State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People's Republic of China.
J Chem Phys. 2013 Jun 7;138(21):214303. doi: 10.1063/1.4807091.
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.
提出了一种新的交叉算子来演化原子团簇的结构。它使用球体而不是平面来切割和拼接父结构。子簇由位于球体内部的一个父结构中的原子和位于球体外部的另一个父结构中的原子构成。它可以可靠地产生合理的后代，并保留父结构中的良好模式，避免经典的平面切割拼接交叉在全局搜索能力和局部优化速度方面的缺点。 Lennard-Jones 团簇（30≤N≤500）的结果表明，在相同的设置下，带有球切割拼接交叉的遗传算法比带有平面切割拼接交叉的遗传算法性能更好。在球体方案中，找到全局最小值所需的局部最小化的平均数量和每个局部最小化的能量评估的平均数量分别为平面方案的 0.8075 和 0.8386。整个测试团簇的平均加速比达到 1.8207。此外，球体方案特别适用于大型团簇，对于 110≤N≤500 的团簇，平均加速比达到 2.3520。与之前研究中其他成功方法的比较也证明了它的良好性能。最后，对切割球体的统计特征进行了进一步分析，并提出了一种减少使用小球体和大球体概率的改进策略，该策略表现出更好的全局搜索能力。
