一种灵活自适应的全局优化网格算法
A flexible and adaptive grid algorithm for global optimization utilizing basin hopping Monte Carlo
摘要：
全局优化是原子模拟中一个活跃的研究领域，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，它执行修改的大都会蒙特卡罗搜索，以探索感兴趣的系统的势能面。这些模拟可能是非常苛刻的，由于高维配置搜索空间。有效的搜索空间可以通过利用原子位置的网格来减少，但如果采用固定网格，则可能会使结果偏置。在本文中，我们提出了一个灵活的网格算法的全局优化，允许利用网格的效率，而不偏置的模拟结果。该方法是通用的，适用于非常异质的系统，如不同晶体结构的两种材料之间的界面或在表面上支持的大集群。作为一个基准案例，我们展示了其性能的著名的全局优化问题的Lennard-Jones集群包含多达100个粒子。尽管这个模型势很简单，但Lennard-Jones团簇代表了一个具有挑战性的测试案例，因为一些“神奇”粒子数的全局最小值表现出与大小略有不同的团簇非常不同的几何形状。
英文摘要：
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 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 structure 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. In spite of 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.
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