## Tuning Local Search for Satisfiability Testing (1996)

Venue: | In Proceedings of AAAI-96 |

Citations: | 42 - 6 self |

### BibTeX

@INPROCEEDINGS{Parkes96tuninglocal,

author = {Andrew J. Parkes and Joachim P. Walser},

title = {Tuning Local Search for Satisfiability Testing},

booktitle = {In Proceedings of AAAI-96},

year = {1996},

pages = {356--362},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Local search algorithms, particularly Gsat and Wsat, have attracted considerable recent attention, primarily because they are the best known approaches to several hard classes of satisfiability problems. However, replicating reported results has been difficult because the setting of certain key parameters is something of an art, and because details of the algorithms, not discussed in the published papers, can have a large impact on performance. In this paper we present an efficient probabilistic method for finding the optimal setting for a critical local search parameter, Maxflips, and discuss important details of two differing versions of Wsat. We then apply the optimization method to study performance of Wsat on satisfiable instances of Random 3SAT at the crossover point and present extensive experimental results over a wide range of problem sizes. We find that the results are well described by having the optimal value of Maxflips scale as a simple power of the number of variables, ...

### Citations

698 | A New Method for Solving Hard Satisfiability Problems - Selman, Levesque, et al. - 1996 |

603 | Where the really hard problems are - Cheeseman, Kanefsky, et al. - 1991 |

374 | Noise strategies for improving local search - Selman, Kautz, et al. - 1994 |

224 | and easy distributions of sat problems - Mitchell, Selman, et al. - 1992 |

140 | Experimental results on the crossover point in Random 3SAT
- Crawford, Auton
- 1996
(Show Context)
Citation Context ...e present the results of experiments to study the performance of the two versions of Wsat on Random 3SAT at the crossover point (Cheeseman, Kanefsky, & Taylor 1991; Mitchell, Selman, & Levesque 1992; =-=Crawford & Auton 1996-=-). By making extensive use of rpv, and fast multi-processor machines, we are able to give results up to 400 variables. We find that the optimal Maxflips setting scales as a simple monomial, and the me... |

138 | Towards an understanding of hill-climbing procedures for SAT
- Gent, Walsh
- 1993
(Show Context)
Citation Context ...can be used to ensure termination (though in our experiments we always set it to infinity). We also assume that the new assignments are all chosen randomly, though other methods have been considered (=-=Gent & Walsh 1993). Two Wsa-=-t Procedures In our experiments, we used two variants of the Wsat -- "walk" satisfiability class of local search procedures. This class was introduced by Selman et. al. (Selman, Kautz, & Coh... |

123 | Optimal Speedup of Las Vegas Algorithms - Luby, Sinclair, et al. - 1993 |

104 |
Efficient local search for very large-scale satisfiability problems
- Gu
- 1992
(Show Context)
Citation Context ...ge n = 25; : : : ; 400. INTRODUCTION In recent years, a variety of local search routines have been proposed for (Boolean) satisfiability testing. It has been shown (Selman, Levesque, & Mitchell 1992; =-=Gu 1992-=-; Selman, Kautz, & Cohen 1994) that local search can solve a variety of realistic and randomly generated satisfiability problems much larger than conventional procedures such as Davis-Putnam. The char... |

101 | An empirical study of greedy local search for satisfiability testing
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...ution of the runtimes. These results, however, are not directly applicable to average runtimes for a collection of instances. Local Search procedures also have close relations to simulated annealing (=-=Selman & Kautz 1993-=-). Indeed, combinations of simulated annealing with Gsat have been tried for hard SAT problems (Spears 1995). We can even look upon the restart as being a short period of very high temperature that wi... |

45 | Unsatisfied variables in local search
- Gent, Walsh
- 1995
(Show Context)
Citation Context ...s for Wsat/G also indicate a very similar scaling of n 2:36 . For comparison Hsat, a nonrandomizedsGsat variant that incorporates a history mechanism, has been observed to have a m scaling of n 1:65 (=-=Gent & Walsh 1995-=-). Scaling of Performance In Figure 5 we plot the variation of Em with n. We can see that the scaling is not as fast as a simple exponential in n, however the upward curve of the corresponding log-log... |

45 | Simulated annealing for hard satisfiability problems
- Spears
- 1995
(Show Context)
Citation Context ...instances. Local Search procedures also have close relations to simulated annealing (Selman & Kautz 1993). Indeed, combinations of simulated annealing with Gsat have been tried for hard SAT problems (=-=Spears 1995-=-). We can even look upon the restart as being a short period of very high temperature that will drive the variable assignment to a random value. In this case we find it interesting that work in simula... |

7 |
On the greedy algorithm for satisfiability. Information Processing Letters
- Koutsoupias, Papadimitriou
- 1992
(Show Context)
Citation Context ...nted) indicates that it is also worse than a simple monomial. Unfortunately, we know of no theoretical scaling result that could be reasonably compared with this data. For example, results are known (=-=Koutsoupias & Papadimitriou 1992-=-) when the number of clauses is \Omega\Gamma n 2 ), but they do not apply because the crossover is at O(n). Hence we approached the scaling from a purely empirical perspective, by trying to fit functi... |

4 |
Solving large-scale constraint satisfcation and scheduling problems using a heuristic repair method
- Minton, Johnston, et al.
- 1990
(Show Context)
Citation Context ...dures such as Davis-Putnam. The characteristic feature of local search is that it starts on a total variable assignment and works by repeatedly changing variables that appear in violated constraints (=-=Minton et al. 1990-=-). The changes are typically made according to some hill-climbing heuristic This work has been supported by ARPA/Rome Labs under contracts F30602-93-C-0031 and F30602-95-1-0023 and by a doctoral fello... |

4 |
An empirical study of random SAT
- Mitchell
- 1993
(Show Context)
Citation Context ...ues. EXPERIMENTAL RESULTS To evaluate performance of satisfiability procedures, a class of randomized benchmark problems, Random 3SAT, has been studied extensively (Mitchell, Selman, & Levesque 1992; =-=Mitchell 1993-=-; Crawford & Auton 1996). Random 3SAT provides a ready source of hard scalable problems. Problems in random k-SAT with n variables and l clauses are generated as follows: a random subset of size k of ... |

1 |
Best-so-far vs. whereyou -are: implications for optimal finite-time annealing. Systems and Control Letters 22(1):71--8
- Boese, Kahng
- 1994
(Show Context)
Citation Context ... high temperature that will drive the variable assignment to a random value. In this case we find it interesting that work in simulated annealing also has cases in which periodic reheating is useful (=-=Boese & Kahng 1994-=-). We intend to explore these connections further. CONCLUSIONS We have tried to address the four issues in the introduction empirically. In order to allow for optimizing Maxflips, we presented retrosp... |