一类不适定问题的粒子群算法求解  

A New Method to Solve a Class of Ill Posed Problems

作　　者：李红艳 万钟林[2] LI Hongyan;WAN Zhonglin(Department of Computer and Information Sciences , City College of Dongguan University of Technology, Dongguan 523419 ,China;Department of Economics and Finance .Dongguan Polytechnic, Dongguan 523808,China)

机构地区：[1]东莞理工学院城市学院计算机与信息科学系,广东东莞523419 [2]东莞职业技术学院财经系,广东东莞523808

出　　处：《济宁学院学报》2019年第2期17-20,共4页Journal of Jining University

基　　金：广东省高校青年创新人才项目"大规模病态线性方程组的高效算法及应用"(2017KQNCX55)

摘　　要：针对测量中的不适定问题,提出了一种基于粒子群算法的优化求解方法。将不适定问题通过Tikhonov正则化,建立优化目标函数,将方程组的求解转化为无约束优化问题。利用L-曲线法确定正则参数,取优化目标函数为粒子群算法的适应度函数,通过改进的变异粒子群算法进行随机搜索最优解。最后通过两个测量中的不适定问题的数值算例,利用粒子群算法进行搜索求解,相较于一般的正则化解法,该方法求得的结果更接近真值。Aiming at the ill - posed problem in measurement. an optimization method based on particle swarm optimization ( PSO) is proposed. The ill - posed problem is regularized by Tikhonov,and the optimization objective function is established. The solution of the equations is transformed into an unconstrained optimization problem. The L-curve method is used to determine the regularization parameters,and the optimization objective function is taken as the fitness function of the particle swarm optimization algorithm. The improved mutation particle swarm optimization algorithm is used to search the optimal solution randomly. Finally .through two numerical examples of ill - posed problems in measurement, the particle swarm optimization algorithm is used to search for solutions. Compared with the general regularization method,the results obtained by this method are closer to the true value.

关 键 词：不适定 正则化 粒子群 智能优化 

分 类 号：O242[理学—计算数学]