Fast optimization of binary clusters using a novel dynamic lattice searching method

Abstract

Global optimization of binary clusters has been a difficult task despite of much effort and many efficient methods. Directing toward two types of elements (i.e., homotop problem) in binary clusters, two classes of virtual dynamic lattices are constructed and a modified dynamic lattice searching (DLS) method, i.e., binary DLS (BDLS) method, is developed. However, it was found that the BDLS can only be utilized for the optimization of binary clusters with small sizes because homotop problem is hard to be solved without atomic exchange operation. Therefore, the iterated local search (ILS) method is adopted to solve homotop problem and an efficient method based on the BDLS method and ILS, named as BDLS-ILS, is presented for global optimization of binary clusters. In order to assess the efficiency of the proposed method, binary Lennard-Jones clusters with up to 100 atoms are investigated. Results show that the method is proved to be efficient. Furthermore, the BDLS-ILS method is also adopted to study the geometrical structures of (AuPd)79 clusters with DFT-fit parameters of Gupta potential.

Application of Optimization Algorithms in Clusters

“…AIOA is an adaptive heuristic GA based algorithm which is used in the biological applications also. Another modified algorithm, MAIOA is used for the structural optimization of bimetallic (Wu et al, 2009;Wu et al, 2017) and ternary clusters.…”

Quasi-combinatorial energy landscapes for nanoalloy structure optimisation

“…Finally, it is worth noting that the concepts of quasicombinatorial landscapes and biminima are also applicable when one of the constituent species represents vacancies (quasiparticles), and so the framework of mixed-variable optimisation could subsume the approach of dynamic-lattice searching. 25,26 However, since vacancies are usually not intrinsically defined in off-lattice atomistic models, they have to be generated by some additional means, and it may require introducing another, distinctly different local neighbourhood structure. In that case the term triminima would be more appropriate for describing the local optima.…”

“…Hence, when performing a global search with random Cartesian moves, we combine biminimisation with another procedure akin to a dynamic-lattice search. 25,26 This procedure relies on a nearestneighbour analysis to generate an appropriate set of vacancies (see below) for a given biminimum. These vacancies and the subset of least-coordinated atoms (irrespective of their chemical identity) define an ad hoc local neighbourhood, and we sequentially attempt quench-assisted swaps between atoms and vacancies within this neighbourhood.…”

Directional Monte Carlo Lattice Search Algorithm for the Structure Search of Alumina Clusters (Al2O3)n (n=1~50)

“…全局优化算法分为两类, 一类属于演 化 算 法 : 例 如 遗 传 算 法 (GA) [9][10][11][12][13] 、 粒 子 群 优 化 算 法 (PSO) [14][15][16][17][18][19] 、人工蜂群算法(ABC) [20][21][22][23] 等. 另一类属于单 结构优化算法: 例如动态格点搜索算法(DLS) [24][25][26][27][28] 、 模拟 退火算法(SA) [29][30] 、Basin-Hopping 及其变种算法 [31][32][33] 等. 目前大多数的全局优化算法都是在探索体系的势能 面, 直到找到全局最小值的最优候选解.…”

“…Northby [34] 提出了一种格点搜索算法并应用于 LJ (Lennard-Jones)团簇的全局最优结构搜索, 通过构造格 点的方式, 将连续空间的极值优化问题转为离散空间的 组合优化问题, 减少了探索的空间, 降低了搜索的难度. 基于这种策略, Shao 和 Cheng 提出了一种高效的动态格 点搜索算法(dynamic lattice searching), 随后 Wu 对算法 进行了改进 [24][25][26][27][28] , 该算法对大尺寸的团簇也能进行高效 的结构优化. Rahm 等 [35] 提出一种将固定格点作为原子 坐标并结合 Metropolis Monte Carlo 的算法, 这样对原子 数为 N atom 的团簇进行结构搜索, 搜索空间由 3×N atom 个 的连续坐标减少到格点中的格点数.…”