摘要
针对传统非线性方程组解法的初始点敏感、收敛性差等问题,结合遗传算法和拟牛顿法的优点,提出了一种用于求解非线性方程组的混合遗传算法。该算法具有遗传算法的群体搜索和全局收敛性,有效地克服了拟牛顿法的初始点敏感问题;同时引入拟牛顿迭代法对精英个体进行局部强搜索,克服了遗传算法收敛速度慢和精度差的缺点,使得算法具有较高的收敛速度和求解精度。选择了几个典型非线性方程组,从收敛可靠性、计算成本和适用性等指标分析对不同算法进行了比较。计算结果表明所设计的混合算法有着可靠的收敛性和较高的收敛速度与精度。
Aiming at the problems such as high sensitivity to the initial guess of the solution and poor convergence reliability of the classical algorithms used to solve systems of nonlinear equations, a hybrid genetic algorithm (HGA) was put forward, which combined the advantages of genetic algorithm (GA) and Quasi-Newton methods. The HGA exerted the advantages of GA such as group search and global convergence, efficiently over-comed the problem of high sensitivity to initial guess; and it also had a high convergence rate and solution precision just because it applied Quasi-Newton method to elite individuals for efficiently local search. Convergence reliability, computational cost and applicability of different algorithms were compared by testing several classical equations of nonlinear equations. The computation results show that the HGA proposed in this paper has reliable convergence, high convergence rate and solution precision.
出处
《华南理工大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2003年第z1期140-142,共3页
Journal of South China University of Technology(Natural Science Edition)
关键词
非线性方程组
遗传算法
拟牛顿迭代法
精英混合策略
system of nonlinear equation
genetic algorithm
Quasi-Newton method
elite-based hybrid approach
