有限元分割的共轭方向优化算法  

Optimization algorithm of conjugate direction for finite element segmentation

作　　者：李有堂[1] 梅鹤龄 LI Youtang;MEI Heling(College of Mechano-Electronic Engineering,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学机电工程学院,甘肃兰州730050

出　　处：《电子设计工程》2021年第24期7-12,共6页Electronic Design Engineering

摘　　要：共轭方向法虽是最经典最实用的一类方法,但是在计算过程会出现维度退化现象,导致只能找到局部最优解,从而漏掉全局最优解。针对共轭方向法的缺点,提出了一种新的改进方法,对其计算过程进行了优化。基于共轭方向法的基本原理对不同维度的约束区间进行有限分割并选取节点,将节点进行排列组合确定为初始寻优点,依次代入共轭方向法求出该初始点所对应的极值,最后对所得的所有极值进行所需筛选,确定目标函数的极值点和极值,从而得到全局最优解。给出了新算法的算法步骤和程序流程图,用MATLAB对两种算法分别进行了编程,保证了研究结果的可重复性。用二次三维目标函数进行了算例验证,对两种算法的计算结果进行了对比。通过对比表明新算法具有更好的寻优效果,且不受维度的限制,可用于多维问题的求解。Although Conjugate Direction Method is the most classical and practical method,the dimension degradation phenomenon will appear in the calculation process,which leads to only find the local optimal solution,thus miss the global optimal solution.In view of the shortcoming of Conjugate direction method,a new improved method is proposed.There is the optimized process of calculation.Based on the basic principle of the Conjugate Direction Method,the constraint intervals of different dimensions are divided and the nodes are selected.The nodes are arranged and combined to determine the initial advantages.And the Conjugate Direction Method is used to calculate the corresponding extremum of the initial point.All the extremum obtained are screened to determine the extreme points and extremum of the objective function,and the global situation is obtained optimal solution.The algorithm steps and program flow chart of the new algorithm are given.The two algorithms are programmed with MATLAB to ensure the repeatability of the research results.The example is given to verify the effectiveness of the method and the results of the two algorithms are compared.The comparison shows that the new algorithm has better optimization effect.It is not limited by the dimension,but can be used to solve multi⁃dimensional problems.

关 键 词：有限元 多维度 优化算法 共轭方向法 

分 类 号：TN01[电子电信—物理电子学]