## Fast Global Optimization of Difficult Lennard-Jones Clusters (2000)

Venue: | Computational Optimization and Applications |

Citations: | 15 - 5 self |

### Citations

116 | Global convergence properties of conjugate gradient methods for optimization
- Gibert, Nocedal
- 1992
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Citation Context ... on 266Mhz Pentium II Personal Computers or on a Sun Ultra 5 Workstation. For local optimization a standard conjugate gradient method was employed and, in particular, the implementation described in (=-=Gilbert and Nocedal, 1992-=-) was used with standard parameter settings. For every choice of the parameters, we ran random 10 000 trials. Experiments performed with different parameter settings, like those in tables 1 and 2, wer... |

35 |
Structure and binding of Lennard-Jones clusters: 13( n ( 147
- Northby
- 1987
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Citation Context .... Despite the complexity of the problem, most putative global optima of micro-clusters (with up to 147 atoms) have been discovered by means of a very simple and efficient algorithm first proposed in (=-=Northby, 1987-=-) and further refined in (Xue, 1994), which is based on the idea of starting local optimization from initial configurations built by placing atoms in predefined points in space, according to lattice s... |

32 |
Structure and dynamics of simple microclusters
- Hoare
- 1979
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Citation Context ...ptimization methods; it is one of the simplest models in the literature of test problems (see e.g. Floudas and Pardalos, 1999 pag. 188--193), yet one of the most difficult as it has been conjectured (=-=Hoare, 1979-=-) that the number of local optimum conformations grows at least exponentially with N . Many computational approaches can be found in the literature, ranging from mathematical programming models (Gocke... |

24 |
The effect of the range of the potential on the structures of clusters
- Doye, Wales, et al.
- 1995
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Citation Context ... the lattice search in (Northby, 1987) and (Xue, 1994), biased towards icosahedral structures, are unable to detect this solution. The new putative global optimum was first observed only recently in (=-=Doye et al., 1995) using a -=-direct approach based on molecular dynamics; more recently, in (Leary, 1997) the putative global optimum was found using the "big bang" global optimization algorithm employing on the average... |

23 |
Improvement on the Northby algorithm for molecular conformation: Better solutions
- Xue
(Show Context)
Citation Context ..., most putative global optima of micro-clusters (with up to 147 atoms) have been discovered by means of a very simple and efficient algorithm first proposed in (Northby, 1987) and further refined in (=-=Xue, 1994-=-), which is based on the idea of starting local optimization from initial configurations built by placing atoms in predefined points in space, according to lattice structures which researchers in chem... |

21 |
Structural optimization of Lennard-Jones clusters by a genetic algorithm
- Deaven, Tit, et al.
- 1996
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Citation Context ...mations grows at least exponentially with N . Many computational approaches can be found in the literature, ranging from mathematical programming models (Gockenbach et al., 1997), to genetic methods (=-=Deaven et al., 1996-=-), to Montecarlo sampling (Wales and Doye, 1997) and many others. For a recent review of the state of the art in this subject, the reader may consult (Wales and Scheraga, 1999). Unfortunately very few... |

19 | Evolution of the potential energy surface with size for Lennard-Jones clusters - Doye - 1999 |

11 |
Global Optima of Lennard-Jones Clusters
- Leary
- 1997
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Citation Context ...g a new strategy for local searches which can be profitably included in any algorithm which is based on local searches, including the basin-hopping method (Wales and Doye, 1997), the big-bang method (=-=Leary, 1997-=-), Leary's descent method (Leary and Doye, 1999) or genetic algorithms (see (Deaven et al., 1996), (Pullan, 1999)). Our method consists in a modification of the objective function, in the first phase ... |

4 | An infeasible point method for minimizing the Lennard-Jones potential
- Gockenbach, Kearsley, et al.
- 1997
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Citation Context ... 1979) that the number of local optimum conformations grows at least exponentially with N . Many computational approaches can be found in the literature, ranging from mathematical programming models (=-=Gockenbach et al., 1997-=-), to genetic methods (Deaven et al., 1996), to Montecarlo sampling (Wales and Doye, 1997) and many others. For a recent review of the state of the art in this subject, the reader may consult (Wales a... |

2 |
Global Optimization Applied to Molecular Architecture
- Pullan
- 1996
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Citation Context ...earches, including the basin-hopping method (Wales and Doye, 1997), the big-bang method (Leary, 1997), Leary's descent method (Leary and Doye, 1999) or genetic algorithms (see (Deaven et al., 1996), (=-=Pullan, 1999-=-)). Our method consists in a modification of the objective function, in the first phase of the descent, which enables a local search algorithm to escape from the enormous number of local optima of the... |

2 | 1997] \Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms - Wales |

1 |
The Leary Tetrahedron: A New Approach to Global Optimization
- Anonymous
- 1999
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Citation Context ... LJ 38 is found in 0.3% of the attempts (Leary, 1997). In our first attempt to attack the LJ 98 case, which was discovered only in summer 1999 (Doye et al., 1999a) using "millions of local search=-=es" (Anonymous, 1999-=-), we were able to find the global optimum in less than 10 000 local searches, on average. 2. A new approach to the detection of Lennard-Jones clusters We consider Multistart-like approaches to the pr... |

1 | 1999a, `The Double Funnel Energy Landscape of the 38-Atom Lennard-Jones Cluster - Doye, Miller, et al. |

1 | Pardalos: 1999, Handbook of Test - Floudas, M |

1 | A Performance Analysis of Appel's Algorithm for Performing Pairwise Calculations in a Many Particle System
- Hingst, Phillips
- 1999
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Citation Context ...ing energy computations; another possibility, which we did not explore up to now, might be that of using faster approximate potential calculation, based on approaches similar to the one described in (=-=Hingst and Phillips, 1999-=-). 4. Appendix: details on the computational experiments All of the experiments have been performed either on 266Mhz Pentium II Personal Computers or on a Sun Ultra 5 Workstation. For local optimizati... |

1 | Doye: 1999, `New Tetrahedral Global Minimum for the 98-Atom Lennard-Jones Cluster - Leary, K |

1 |
Forward and CorrectTwo Phase Procedures for the Optimization of Lennard-Jones Clusters'. Technical report, Dipartimento di Sistemi e Informatica, Universit`a di Firenze. LJPAPER.tex; 13/01/2000; 10:31; p.16 Preprint: not to be quoted without explicit perm
- Locatelli, Schoen
- 1999
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Citation Context ...acement of two atoms randomly chosen among those with highest energy contribution into a different position, followed by the usual two-phase optimization. Details on these procedures can be found in (=-=Locatelli and Schoen, 1999-=-), where it is shown that all those configurations which could not be observed through our two-phase Multistart method can be obtained by these more specialized methods. Another critic to the proposed... |

1 | Scheraga: 1999, `Global - Wales, A |