基于改进的填充函数法求解全局优化问题的全局最优解  

Finding Global Minima for Global Optimization via an Improved Filled Function Method

作　　者：苏爽 尚有林[1] 孙广磊 SU Shuang;SHANG Youlin;SUN Guanglei(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471000,China)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471000

出　　处：《应用数学》2024年第3期661-671,共11页Mathematica Applicata

基　　金：the National Natural Science Foundation of China(12071112,11471102);Basic Research Projects for Key Scientific Research Projects in Henan Province of China(20ZX001)。

摘　　要：本文构造一个新的单参数填充函数.此函数用于寻求全局优化问题的全局最优解.首先在合理的假设条件下,探究并且证明了该填充函数的填充性质和其他的必要性.此单参数填充函数与目标函数有相同的局部极小值点.意味着在算法执行中仅需在第一步迭代中极小化目标函数.此外,极小化填充函数得到的点就是原问题更优的局部极小点.其次,给出相应的填充函数算法.最后,进行了经典数值实验,并与其他文献的结果比较.结果表明,该算法迭代次数较少,结果精确度较高,算法有效.A new filled function with one parameter is constructed.This function is to seek the global optimal solution of the global optimization problem.Firstly,the filling property and other necessary properties of the function are investigated and proved under reasonable assumptions.The function has the same local minimizers as the objective function.It means that the objective function only needs to be minimized in the first iteration of the algorithm.Additionally,the point obtained by minimizing the filled function is the better local minimum point of the original problem.Secondly,the corresponding filled function algorithm is given.Finally,the classical numerical experiments are carried out.The results are compared with those in other papers.It is indicated that the algorithm with fewer iterations and higher accuracy is effective.

关 键 词：全局优化 填充函数 极小点 单参数 

分 类 号：O221.2[理学—运筹学与控制论]