rip neighborhoods for r 2, and propose, for r = 2; 3, new implementations that reduce the number of candidates in the neighborhood without sacri cing the solution quality. For 2ip (resp., 3ip) neighborhood, we show that its expected size is O(n + m) (resp., O(m+ t n)), which is usually much smaller than the original size O(n ) (resp., O(n )), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance.
Unique Solution Instance Generation for the 3Satisfiability (3SAT) Problem
"... . For the 3Satisability Problem (3SAT), we propose three algorithms for generating its positive instance (and its solution) randomly. We design these algorithms so that they produce, with high probability, a unique solution 3SAT instances, i.e., a 3SAT instances with only one satisfying assignment. ..."
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Cited by 2 (0 self)
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. For the 3Satisability Problem (3SAT), we propose three algorithms for generating its positive instance (and its solution) randomly. We design these algorithms so that they produce, with high probability, a unique solution 3SAT instances, i.e., a 3SAT instances with only one satisfying assignment. For our rst algorithm, we proved theoretically that the algorithm yields a unique solution 3SAT instance with high probability if the number of clauses m is larger than (7=3)n ln n + O(n); furthermore, we also proved that (7=3)n ln n clauses are necessary. Then by modifying this algorithm, we obtain two algorithms that need only O(n) clauses to yield a unique solution 3SAT instance with high probability. Hardness against of generated instances against standard heuristics is also investigated experimentally. 1 Introduction We propose algorithms for generating random instances of the 3SAT problem and investigate statistical features and hardness of generated instances. The Satisability ...