Geometric methods for the construction of three structural motifs, the icosahedron, Ino's decahedron, and the complete octahedron, are proposed. On the basis of the constructed lattices and the genetic algorithm, a method for optimization of large size Lennard-Jones (LJ) clusters is presented. Initially, the proposed method is validated by optimization of LJ clusters with the above structural motifs. Results show that the proposed method successfully located all the lowest known minima with an excellent performance; for example, based on Ino's decahedron with 147 lattice sites, the mean time consumed for successful optimization of LJ is only 0.61 s (Pentium III, 1 GHz), and the percentage success is 100%. Then, putative global minima of LJ clusters are predicted with the method. By theoretical analysis, these global minima are reasonable, although further verification or proof is still needed.

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A random tunneling algorithm (RTA) is derived from the terminal repeller unconstrained subenergy tunneling (TRUST) algorithm, and the parallelization of the RTA is implemented with an island parallel paradigm. Combined with the techniques of angular moving, the parallel random tunneling algorithm (PRTA) is applied to the optimization of Lennard-Jones (LJ) atomic clusters, and all the global minima of LJ clusters with size up to 200 are successfully located. For the optimization of larger cluster, a PRTA with an improved seeding technique is developed and successfully applied to the optimization of LJ151-LJ309. Furthermore, the optimized structures of LJ309-330 with the PRTA, which have not been studied before, are also provided.

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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.

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