摘要
针对多项式方程求实根问题,提出了一种混合差分进化算法。在该算法中,先对标准差分进化算法进行了一些改进,对计算种群个体的适应度并排序,利用二分之一规则选取个体,并引入自适应变异算子和进化策略重组算子,用改进的差分进化算法对种群进行优化,然后引入模拟退火算法和小生境技术对生成的新个体进一步优化。通过典型算例的数值仿真表明,文中提出的算法克服了标准差分进化算法易陷入局部极优等缺点,可以求任意高次多项式方程的全部实根,而且求解效率高,是一种求解多项式方程全部实根的有效算法。
Aiming at solving real roots of polynomial equation, a mixed differential evolution algorithm is put forward. In this algorithm, standard differential evolution algorithm is modified. Computing the fitness of each individual, the new individuals are chosen by the first - two rule, and self - adaptive mutation of differential evolution and reorganization of evolution strategies are introduced. The modified differential evolution algorithm is used to optimize the population individual, and then using the Simulated Annealing Algorithms and Niche to optimize the new individuals. The simulations based on benchmarks confirm that this algorithm can overcome some defects of standard differential evolution algorithm and it can not only apply any high order polynomial equation, but has high efficiency. It is a successful approach for finding all real roots of polynomial equation.
出处
《计算机仿真》
CSCD
2008年第8期169-173,共5页
Computer Simulation
基金
国家自然科学基金(60461001)
广西自然科学基金(0542048)
广西民族大学研究生教育创新计划项目(gxun-chx0750)
关键词
多项式方程
实根
差分进化
模拟退火
小生境
Polynomial equation
Real root
Differential evolution algorithm
Simulated annealing algorithm
Niche
