Comparison study of pivot methods for global optimization

Pablo Serra, Aaron F. Stanton, Sabre Kais, Richard E. Bleil

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42 Citations (Scopus)


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 languageEnglish
Pages (from-to)7170-7177
Number of pages8
JournalJournal of Chemical Physics
Issue number17
Publication statusPublished - 1 May 1997
Externally publishedYes


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Serra, P., Stanton, A. F., Kais, S., & Bleil, R. E. (1997). Comparison study of pivot methods for global optimization. Journal of Chemical Physics, 106(17), 7170-7177.