## Guided local search for solving SAT and weighted MAX-SAT problems (2000)

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Venue: | Journal of Automated Reasoning |

Citations: | 33 - 7 self |

### BibTeX

@INPROCEEDINGS{Mills00guidedlocal,

author = {Patrick Mills and Edward Tsang},

title = {Guided local search for solving SAT and weighted MAX-SAT problems},

booktitle = {Journal of Automated Reasoning},

year = {2000},

pages = {89--106},

publisher = {IOS Press}

}

### Years of Citing Articles

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### Abstract

Abstract. In this paper, we show how Guided Local Search (GLS) can be applied to the SAT problem and show how the resulting algorithm can be naturally extended to solve the weighted MAX-SAT problem. GLS is a general, penalty-based metaheuristic, which sits on top of local search algorithms to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real life problems, such as the travelling salesman problem, BT's workforce scheduling problem, the radio link frequency assignment problem and the vehicle routing problem. We present empirical results of applying GLS to instances of the SAT problem from the DIMACS archive and also a small set of weighted MAX-SAT problem instances and compare them against the results of other local search algorithms for the SAT problem. Keywords: SAT problem, Local Search, Meta-heuristics, Optimisation 1.

### Citations

820 | Foundations of Constraint Satisfaction
- Tsang
- 1993
(Show Context)
Citation Context ...roblems, comparing the results against the results of similar local search algorithms. 2. The SAT and weighted MAX-SAT problem The SAT problem is an important class of constraint satisfaction problem =-=[39]-=-, where the domain of a variable is always f false, true g, and each constraint is a clause. The SAT problem is important in solving many practical problems in mathematical logic, constraint satisfact... |

361 | B.: Noise strategies for improving local search
- Selman, Kautz, et al.
- 1994
(Show Context)
Citation Context ...lution. Of the incomplete stochastic algorithms, the best known is probably GSAT ( rst reported in [35]), based on steepest gradient descent and the related GLSSAT.tex; 30/08/1999; 15:26; p.2sWalkSAT =-=[33]-=- based on random walk with greedy variable selection heuristics. Whilst a lot of work has been done on the basic SAT problem, only a small amount of work has been done on the weighted MAX-SAT problem ... |

360 | GSAT and dynamic backtracking - Ginsberg, McAllester - 1994 |

215 | Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...ry similar scheme called Breakout, which increases the weights of all violated constraints, every time there are no local moves available which will decrease the objective function. Selman and Kautz (=-=[32]-=-) modify GSAT to include clause weights, increasing the weights of all clauses which are unsatis ed at the end of each try (when the maximum number of ips of variable values has been exhausted and the... |

195 |
The Breakout Method for Escaping From Local Minima
- Morris
- 1993
(Show Context)
Citation Context ...tworks and the earliest such scheme we know of which has been applied to solving CSPs, where the weights of all constraints are increased each time the algorithm converges to a local minimum. Morris (=-=[27]-=-) describes a very similar scheme called Breakout, which increases the weights of all violated constraints, every time there are no local moves available which will decrease the objective function. Se... |

184 | Evidence for Invariants in Local Search - McAllester, Selman, et al. - 1997 |

136 | Towards an understanding of hill-climbing procedures for SAT
- Gent, Walsh
- 1993
(Show Context)
Citation Context ... as our basic objective function, g, given in ( 1), below. g(s) =]fci j ci is violated by the truth assignment sg (1) The local search algorithm we use is based on ideas reported by Gent and Walsh in =-=[12]-=-, who conduct extensive experiments on lots of di erent variations of the basic GSAT algorithm ([35]), and nd HSAT to be the best hill climbing algorithm to use with GSAT at that time (although other ... |

99 | An empirical study of greedy local search for satisfiability testing - Selman, Kautz - 1993 |

96 | GENET: A connectionist architecture for solving constraint satisfaction problems by iterative improvement
- Davenport, Tsang, et al.
- 1994
(Show Context)
Citation Context ...of the weighted MAX-SAT problem as GRASP with excellent results. Later, in this paper we also give results compared with GRASP and DLM for these problems. 3. Other methods related to GLS GENET ([46], =-=[5]-=-, [4]), the direct ancestor of GLS, is a Min-Con icts ([26]) based repair algorithm with a simple weight update scheme for solving constraint satisfaction problems (CSPs), inspired by neural networks ... |

81 | Ten challenges in propositional reasoning and search - Selman, Kautz, et al. - 1997 |

65 | When gravity fails: local search topology
- Frank, Cheeseman, et al.
- 1997
(Show Context)
Citation Context ...=5) g while (h(s) > 0 or termination condition) return s Figure 4. Pseudo code for GLSSAT2 wrong features, so that the search landscape becomes more and more rugged (the reader might like to refer to =-=[7]-=- for a study of the search landscape of the SAT problem) as time goes on, making it slower and slower to traverse, crippling the local search algorithm and forcing GLS to do all the work, and making i... |

60 | A discrete Lagrangian-based global-search method for solving satisfiability problems
- Shang, Wah
- 1998
(Show Context)
Citation Context ...d clauses after each ip, and later ([9]) re nes his scheme, with decaying weights, where after each ip, weights of all clauses are multiplied by a constant very close to 1.0. Recently, Shang and Wah (=-=[38]-=-) have applied DLM to the weighted MAX-SAT 3 GLSSAT.tex; 30/08/1999; 15:26; p.3s4 and SAT problem with excellent results. DLM could be seen to be quite similar to GLS, although it does not use selecti... |

58 |
A new method for solving hard satis ability problems
- Selman, Levesque, et al.
- 1992
(Show Context)
Citation Context ... the weights of violated clauses. In this paper, we show how GLS can be used to solve the SAT and weighted MAX-SAT problems, by sitting it on top of a local search algorithm, which is similar to GSAT =-=[35]-=- without restarts. We give an evaluation of GLS's performance on benchmarks from the DIMACS archive, and a set of weighted MAX-SAT problems, comparing the results against the results of similar local ... |

52 | Evaluating las vegas algorithms: Pitfalls and remedies - Hoos, Stützle - 1998 |

50 | Guided local search and its application to the travelling salesman problem
- Voudouris, Tsang
- 1998
(Show Context)
Citation Context ...heuristics, Optimisation 1. Introduction Guided Local Search [41] has been applied to a number of real life problems, including BT's workforce scheduling problem [40], the travelling salesman problem =-=[43]-=-, the vehicle routing problem [20], function optimization [42] and the radio link frequency assignment problem [44]. GLS is a meta-heuristic, which sits on top of local search procedures for helping t... |

44 | Guided local search for the vehicle routing problem
- Kilby, Prosser, et al.
- 1997
(Show Context)
Citation Context ...uction Guided Local Search [41] has been applied to a number of real life problems, including BT's workforce scheduling problem [40], the travelling salesman problem [43], the vehicle routing problem =-=[20]-=-, function optimization [42] and the radio link frequency assignment problem [44]. GLS is a meta-heuristic, which sits on top of local search procedures for helping them escape from local minima. GLS ... |

43 | Adding new clauses for faster local search
- Cha, Iwama
- 1996
(Show Context)
Citation Context ...ugmented cost function (see Equation 4, below), to allow it to guide the local search algorithm out of the local minimum, by penalising features present in that local minimum. The idea is to make (2) =-=(3)-=- GLSSAT.tex; 30/08/1999; 15:26; p.6sIf (s) = i 1 if clause Ci violated by solution s 0 otherwise cf (s) = i 1 if standard SAT problem if weighted MAX-SAT problem wC i Figure 2. Clauses as features in ... |

43 |
Guided Local Search for Combinatorial Optimisation Problems
- Voudouris
- 1997
(Show Context)
Citation Context ...ances and compare them against the results of other local search algorithms for the SAT problem. Keywords: SAT problem, Local Search, Meta-heuristics, Optimisation 1. Introduction Guided Local Search =-=[41]-=- has been applied to a number of real life problems, including BT's workforce scheduling problem [40], the travelling salesman problem [43], the vehicle routing problem [20], function optimization [42... |

42 | Solving problems with hard and soft constraints using a stochastic algorithm for MAX-SAT
- Jiang, Kautz, et al.
- 1995
(Show Context)
Citation Context ...y variable selection heuristics. Whilst a lot of work has been done on the basic SAT problem, only a small amount of work has been done on the weighted MAX-SAT problem by comparison. Examples include =-=[18]-=-, where GSAT is extended to solve instances based network steiner trees, and their results compared against non-MAX-SAT techniques for the native network steiner tree problems. Resende et al. ([29]) s... |

41 |
A Computing Procedure for Quanti cation Theory
- Davis, Putnam
- 1960
(Show Context)
Citation Context ...he sum of weights of violated clauses. Both complete and incomplete algorithms have been used to solve the SAT problem. Of the complete algorithms, one of the best known is the Davis-Putnam procedure =-=[6]-=-, which is based on resolution. Of the incomplete stochastic algorithms, the best known is probably GSAT ( rst reported in [35]), based on steepest gradient descent and the related GLSSAT.tex; 30/08/1... |

37 | Performance tests of local search algorithms using new types
- Cha, Iwama
- 1995
(Show Context)
Citation Context ...ing when to restart, based on the number of ips required to reach the current plateau, according to how many ips it took to reach the current plateau, from the initial solution. Later, Cha and Iwama (=-=[2]-=-) suggest a scheme called weight, which is the equivalent to breakout. Frank ([8]) increases the weights of violated clauses after each ip, and later ([9]) re nes his scheme, with decaying weights, wh... |

37 | Solving constraint satisfaction problems using neuralnetworks
- Wang, Tsang
- 1991
(Show Context)
Citation Context ...ances of the weighted MAX-SAT problem as GRASP with excellent results. Later, in this paper we also give results compared with GRASP and DLM for these problems. 3. Other methods related to GLS GENET (=-=[46]-=-, [5], [4]), the direct ancestor of GLS, is a Min-Con icts ([26]) based repair algorithm with a simple weight update scheme for solving constraint satisfaction problems (CSPs), inspired by neural netw... |

33 | Minimizing con icts: a heuristic repair methodfor constraint satisfaction andscheduling problems
- Minton, Johnston, et al.
- 1992
(Show Context)
Citation Context ...sults. Later, in this paper we also give results compared with GRASP and DLM for these problems. 3. Other methods related to GLS GENET ([46], [5], [4]), the direct ancestor of GLS, is a Min-Con icts (=-=[26]-=-) based repair algorithm with a simple weight update scheme for solving constraint satisfaction problems (CSPs), inspired by neural networks and the earliest such scheme we know of which has been appl... |

32 | Approximate solution of weighted MAX-SAT problems using GRASP, tech
- Resende, Pitsoulis, et al.
- 1996
(Show Context)
Citation Context ...de [18], where GSAT is extended to solve instances based network steiner trees, and their results compared against non-MAX-SAT techniques for the native network steiner tree problems. Resende et al. (=-=[29]-=-) show how GRASP can be applied to the instances of the weighted MAX-SAT problem based on soluble and insoluble instances of the jnh* problems from the DIMACS benchmarks archive with random weights as... |

31 | Discrete lagrangian-based search for solving MAX-SAT problems
- Wah, Shang
- 1997
(Show Context)
Citation Context ...ive with random weights associated with each clause. Borchers et al. ([1]) show how a branch and cut algorithm can be used to solve the MAX-SAT and weighted MAX-SAT problems. Recently, Wah and Shang (=-=[45]-=-) have shown how DLM how can be applied to the same set of instances of the weighted MAX-SAT problem as GRASP with excellent results. Later, in this paper we also give results compared with GRASP and ... |

30 | Weighting for Godot: Learning Heuristics For GSAT
- Frank
- 1996
(Show Context)
Citation Context ...teau, according to how many ips it took to reach the current plateau, from the initial solution. Later, Cha and Iwama ([2]) suggest a scheme called weight, which is the equivalent to breakout. Frank (=-=[8]-=-) increases the weights of violated clauses after each ip, and later ([9]) re nes his scheme, with decaying weights, where after each ip, weights of all clauses are multiplied by a constant very close... |

28 | A two phase algorithm for solving a class of hard satisfiability problems
- Warners, Maaren
- 1999
(Show Context)
Citation Context ...owever, we could not nd solutions to the following problems using GLSSAT1 or GLSSAT2 in the DIMACS archive within 30 minutes: Hanoi4, Hanoi5, par16-*, par32-*, par32-*-c, f2000. Warner and van Maaren =-=[47]-=-, report on a new approach to solving the parity problems, whereby they use linear programming to extract conjunctions of equivalencies from the original SAT formulation, so that they can solve a redu... |

22 | Plateaus and plateau search in Boolean satisfiability problems: When to give up searching and start again
- Hampson, Kibler
- 1993
(Show Context)
Citation Context ...satis ed at the end of each try (when the maximum number of ips of variable values has been exhausted and the algorithm is restarted from a new point in the search space) of GSAT. Hampson and Kibler (=-=[16]-=-) suggest a heuristic for deciding when to restart, based on the number of ips required to reach the current plateau, according to how many ips it took to reach the current plateau, from the initial s... |

17 | Guided Local Search { An Illustrative Example in Function Optimization
- Voudouris
- 1998
(Show Context)
Citation Context ...41] has been applied to a number of real life problems, including BT's workforce scheduling problem [40], the travelling salesman problem [43], the vehicle routing problem [20], function optimization =-=[42]-=- and the radio link frequency assignment problem [44]. GLS is a meta-heuristic, which sits on top of local search procedures for helping them escape from local minima. GLS is a generalisation of the G... |

15 | Global Search Methods for Solving Nonlinear Optimization Problems
- Shang
- 1997
(Show Context)
Citation Context ...plied to a number of problems (e.g. nonlinear integer programming problems, nonlinear mixed integer programming problems, and the design of multiplierless lter banks), as well as the SAT problem (see =-=[36]-=- and [49] for a full description), whilst the GLS framework is more general and has also been applied to a wide variety of other problems (and local search algorithms, for example in the travelling sa... |

14 | Solving the Radio Link Frequency Assignment Problem using Guided Local Search'. Frequency Assignment
- Voudouris, Tsang
- 1999
(Show Context)
Citation Context ...s, including BT's workforce scheduling problem [40], the travelling salesman problem [43], the vehicle routing problem [20], function optimization [42] and the radio link frequency assignment problem =-=[44]-=-. GLS is a meta-heuristic, which sits on top of local search procedures for helping them escape from local minima. GLS is a generalisation of the GENET neural network [4], for solving constraint satis... |

13 |
Extensions and evaluation of GENET in constraint satisfaction
- Davenport
- 1997
(Show Context)
Citation Context ...frequency assignment problem [44]. GLS is a meta-heuristic, which sits on top of local search procedures for helping them escape from local minima. GLS is a generalisation of the GENET neural network =-=[4]-=-, for solving constraint satisfaction and optimisation problems. Recently, Lau and Tsang [22, 23] have shown how GLS can be sat on top of a specialised Genetic Algorithm, resulting in the Guided Genet... |

11 |
Learning short-term clause weights for GSAT
- Frank
- 1997
(Show Context)
Citation Context ...m the initial solution. Later, Cha and Iwama ([2]) suggest a scheme called weight, which is the equivalent to breakout. Frank ([8]) increases the weights of violated clauses after each ip, and later (=-=[9]-=-) re nes his scheme, with decaying weights, where after each ip, weights of all clauses are multiplied by a constant very close to 1.0. Recently, Shang and Wah ([38]) have applied DLM to the weighted ... |

11 |
Guided Genetic Algorithm
- Lau
- 1998
(Show Context)
Citation Context ...raint satisfaction and optimisation problems. Recently, Lau and Tsang [22, 23] have shown how GLS can be sat on top of a specialised Genetic Algorithm, resulting in the Guided Genetic Algorithm (GGA, =-=[21]-=-) for solving constraint satisfaction and optimisation problems. They apply GGA to a number of problems including the processor con guration problem [23] and the generalised assignment problem [22]. I... |

11 | Non-systematic search and learning: An empirical study - Richards, Richards - 1998 |

8 |
A branch-and-cut algorithm for MAX-SAT and weighted MAX-SAT
- Joy, Mitchell, et al.
- 1997
(Show Context)
Citation Context ...nces of the weighted MAX-SAT problem based on soluble and insoluble instances of the jnh* problems from the DIMACS benchmarks archive with random weights associated with each clause. Borchers et al. (=-=[1]-=-) show how a branch and cut algorithm can be used to solve the MAX-SAT and weighted MAX-SAT problems. Recently, Wah and Shang ([45]) have shown how DLM how can be applied to the same set of instances ... |

8 |
Local search for satis ability (SAT) problem
- Gu
- 1993
(Show Context)
Citation Context ...successfully applied to the SAT problem and weighted MAXSAT problem. The SAT problem is an important problem in mathematical logic, inference, machine learning, VLSI engineering, and computing theory =-=[14]-=-, and has been the focus of a lot of successful research into local search algorithms. The SAT problem is a special case of a constraint c 1999 Kluwer Academic Publishers. Printed in the Netherlands. ... |

8 | Exploiting variable dependency - Kautz, McAllester, et al. - 1997 |

7 | The discrete Lagrangian theory and its application to solve nonlinear discrete constrained optimization problems
- Wu
- 1998
(Show Context)
Citation Context ...a number of problems (e.g. nonlinear integer programming problems, nonlinear mixed integer programming problems, and the design of multiplierless lter banks), as well as the SAT problem (see [36] and =-=[49]-=- for a full description), whilst the GLS framework is more general and has also been applied to a wide variety of other problems (and local search algorithms, for example in the travelling saleman pro... |

6 | Global optimization for satis ability (SAT) problem - Gu - 1994 |

4 |
Solving the generalized assignment problem with the guided genetic algorithm
- Lau, Tsang
- 1998
(Show Context)
Citation Context ...h procedures for helping them escape from local minima. GLS is a generalisation of the GENET neural network [4], for solving constraint satisfaction and optimisation problems. Recently, Lau and Tsang =-=[22, 23]-=- have shown how GLS can be sat on top of a specialised Genetic Algorithm, resulting in the Guided Genetic Algorithm (GGA, [21]) for solving constraint satisfaction and optimisation problems. They appl... |

4 | Improving the Performance of Discrete LagrangeMultiplier Search for Solving Hard SAT Problems - Shang, Wah - 1998 |

3 | Unsatis ed variables in local search - Gent, Walsh - 1995 |

3 |
Guided Genetic algorithm and its application to the large processor configuration problem
- Lau, Tsang
- 1998
(Show Context)
Citation Context ...h procedures for helping them escape from local minima. GLS is a generalisation of the GENET neural network [4], for solving constraint satisfaction and optimisation problems. Recently, Lau and Tsang =-=[22, 23]-=- have shown how GLS can be sat on top of a specialised Genetic Algorithm, resulting in the Guided Genetic Algorithm (GGA, [21]) for solving constraint satisfaction and optimisation problems. They appl... |

2 | Computers and intractibility', W.H.Freeman and Company - Garey, Johnson - 1979 |

2 | Look-ahead versus look-back for satis ability problems - Li, Anbulagan - 1997 |

1 | A GRASP for Satis ability In "Cliques, Coloring, and Satis ability: Second DIMACS Implementation Challenge - Resende, Feo - 1996 |

1 |
Voudouris C.: 1997 Fast local search and guided local search and their application to British Telecom's workforce scheduling problem
- Tsang
- 1997
(Show Context)
Citation Context ...ords: SAT problem, Local Search, Meta-heuristics, Optimisation 1. Introduction Guided Local Search [41] has been applied to a number of real life problems, including BT's workforce scheduling problem =-=[40]-=-, the travelling salesman problem [43], the vehicle routing problem [20], function optimization [42] and the radio link frequency assignment problem [44]. GLS is a meta-heuristic, which sits on top of... |

1 | Satis ability problems with balanced polynomial representation - Warners, Maaren - 1997 |