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January  2010, 6(1): 29-46. doi: 10.3934/jimo.2010.6.29

A recursive topographical differential evolution algorithm for potential energy minimization

M. Montaz Ali 1,

1. 

School of Computational and Applied Mathematics, University of the Witwatersrand, Wits-2050, Johannesburg, South Africa

Received  February 2008 Revised  July 2009 Published  November 2009

The problem of the determination of the minimum energy configuration of an arrangement of $N$ point particles under the interaction of their interatomic forces is discussed. The interatomic force is described by a classical many body potential, namely the Tersoff potential for silicon. We propose a global optimization algorithm for minimization of energy of clusters of particles using Tersoff potential. The algorithm combines the topographical differential evolution (TDE) with the modified recursive procedure of the recursive differential evolution (RDE) algorithm. It also introduces an initialization procedure for the population set. Two important features of the new algorithm are that it makes use of the \lq graph minima' for local search, and that the initial population set is generated with low function values. The global minima of clusters consisting of up to 20 particles are investigated. The new algorithm is compared with a recent genetic algorithm.
Keywords: graph minima, global optimization, differential evolution., many-body potentials, recursive, Atomic clusters.
Mathematics Subject Classification: Primary: Primary: 90B05; Secondary: 65K0.
Citation: M. Montaz Ali. A recursive topographical differential evolution algorithm for potential energy minimization. Journal of Industrial and Management Optimization, 2010, 6 (1) : 29-46. doi: 10.3934/jimo.2010.6.29
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