A flexible and adaptive grid algorithm for global optimization utilizing basin hopping Monte Carlo.
A flexible and adaptive grid algorithm for global optimization utilizing basin hopping Monte Carlo.
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DOI：
10.1063/1.5142363
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发表时间：
2020-02
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通讯作者：
M. Paleico;J. Behler
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文献类型：
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作者：
M. Paleico;J. Behler
全局优化是原子模拟研究的一个活跃领域，迄今为止已经提出了许多算法。一个突出的例子是盆地跳跃蒙特卡罗，它执行一个改进的Metropolis蒙特卡罗搜索来探索感兴趣的系统的势能面。由于高维配置搜索空间，这些模拟可能要求很高。通过对原子位置使用网格可以减少有效的搜索空间，但如果使用固定的网格，则可能会使结果产生偏差。在本文中，我们提出了一种灵活的网格算法进行全局优化，使我们能够在不影响模拟结果的情况下利用网格的效率。该方法是通用的，适用于非常不均匀的系统，例如两种不同晶体结构的材料之间的界面或表面支撑的大簇。作为一个基准案例，我们展示了它在包含多达100个粒子的Lennard-Jones簇的全局优化问题上的性能。尽管这个模型很简单，但伦纳德-琼斯星团代表了一个具有挑战性的测试案例，因为一些“神奇”粒子数量的全局最小值所表现出的几何形状与那些大小略有不同的星团非常不同。
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore the potential energy surface of the system of interest. These simulations can be very demanding due to the high-dimensional configurational search space. The effective search space can be reduced by utilizing grids for the atomic positions, but at the cost of possibly biasing the results if fixed grids are employed. In this paper, we present a flexible grid algorithm for global optimization that allows us to exploit the efficiency of grids without biasing the simulation outcome. The method is general and applicable to very heterogeneous systems, such as interfaces between two materials of different crystal structures or large clusters supported at surfaces. As a benchmark case, we demonstrate its performance for the well-known global optimization problem of Lennard-Jones clusters containing up to 100 particles. Despite the simplicity of this model potential, Lennard-Jones clusters represent a challenging test case since the global minima for some "magic" numbers of particles exhibit geometries that are very different from those of clusters with only a slightly different size.