## Simulated Annealing for Hard Satisfiability Problems (1993)

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Venue: | In, Workshop |

Citations: | 43 - 0 self |

### BibTeX

@INPROCEEDINGS{Spears93simulatedannealing,

author = {William M. Spears},

title = {Simulated Annealing for Hard Satisfiability Problems},

booktitle = {In, Workshop},

year = {1993},

pages = {533--558},

publisher = {American Mathematical Society}

}

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### Abstract

Satisfiability (SAT) refers to the task of finding a truth assignment that makes an arbitrary boolean expression true. This paper compares a simulated annealing algorithm (SASAT) with GSAT (Selman et al., 1992), a greedy algorithm for solving satisfiability problems. GSAT can solve problem instances that are extremely difficult for traditional satisfiability algorithms. Results suggest that SASAT scales up better as the number of variables increases, solving at least as many hard SAT problems with less effort. The paper then presents an ablation study that helps to explain the relative advantage of SASAT over GSAT. Next, an improvement to the basic SASAT algorithm is examined, based on a random walk implemented in GSAT (Selman et al., 1993). Finally, we examine the performance of SASAT on a test suite of satisfiability problems produced by the 1993 DIMACS challenge. 1 Introduction Satisfiability (SAT) refers to the task of finding a truth assignment that makes an arbitrary boolean exp...

### Citations

270 | Local Search Strategies for Satisfiability Testing
- Selman, Kautz, et al.
- 1996
(Show Context)
Citation Context ...). 4 A Modification to SASAT As stated above, comparisons of SASAT with GSAT are difficult to make. Selman also has reported comparisons of GSAT with simulated annealing. The results have been mixed (=-=Selman and Kautz, 1993-=-a; Selman et al. 1993). Given the difficulty of making a comparison it is reasonable to wonder if SASAT is really doing better than GSAT, and if so, why? To help answer these questions we modified SAS... |

215 | Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...fication to SASAT As stated above, comparisons of SASAT with GSAT are difficult to make. Selman also has reported comparisons of GSAT with simulated annealing. The results have been mixed (Selman and =-=Kautz, 1993-=-a; Selman et al. 1993). Given the difficulty of making a comparison it is reasonable to wonder if SASAT is really doing better than GSAT, and if so, why? To help answer these questions we modified SAS... |

103 |
Efficient local search for very large-scale satisfiability problems
- Gu
- 1992
(Show Context)
Citation Context ... difficult for the traditional algorithms. Other recent work has also concentrated on sound but incomplete algorithms for satisfiability (De Jong and Spears, 1989; Spears, 1990; Young and Reel, 1990; =-=Gu, 1992-=-). However, comparisons between the algorithms have been difficult to perform, due to a lack of agreement on what constitutes a reasonable test set of problems. One nice feature of the Selman et al. (... |

99 | An empirical study of greedy local search for satisfiability testing
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...fication to SASAT As stated above, comparisons of SASAT with GSAT are difficult to make. Selman also has reported comparisons of GSAT with simulated annealing. The results have been mixed (Selman and =-=Kautz, 1993-=-a; Selman et al. 1993). Given the difficulty of making a comparison it is reasonable to wonder if SASAT is really doing better than GSAT, and if so, why? To help answer these questions we modified SAS... |

15 | Using Neural Networks and Genetic Algorithms as Heuristics for NP-Complete Problems
- Spears
- 1990
(Show Context)
Citation Context ...en solve problems that are extremely difficult for the traditional algorithms. Other recent work has also concentrated on sound but incomplete algorithms for satisfiability (De Jong and Spears, 1989; =-=Spears, 1990-=-; Young and Reel, 1990; Gu, 1992). However, comparisons between the algorithms have been difficult to perform, due to a lack of agreement on what constitutes a reasonable test set of problems. One nic... |

13 | A New Method for Solving Hard Satisfiability - Selman, Levesque, et al. - 1992 |

9 | Using Genetic Algorithms to Solve NP Complete - Jong, Spears - 1989 |

9 | Hard and Easy - Mitchell, Selman, et al. - 1992 |

2 | A NN Algorithm for Hard Satisfiability problems
- Spears
- 1993
(Show Context)
Citation Context ... when the temperature is low SASAT is similar to GSAT. The annealing schedule is calculated using: −j temperature = MAX_TEMP * e * decay_rate We used our experience with the neural network algorithm (=-=Spears, 1993-=-) to roughly estimate the temperature parameters. We set MAX_TEMP to 0.3, MIN_TEMP to 0.01, and the decay rate to be: _____ 1 decay_rate = i * V where V is the number of variables and i is a loop vari... |

1 |
Optimal Mutation Rates
- Baeck
- 1993
(Show Context)
Citation Context ...of this algorithm depends greatly on the value chosen for p. Results from the genetic algorithm community suggest that such perturbations should occur roughly once for each pass over the V variables (=-=Baeck, 1993-=-). Drawing on these results, and some preliminary empirical experiments, we set p to 1 / V and reran SASAT. Table 11 presents the results. __ __________________________________________________________... |

1 |
A NN Algorithm for Hard Satisfiability problems, Arti ficial Intelligence Center
- Spears
- 1993
(Show Context)
Citation Context ... However, a good heuristic is to reduce the decay rate before making another attempt, in order to perform more flips during the next attempt. We used our experience with the neural network algorithm (=-=Spears, 1993-=-) to set the decay rate to be: decay_rate = i * V 1 _____ where V is the number of variables. Thus, each time i is incremented the decay rate decreases. Also, the decay rate is dependent on the number... |

1 | Probabilistic Satisfiability - Spears - 1992 |