遗传算法性能与所求解问题关系的研究

Study of the relations between GAs performance and the problem to be solved

遗传算法的性能与所求解的问题有什么关系，一直没有合理答案．文中采用Ｗａｌｓｈ多项式构造满足一定性质的函数，并对遗传算法的运行结果进行了分析．令适应度最大值对应的状态组成的集合为Ｈ０，与Ｈ０ 汉明距离为ｍ 的状态组成的集合称为Ｈｍ ．实验结果表明：如果｛Ｈｍ ｝ 之间的相对生存能力随着ｍ 的增加而逐渐减小。

It is not clear what relations exist between Genetic Algorithm and the problem to be solved. In this paper, some functions with expected features are constructed by using Walsh polynomial and the results of Genetic Algorithm are analyzed. Let H 0 denote the set whose elements have maximum fitness and  H m denote the set whose elements have a Hamming distance of m from the elements in H 0. If the relative survival abilities of { H m} decrease gradually with the increase of m, experimental results show that such a problem can be easily solved by GA.