## A New Population-Based Method for Satisfiability Problems (1994)

Venue: | Proceedings of the ECAI Workshop on Applied Genetic and other Evolutionary Algorithms |

Citations: | 15 - 3 self |

### BibTeX

@INPROCEEDINGS{Hao94anew,

author = {Jin-kao Hao and Raphaël Dorne},

title = {A New Population-Based Method for Satisfiability Problems},

booktitle = {Proceedings of the ECAI Workshop on Applied Genetic and other Evolutionary Algorithms},

year = {1994},

pages = {135--139},

publisher = {John Wiley & Sons}

}

### Years of Citing Articles

### OpenURL

### Abstract

. This paper presents the mask method (MASK), a new population-based, evolutionary search procedure for finding models for satisfiability problems (SAT). In this method, a partial truth assignment for a given boolean expression containing N variables is represented by a partially instantiated 0/1 string with N positions (called mask), with each position coding one variable. The mask method begins with a population of masks. An iteration process follows to evaluate each mask in the population using an evaluation mechanism, then to discard half of them, and finally to divide each remaining mask into two new ones by fixing a free position in the mask to 0 and 1 respectively. This process continues until all the positions in the mask have a fixed value. The method is compared with a class of genetic algorithms (GAs) on a set of SAT instances and proves to be much more efficient. 1 INTRODUCTION The satisfiability problem or SAT [5] is of great importance in Artificial Intelligence both in...

### Citations

11809 |
Computers and Intractability; A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...sk have a fixed value. The method is compared with a class of genetic algorithms (GAs) on a set of SAT instances and proves to be much more efficient. 1 INTRODUCTION The satisfiability problem or SAT =-=[5]-=- is of great importance in Artificial Intelligence both in theory and in practice. The statement of the problem is very simple. Given a well-formed boolean expression E, is there a truth assignment th... |

713 | A new method for solving hard satisfiability problems
- Selman, Levesque, et al.
- 1992
(Show Context)
Citation Context ...is explosion as late as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems ([3], [14], =-=[10]-=-, [6], [8], [13] [11]). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedure. MASK has... |

382 | Noise strategies for improving local search
- Selman, Kautz, et al.
- 1994
(Show Context)
Citation Context ...as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems ([3], [14], [10], [6], [8], [13] =-=[11]-=-). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedure. MASK has some characteristics... |

206 | Experimental results on the crossover point in satis problems
- Crawford, Auton
- 1993
(Show Context)
Citation Context ...d with the method. We are currently trying to compare our method with other incomplete methods such as GSAT [10][11] as well as efficient implementations of the Davis-Putnam procedure such as Tableau =-=[2]-=-. In order to do this, we must select a sufficiently large set of objective test examples and good comparison criteria to make comparisons really meaningful. As the first 4 The notion of importance ca... |

137 | Using genetic algorithms to solve npcomplete problems. Genetic Algorithms
- Jong, Spears
- 1989
(Show Context)
Citation Context ...to delay this explosion as late as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems (=-=[3]-=-, [14], [10], [6], [8], [13] [11]). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedu... |

105 |
Efficient local search for very largescale satisfiability problems
- Gu
- 1992
(Show Context)
Citation Context ...losion as late as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems ([3], [14], [10], =-=[6]-=-, [8], [13] [11]). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedure. MASK has some... |

83 |
Introduction to Algorithms
- Rivest, Stein
- 2001
(Show Context)
Citation Context ...is paper, we use the function Eval defined below. Let E be a succinct boolean expression 2 , V(E)=fV1 ...VN g the ordered set of all the variables in E, and S a 0/1 string of length N. Eval: E\ThetaS!=-=[0,1]-=- is then recursively defined as follows: 1. Eval(V i ,S) =0 if the ith position of S is 0 =1 if the ith position of S is 1 2. Eval(V i ,S)=1-Eval(V i ,S) 3. Eval(E1s. . .sEm,S)= Ave(Eval(E1 ,S) . . . ... |

71 | An Analysis of the Interacting Roles of Population Size and Crossover - Jong, Spears - 1991 |

45 | Simulated annealing for hard satisfiability problems
- Spears
- 1995
(Show Context)
Citation Context ...late as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems ([3], [14], [10], [6], [8], =-=[13]-=- [11]). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedure. MASK has some characteri... |

16 | Using Neural Networks and Genetic Algorithms as Heuristics for NP-Complete Problems
- Spears
- 1990
(Show Context)
Citation Context ...ulation, the size of the RGS-set, the number of independent runs and so on. To test MASK, we have used several structured SAT instances and a family of Hamiltonian Circuit (HC) problems defined in [3]=-=[12]-=- and Hamilton's World Tour (WT) problem [1]. The desirable property of these problems is that we can control their size and difficulty. Most of them, especially HC and WT, are believed to be hard SAT ... |

9 |
Hard and Easy
- Mitchell, Selman, et al.
- 1992
(Show Context)
Citation Context ...mportant than a variable appearing only once. In terms of constraints, a variable having more constraints on it will be an important one. choice, we will use such hard random instances as proposed in =-=[9]-=- and those used in the second DIMACS challenge. Indeed, research on random formulae has recently drawn much attention and important progress has been carried out in this field. Besides, SAT encodings ... |

6 |
An empirical comparison of two evolutionary methods for satisfiability problems
- Hao, Dorne
(Show Context)
Citation Context ... indicate that MASK outperforms DSGA in all the test examples used by [3][12]. In this section, we give some examples. More details about the context of the comparison and the results can be found in =-=[7]-=-. Like [3][12], we use the evaluation number (EN) (defined as the number of evocations of the Eval evaluation function) as the first comparison criterion. For MASK, a second criterion used is the numb... |

3 |
A hybrid genetic algorithm for a logic problem
- Young, Reel
- 1990
(Show Context)
Citation Context ...lay this explosion as late as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems ([3], =-=[14]-=-, [10], [6], [8], [13] [11]). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedure. MA... |

2 |
Papadimitriou C.H. "On the greedy algorithm for satisfiability
- Koutsoupias
- 1992
(Show Context)
Citation Context ...n as late as possible at the expense of completeness. Indeed, incomplete methods have recently proven that they are able to solve hard SAT instances in a wide class of problems ([3], [14], [10], [6], =-=[8]-=-, [13] [11]). We are especially interested in model finding. In this paper, we present the mask method, MASK for short, a populationbased, incomplete, evolutionary search procedure. MASK has some char... |