Zhou Yi, Su Wu-Pei
Department of Physics and Texas Center for Superconductivity and Advanced Materials, University of Houston, 77204, USA.
Acta Crystallogr A. 2004 Jul;60(Pt 4):306-10. doi: 10.1107/S0108767304010001. Epub 2004 Jun 24.
Sayre's equations give a set of relationships that exist among the structure factors of an equal-atom structure. In order to obtain the correct phases of the structure factors, a genetic algorithm is used to minimize a least-squares residual of Sayre's equations. In the genetic algorithm, a phase is treated as a gene and the whole set of phases is considered as a chromosome. Every chromosome is relaxed to a nearby local minimum by quenching after being produced from a previous generation. Trial calculations for a structure containing 92 non-H equal atoms with synthetic data and another structure containing 62 non-H equal atoms with real data are presented. Compared to simulated annealing, a genetic algorithm is a more efficient means of global optimization.
塞尔方程给出了等原子结构的结构因子之间存在的一组关系。为了获得结构因子的正确相位，采用遗传算法来最小化塞尔方程的最小二乘残差。在遗传算法中，一个相位被视为一个基因，而整个相位集被视为一条染色体。每条染色体在从上一代产生后通过淬火松弛到附近的局部最小值。给出了对含有92个非氢等原子的结构使用合成数据以及对含有62个非氢等原子的另一个结构使用真实数据的试算。与模拟退火相比，遗传算法是一种更有效的全局优化方法。
