遗传算法的一个改进及其在气动设计中的应用

An Improvement of Genetic Algorithm and Its Application to Aerodynamic Design

提出一个概率型二值搜索思想，对标准遗传算法进行改进，改进是在原算法中增设一个概率型二值决策步。在该步中，首先通过计算种群中每个个体染色体（二值串）各分量的适应值，统计染色体分量所在位置（基因位）取值的历史表现，由此给每一个分量位赋予一个分值；然后，利用该分值以概率方式产生若个干新个体，并加入新代种群参与进化。由于分量位分值包含全局收敛信息，以此为基础产生的新个体可望具有良好素质，从而提高收敛速度，这在一个二维多峰函数极大值搜素问题中得到了验证。最后将所提出的方法应用于一离心压缩机扩压器叶片逆命题设计问题，与标准遗传算法求解过程的对比。

An idea of a probabilistic binary search is proposed to improve the standard genetic algorithm (SGA) by adding a step of probabilistic binary decision in the SGA procedure. In the added step, the fitness for each components of chromosomes (binary strings) in the population is first calculated, and then is used to count statistically the values at the components positions (i.e. genic position) during the past evolution, and each components position will be assigned with a score. Finally, based on these scores, several new individuals were generated and joined to the population in next generation to be evolved. Due to the inclusion of some global evolution information in the scores, it is expected that so obtained individuals have “better” qualities, and can make the algorithm improving convergence. The improved genetic algorithm was verified with a maximum value searching problem of a 2 dimensional multimodal function. It was then applied to carry out the blade inverse design of a centrifugal compressor diffurer. The comparison between the result of the new approach with that of SGA demonstrates the new algorithm is superior to the SGA for solving the chosen problem.