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求解非线性方程组的混沌粒子群算法及应用
引用本文:莫愿斌,陈德钊,胡上序.求解非线性方程组的混沌粒子群算法及应用[J].计算力学学报,2007,24(4):505-508.
作者姓名:莫愿斌  陈德钊  胡上序
作者单位:浙江大学,智能信息工程研究所,浙江,杭州,310027
基金项目:国家自然科学基金(20276063)资助项目
摘    要:针对非线性方程组的求解在工程上具有广泛的实际意义,经典的数值算法如牛顿法存在其收敛性依赖于初值而实际计算中初值难确定的问题,提出以混沌粒子群算法求解非线性方程。它通过将混沌搜索机制有机地引入粒子群算法,使每个粒子从混沌搜索机制与粒子群算法搜索机制中获得适当的搜索方向,以混沌变量的遍历性增强粒子的搜索性能与更全面地应用目标函数的信息,并反映到逐代更新的个体极值和群体极值中,可更有效地调整粒子的移向并最终获得最优解。测试结果表明这一尝试的有效性。最后将所提的方法用于建立复合材料结构的疲劳寿命与应力、温度、湿度的关系模型。

关 键 词:非线性方程组  优化  粒子群优化算法  混沌  复合材料疲劳寿命
文章编号:1007-4708(2007)04-0505-04
修稿时间:2005-06-13

Chaos particle swarm optimization algorithm for solving systems of nonlinear equations and it's application
MO Yuan-bin,CHEN De-zhao,HU Shang-xu.Chaos particle swarm optimization algorithm for solving systems of nonlinear equations and it''s application[J].Chinese Journal of Computational Mechanics,2007,24(4):505-508.
Authors:MO Yuan-bin  CHEN De-zhao  HU Shang-xu
Institution:Institute of Intelligent Information Engineering,Zhejiang University, Hangzhou 310027, China
Abstract:Aimed at the widespread practical significance of solving nonlinear equations in engineering,classic numerical methods such as Newton method are highly sensitive to the initial guess,but it is difficult to find a suitable good initial guess in practical operation,chaos particle swarm optimization(CPSO) algorithm was proposed to solve nonlinear equations.It introduced chaos to particle swarm optimization(PSO),making every particle selected a suitable search direction from PSO search mechanism and chaos search mechanism.By virtue of chaos's ergodicity,it enhanced every particle with search property and made every particle could comprehensively get the useful information about the objective function,which was reflected in present global optimal point and the optimal point of each particle in every iteration.By this,CPSO could more effectively adjust search direction of each particle and finally got the global optimal point of the problem.Experimental results show the effectiveness of the proposed tactics is obvious.At last the algorithm was applied to model relations between composite structures fatigue life with stress,temperature and moisture.
Keywords:systems of nonlinear equations  optimization  particle swarm optimization  chaos  composite structures fatigue life
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