求分圆多项式近似根的遗传算法

新提出的求分圆多项式近似根的遗传算法,是取m个个体,在初始群体中随机产生m个初始点,再用适应度函数1/(1 |f(x)|)计算个体适应度,对种群进行选择、交叉、变异操作,将适应度好的个体组成下一代群体,直到达到规定近似根的个数和精度,就输出结果.该算法采用动态自适应技术、重新启动法、多项式除法等措施进行优化,可以有效地防止出现未成熟收敛问题.该算法在求分圆多项式的近似根方面是可行的,并取得比较好的效果,为判定一个多项式是否分圆提供了一种新方法.

Genetic Algorithm for Finding Approximate Roots of a Cyclotomic Polynomial

The newly-proposed genetic algorithm for finding approximate roots of a cyclotomic polynomial in this paper refers to the process in which m individuals are selected to produce randomly m original points in the original groups.Then by using the fitness function 1/(1+|f(x)|),individuals' fitness is calculated,selection,crossover and mutation of initial population are performed to integrate individuals with good fitness into the next generation.The result will come out when the ordered number of the approximate roots and the precision are achieved.The algorithm is optimized by using dynamic adaptive,restartion,polynomial division to restrain the premature convergence efficiently.The algorithm is practicable and efficient in finding approximate roots of a cyclotomic polynomial,and gives a new method to judge a polynomial that can pitch cirle.