A sphere-cut-splice crossover for the evolution of cluster structures.

A new crossover operator is proposed to evolve the structures of the atomic clusters. It uses a sphere rather than a plane to cut and splice the parent structures. The child cluster is constructed by the atoms of one parent which lie inside the sphere, and the atoms of the other parent which lie outside the sphere. It can reliably produce reasonable offspring and preserve the good schemata in parent structures, avoiding the drawbacks of the classical plane-cut-splice crossover in the global searching ability and the local optimization speed. Results of Lennard-Jones clusters (30 ≤ N ≤ 500) show that at the same settings the genetic algorithm with the sphere-cut-splice crossover exhibits better performance than the one with the plane-cut-splice crossover. The average number of local minimizations needed to find the global minima and the average number of energy evaluation of each local minimization in the sphere scheme is 0.8075 and 0.8386 of that in the plane scheme, respectively. The mean speed-up ratio for the entire testing clusters reaches 1.8207. Moreover, the sphere scheme is particularly suitable for large clusters and the mean speed-up ratio reaches 2.3520 for the clusters with 110 ≤ N ≤ 500. The comparison with other successful methods in previous studies also demonstrates its good performance. Finally, a further analysis is presented on the statistical features of the cutting sphere and a modified strategy that reduces the probability of using tiny and large spheres exhibits better global search.