一个新的填充函数及其在数据拟合问题中的应用  

A new filled function and its application in data fitting problems

作　　者：陈佳利 张莹 王胜刚[2] 谢笑盈 CHEN Jiali;ZHANG Ying;WANG Shenggang;XIE Xiaoying(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,Zhejiang,China;College of Agriculture and Biological Engineering,Jinhua Polytechnic,Jinhua 321007,Zhejiang,China;College of Economics and Management,Zhejiang Normal University,Jinhua 321004,Zhejiang,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004 [2]金华职业技术学院农业与生物工程学院,浙江金华321007 [3]浙江师范大学经济与管理学院,浙江金华321004

出　　处：《运筹学学报》2021年第1期81-88,共8页Operations Research Transactions

基　　金：浙江省科技厅公益项目(Nos.LGN19C040001,2017C32034);国家社会科学基金(No.17BTJ028)。

摘　　要：填充函数法是求解全局优化问题的有效方法之一,针对无约束优化问题,提出一个新的连续可微的无参数填充函数,证明其相关性质并给出相应的算法,数值实验结果表明该算法是有效可行的。同时用此填充函数对切削温度实验数据这一拟合实例进行求解,与已有的最小二乘法和遗传算法的求解结果相比较,拟合效果较好。The filled function method is one of the effective methods to solve the global optimization problem.In this paper,a new continuous and differentiable nonparameter filled function is proposed for the unconstrained optimization problem.The related properties of the filled function are proved and the corresponding algorithm is designed.By comparing with the numerical experimental results in previous literature,it is shown that the proposed filled function algorithm is effective and feasible.Then,the proposed filled function method is used to solve the data fitting example of cutting temperature experimental data,compared with the existing least squares method and genetic algorithm,the fitting effect is better.

关 键 词：全局优化 填充函数 无参数 数据拟合 

分 类 号：O221.2[理学—运筹学与控制论]