### Abstract

We compare two implementations of a new algorithm called the pivot method for the location of the global minimum of a multiple minima problem. The pivot method uses a series of randomly placed probes in phase space, moving the worst probes to be near better probes iteratively until the system converges. The original implementation, called the "lowest energy pivot method," chooses the pivot probes with a probability based on the energy of the probe. The second approach, called the "nearest neighbor pivot method," chooses the pivot probes to be the nearest neighbor points in the phase space. We examine the choice of distribution by comparing the efficiency of the methods for Gaussian versus generalized q-distribution, based on the Tsallis entropy in the relocation of the probes. The two implementations of the method are tested with a series of test functions and with several Lennard-Jones clusters of various sizes. It appears that the nearest neighbor pivot method using the generalized q-distribution is superior to previous methods.

Original language | English |
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Pages (from-to) | 7170-7177 |

Number of pages | 8 |

Journal | Journal of Chemical Physics |

Volume | 106 |

Issue number | 17 |

Publication status | Published - 1 May 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*106*(17), 7170-7177.

**Comparison study of pivot methods for global optimization.** / Serra, Pablo; Stanton, Aaron F.; Kais, Sabre; Bleil, Richard E.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 106, no. 17, pp. 7170-7177.

}

TY - JOUR

T1 - Comparison study of pivot methods for global optimization

AU - Serra, Pablo

AU - Stanton, Aaron F.

AU - Kais, Sabre

AU - Bleil, Richard E.

PY - 1997/5/1

Y1 - 1997/5/1

N2 - We compare two implementations of a new algorithm called the pivot method for the location of the global minimum of a multiple minima problem. The pivot method uses a series of randomly placed probes in phase space, moving the worst probes to be near better probes iteratively until the system converges. The original implementation, called the "lowest energy pivot method," chooses the pivot probes with a probability based on the energy of the probe. The second approach, called the "nearest neighbor pivot method," chooses the pivot probes to be the nearest neighbor points in the phase space. We examine the choice of distribution by comparing the efficiency of the methods for Gaussian versus generalized q-distribution, based on the Tsallis entropy in the relocation of the probes. The two implementations of the method are tested with a series of test functions and with several Lennard-Jones clusters of various sizes. It appears that the nearest neighbor pivot method using the generalized q-distribution is superior to previous methods.

AB - We compare two implementations of a new algorithm called the pivot method for the location of the global minimum of a multiple minima problem. The pivot method uses a series of randomly placed probes in phase space, moving the worst probes to be near better probes iteratively until the system converges. The original implementation, called the "lowest energy pivot method," chooses the pivot probes with a probability based on the energy of the probe. The second approach, called the "nearest neighbor pivot method," chooses the pivot probes to be the nearest neighbor points in the phase space. We examine the choice of distribution by comparing the efficiency of the methods for Gaussian versus generalized q-distribution, based on the Tsallis entropy in the relocation of the probes. The two implementations of the method are tested with a series of test functions and with several Lennard-Jones clusters of various sizes. It appears that the nearest neighbor pivot method using the generalized q-distribution is superior to previous methods.

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UR - http://www.scopus.com/inward/citedby.url?scp=0000591831&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000591831

VL - 106

SP - 7170

EP - 7177

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 17

ER -