Global Optimization of Lennard-Jones Clusters by a Parallel Fast Annealing Evolutionary Algorithm

Abstract

A parallel fast annealing evolutionary algorithm (PFAEA) was presented and applied to optimize Lennard-Jones (LJ) clusters. All the lowest known minima up to LJ(116) with both icosahedral and nonicosahedral structure, including the truncated octahedron of LJ(38), central fcc tetrahedron of LJ(98), the Marks' decahedron of LJ(75)(-)(77), and LJ(102)(-)(104), were located successfully by the unbiased algorithm. PFAEA is a parallel version of fast annealing evolutionary algorithm (FAEA) that combines the aspect of population in genetic algorithm and annealing algorithm with a very fast annealing schedule. A master-slave paradigm is used to parallelize FAEA to improve the efficiency. The performance of PFAEA is studied, and the scaling of execution time with the cluster size is approximately cubic, which is important for larger scale energy minimization systems.