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## Efficient initial solution to extremal optimization algorithm for weighted MAXSAT problem (2003)

Venue: | In Proceedings of the 16th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems (IEA/AIE-2003), LNAI 2718 |

Citations: | 2 - 2 self |

### Citations

5154 | Optimization by simulated annealing
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ...partitioning problem. Furthermore, its application to handle unweighted MAXSAT problem instances [17] showed that this method improves significantly previous results obtained with Simulated Annealing =-=[14]-=- and Tabu Search [10], [11] methods on a bed test of random unweighted MAX3SAT and MAX4SAT instances. In addition, several MAXSAT studies have shown that providing interesting start-up assignments to ... |

3620 | Equation of state calculations by fast computing machines
- Metropolis, Rosenbluth, et al.
- 1953
(Show Context)
Citation Context ...minimum energy may be attained by cooling the system slowly according to a temperature schedule. SA local search algorithm moves through the space configurations according to the Metropolis algorithm =-=[18]-=- driving the system to equilibrium dynamics. Selman et al [23] affirm that they were unable to find a cooling schedule that outperformed GSAT. 0sEfficient Initial Solution to Extremal Optimization for... |

1300 | Ant System: Optimization by a Colony of Cooperating Agents”.
- Dorigo, Maniezzo, et al.
- 1996
(Show Context)
Citation Context ...gy to escape from these local minima and to guide the search toward good solutions. Different strategies can be cited : Simulated Annealing [14], [24], Tabu Search [10], [11], Ant Colony Optimization =-=[8]-=- and Reactive Search [3]. Although, the list of competitive heuristics is not exhaustive. In the literature, effective local search algorithms to solve MAXSAT have been proposed. The most popular one ... |

826 |
Approximation algorithms for combinatorial problems
- Johnson
- 1974
(Show Context)
Citation Context ...for a hill climbing heuristic. The experimental results obtained on unweighted MAXSAT problem instances from the DIMACS repository, prove its efficiency according to a heuristic introduced by Johnson =-=[13]-=-. In this paper, we introduce an algorithm based on the Bose-Einstein distribution which provides a new stochastic initialization scheme to an Extremal Optimization procedure and compare it to the mor... |

733 |
Introduction to Probability Models
- Ross
- 2003
(Show Context)
Citation Context ...at X [ S] is uniformly distributed on { ,..., S } of V : ∀k ∈ { 0,..., S } , ∀S ⊆ V , P( X S = k) 1 = S + 1 0 for all subsets S The Bose-Einstein distribution satisfies the Eqn.5 and it is defined by =-=[20]-=- : n { 0 , 1} ∀X ∈ , pX Its conditional probability is given by : 4.2 BE-EO Algorithm X ( ) [ S] x = 1 = + 1 = ( n + 1) 1 ⎛ n ⎜ ⎝ X ⎞ [ ] ⎟⎟ V p j where S = { 1,..., ( j −1) } ( j −1) + 2 Let us consi... |

679 | Tabu search—Part I
- Glover
- 1989
(Show Context)
Citation Context ... Furthermore, its application to handle unweighted MAXSAT problem instances [17] showed that this method improves significantly previous results obtained with Simulated Annealing [14] and Tabu Search =-=[10]-=-, [11] methods on a bed test of random unweighted MAX3SAT and MAX4SAT instances. In addition, several MAXSAT studies have shown that providing interesting start-up assignments to a local search algori... |

586 |
The Complexity of Theorem Proving Procedures
- Cook
- 1971
(Show Context)
Citation Context ...Introduction The satisfiability problem (SAT) in propositional logic is known to be NP-complete (NP denotes the set of all decision problems solvable by a non deterministic polynomial time algorithm) =-=[7]-=- and requires algorithms of exponential time complexity to solve in the worst case : Given a propositional formula, decide whether it has a model. Many problems in artificial intelligence, mathematica... |

444 |
Self-organized criticality: an explanation of 1/f noise.
- BAK, TANG, et al.
- 1987
(Show Context)
Citation Context ...for a random update which impacts obviously the fitness of interconnected species. After a sufficient number of steps, the system reaches a highly correlated state known as self-organized criticality =-=[1]-=- in which all species have reached a fitness of optimal adaptation. A general modification of EO [4], [5] noted τ -EO, consists to rank all variables from rank k = 1for the worst fitness to rank k = n... |

400 | Noise strategies for improving local search.
- Selman, Kautz, et al.
- 1994
(Show Context)
Citation Context ... increase it. The process is repeated until a maximum number of nonimproving moves is reached. Different noise strategies to escape from basins of attraction are added to GSAT. Its variants like WSAT =-=[23]-=-, Novelty and R-Novelty [16] were generalized to handle weighted MAXSAT problems. In the Tabu Search method [10], [11], a list of forbidden moves tabu list is used to avoid the search process revisiti... |

387 | Tabu search — part II
- Glover
- 1990
(Show Context)
Citation Context ...ermore, its application to handle unweighted MAXSAT problem instances [17] showed that this method improves significantly previous results obtained with Simulated Annealing [14] and Tabu Search [10], =-=[11]-=- methods on a bed test of random unweighted MAX3SAT and MAX4SAT instances. In addition, several MAXSAT studies have shown that providing interesting start-up assignments to a local search algorithm ca... |

245 |
Punctuated equilibrium and criticality in a simple model of evolution,”
- Bak, Sneppen
- 1993
(Show Context)
Citation Context ...tion for Weighted MAXSAT 3 Extremal Optimization Method Extremal Optimization (EO) is a recently introduced meta-heuristic [4] for hard optimization problems. It was inspired by the Bak-Sneppen model =-=[2]-=- which was proposed to describe the self-organization phenomenon in the biological evolution of species. In this model, species xi have an associated value [ ] 1 , 0 ∈ λ i called fitness and a selecti... |

227 | Domain-independent extensions to gsat: Solving large structured satisfiability problems. In:
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...petitive heuristics is not exhaustive. In the literature, effective local search algorithms to solve MAXSAT have been proposed. The most popular one is for sure GSAT (for Greedy SATisfiability) [21], =-=[22]-=- defined initially for SAT and applied next to MAXSAT. It works as follows : It starts with an initial random assignment and, at each iteration, flips the variable which decreases the number of the mo... |

195 | Evidence for invariants in local search.
- McAllester, Selman, et al.
- 1997
(Show Context)
Citation Context ... repeated until a maximum number of nonimproving moves is reached. Different noise strategies to escape from basins of attraction are added to GSAT. Its variants like WSAT [23], Novelty and R-Novelty =-=[16]-=- were generalized to handle weighted MAXSAT problems. In the Tabu Search method [10], [11], a list of forbidden moves tabu list is used to avoid the search process revisiting the previously found solu... |

135 | Towards an Understanding of Hill-Climbing Procedures for SAT,
- Gent, Walsh
- 1993
(Show Context)
Citation Context ...rent history-based heuristics have been proposed to intensify and diversify the search into previously unexplored regions of the search space with collecting information from the previous phase. HSAT =-=[9]-=- introduces a tie-breaking rule into GSAT so that if more moves produce the same best results, the preferred move is the one that has been applied for the longest period. HSAT can be considered as a v... |

117 |
Algorithms for the maximum satisfiability problem.
- Hansen, Jaumard
- 1990
(Show Context)
Citation Context ... the Tabu Search method [10], [11], a list of forbidden moves tabu list is used to avoid the search process revisiting the previously found solutions. MAXSAT problem was one of its first applications =-=[12]-=-, but GSAT seemed to outperform its best results. Different history-based heuristics have been proposed to intensify and diversify the search into previously unexplored regions of the search space wit... |

104 | An empirical study of greedy local search for satisfiability testing’. In:
- Selman, Kautz
- 1993
(Show Context)
Citation Context ...of competitive heuristics is not exhaustive. In the literature, effective local search algorithms to solve MAXSAT have been proposed. The most popular one is for sure GSAT (for Greedy SATisfiability) =-=[21]-=-, [22] defined initially for SAT and applied next to MAXSAT. It works as follows : It starts with an initial random assignment and, at each iteration, flips the variable which decreases the number of ... |

53 | Optimization with extremal dynamics.
- Boettcher, Persus
- 2001
(Show Context)
Citation Context ...-Verlag Berlin Heidelberg 2003sEfficient Initial Solution to Extremal Optimization for Weighted MAXSAT The present work is encouraged by the recent remarkable results obtained by Boettcher and Percus =-=[5]-=-, [6] with their new meta-heuristic method called Extremal Optimization (EO) on graph partitioning problem. Furthermore, its application to handle unweighted MAXSAT problem instances [17] showed that ... |

51 | Nature’s way of optimizing,”
- Boettcher, Percus
- 2000
(Show Context)
Citation Context ...ule that outperformed GSAT. 0sEfficient Initial Solution to Extremal Optimization for Weighted MAXSAT 3 Extremal Optimization Method Extremal Optimization (EO) is a recently introduced meta-heuristic =-=[4]-=- for hard optimization problems. It was inspired by the Bak-Sneppen model [2] which was proposed to describe the self-organization phenomenon in the biological evolution of species. In this model, spe... |

50 | Tabu search for SAT
- Mazure, Sais, et al.
- 1997
(Show Context)
Citation Context ...king rule into GSAT so that if more moves produce the same best results, the preferred move is the one that has been applied for the longest period. HSAT can be considered as a version of Tabu Search =-=[15]-=- and the results obtained on some MAXSAT benchmark tasks present a better performance with respect to WSAT. Simulated Annealing (SA) is a method inspired by natural systems [14], [24]. It emulates the... |

46 | Simulated Annealing for Hard Satisfiability Problems.
- Spears
- 1996
(Show Context)
Citation Context ...oor minima or plateaux, it requires therefore a strategy to escape from these local minima and to guide the search toward good solutions. Different strategies can be cited : Simulated Annealing [14], =-=[24]-=-, Tabu Search [10], [11], Ant Colony Optimization [8] and Reactive Search [3]. Although, the list of competitive heuristics is not exhaustive. In the literature, effective local search algorithms to s... |

34 | Approximate solution of weighted MAXSAT problems using GRASP.
- Resende, Pitsoulis, et al.
- 1997
(Show Context)
Citation Context ...T and MAX4SAT instances. In addition, several MAXSAT studies have shown that providing interesting start-up assignments to a local search algorithm can improve its performance. In the GRASP procedure =-=[19]-=- each iteration consists of a construction phase which provides a start-up assignments to a local search phase. The GRASP solution for MAXSAT [19] is generally significantly better than that obtained ... |

30 |
Reactive search, a history-sensitive heuristic for MAX-SAT
- Battiti, Protasi
- 1997
(Show Context)
Citation Context ...local minima and to guide the search toward good solutions. Different strategies can be cited : Simulated Annealing [14], [24], Tabu Search [10], [11], Ant Colony Optimization [8] and Reactive Search =-=[3]-=-. Although, the list of competitive heuristics is not exhaustive. In the literature, effective local search algorithms to solve MAXSAT have been proposed. The most popular one is for sure GSAT (for Gr... |

23 |
Extremal optimization for graph partitioning
- Boettcher, Percus
- 2001
(Show Context)
Citation Context ...ag Berlin Heidelberg 2003sEfficient Initial Solution to Extremal Optimization for Weighted MAXSAT The present work is encouraged by the recent remarkable results obtained by Boettcher and Percus [5], =-=[6]-=- with their new meta-heuristic method called Extremal Optimization (EO) on graph partitioning problem. Furthermore, its application to handle unweighted MAXSAT problem instances [17] showed that this ... |

13 | Efficient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT: Experimental Evaluation
- Yagiura, Ibaraki
(Show Context)
Citation Context ...cussed on 10 random weighted MAXSAT instances of n=1000 and m=11050 where clause weights are integers uniformly distributed between 1 and 1000, and available at the same web site. Yagiura and Ibaraki =-=[26]-=- observed that no satisfying assignments usually exist for such instances. We finally tested 17 random instances (identified by jnh1-jnh19) of n=100 and m=850 where clause weights are chosen randomly ... |

2 | How to find more efficient initial solutions for searching
- Szedmak
- 2001
(Show Context)
Citation Context ... of geometric graphs by using a clustering algorithm which separates initially the graph into domains. They indicate that EO can perform extremely better when using a clever start-up routine. Szedmak =-=[25]-=- has applied the Bose-Einstein distribution, well known in quantum physics, rather than the uniform one to generate initial solutions for a hill climbing heuristic. The experimental results obtained o... |

1 |
M.: Extremal Optimization for MAXSAT
- Menai, Batouche
(Show Context)
Citation Context ...er and Percus [5], [6] with their new meta-heuristic method called Extremal Optimization (EO) on graph partitioning problem. Furthermore, its application to handle unweighted MAXSAT problem instances =-=[17]-=- showed that this method improves significantly previous results obtained with Simulated Annealing [14] and Tabu Search [10], [11] methods on a bed test of random unweighted MAX3SAT and MAX4SAT instan... |