基于膜计算的一种新型求解非线性方程组的优化算法  

A NEW OPTIMISED ALGORITHM FOR SOLVING NONLINEAR EQUATIONS BASED ON MEMBRANE COMPUTING

作　　者：郭德龙[1] 夏慧明[2] 周永权[3] 

机构地区：[1]黔南民族师范学院数学系,贵州都匀558000 [2]南京师范大学泰州学院数学系,江苏泰州225300 [3]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《计算机应用与软件》2013年第2期165-167,共3页Computer Applications and Software

基　　金：国家民委科研基金项目(08GX01);广西自然科学基金项目(0832082);贵州省教育厅科研项目(黔教科2010093)

摘　　要：非线性方程组的数值求解问题是一个很重要的课题。大多数的求解算法,例如梯度下降法和牛顿法,其收敛性和性能特征在很大程度上依赖于初始点。对于很多非线性方程组,选择好的初始点是一件非常困难的事情。针对以上这些问题提出一种基于膜计算优化算法,算法首先对搜索的空间分割,每个子空间作为一基本膜,在其中的区域中应用进化策略,并且对于每个膜区域把最好的解传给最外层膜。最外层膜区域采用全局搜索策略粒子群算法寻找最优解。仿真实验结果表明该算法比其他算法收敛速度快、精度高。Numerical solution of nonlinear equations is a very important subject.Most of the solving algorithms such as gradient descent method and Newton method,their convergence and performance characteristics depend on the initial point,but for many nonlinear equations,it is a very difficult thing to choose a good initial point.To solve these problems,an optimised algorithm based on membrane computing is proposed.The algorithm first segments the space searched,and each subspace is taken as a basic membrane,the evolution strategy is then applied on the regions of them.And for each membrane region,the best solution is to be transferred to the outer membrane.The global search strategy particle swarm algorithm is used on the outermost membrane region for finding the optimal solution.Finally,the new algorithm is shown through simulation test results to have fast convergence speed and high accuracy compared with other algorithms.

关 键 词：膜计算 进化策略 全局优化 区域 膜结构 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]