Global Optimization of Atomic Cluster Structures Using Parallel Genetic Algorithms
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Global Optimization of Atomic Cluster Structures Using Parallel Genetic Algorithms Ofelia Oña,b Victor E. Bazterra,a,b María C. Caputo,b Marta B. Ferraro,b and Julio C. Facellia a Center for High Performance Computing, University of Utah, 155 South 1452 East Rm 405, Salt Lake City, UT 84112-0190, b Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I (1428), Buenos Aires, Argentina. ABSTRACT The study of the structure and physical properties of atomic clusters is an extremely active area of research due to their importance, both in fundamental science and in applied technology. For medium size atomic clusters most of the structures reported today have been obtained by local optimizations of plausible structures using DFT (Density Functional Theory) methods and/or by global optimizations in which much more approximate methods are used to calculate the cluster’s energetics. Our previous work shows that these approaches can not be reliably used to study atomic cluster structures and that approaches based on global optimization schemes are needed. In this paper, we report the implementation and application of a parallel Genetic Algorithm (GA) to predict the structure of medium size atomic clusters. INTRODUCTION Systematic global geometry optimizations of atomic clusters are complex and time consuming due to the large number of possible structures [1], the time required for the calculation of their total energy and the lack of effective methods to perform global searches. Our recent research efforts have been focused on using Genetic Algorithms [2, 3] (GA) to predict crystalline [4-7] and cluster structures [8-10]. GA are a family of search techniques rooted in the ideas of Darwinian biological evolution. These methods are based on the principle of survival of the fittest, considering that each string or genome represents a trial solution candidate of the problem. At any generation the genomes or “individuals” compete with each other in the population for survival and offspring production of the next generation by prescribed propagation rules. GA, as well as other metaheuristic methods show excellent scaling properties [11] making them amenable to efficient parallelization in large scale computing systems. METHODS We have implemented the MGAC (Modified Genetic Algorithms for Crystals and Clusters in C++ using the GALib library [12] for the GA implementation, this makes it very portable as well as easy to maintain and upgrade. The evaluation of the objective function for our GA, i.e. the local energy minimizations, can be performed using empirical potential methods, CHARMM [13, 14], semiempirical methods, MSINDO [15], and DFT methods, CPMD [16]. The code uses a global parallelization scheme of the genetic algorithm. Such parallelization scheme rely on the simultaneous evaluation of the fitness of the individuals belonging to the same population in every generation using our Adaptive Parallel Genetic Algorithm (APGA) [17] strategy. APGA
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