景书杰, 段晓辉, 牛海峰.求解非线性全局优化问题的填充函数算法[J].河南理工大学学报（自然科学版）,2022,41(6):169-173.

JING S J, DUAN X H, NIU H F.A filled function algorithm for solving nonlinear global optimization problems[J].Journal of Henan Polytechnic University(Natural Science) ,2022,41(6):169-173.

求解非线性全局优化问题的填充函数算法

景书杰, 段晓辉, 牛海峰

河南理工大学 数学与信息科学学院，河南 焦作 454000

摘要:填充函数是目标函数的复合函数，当目标函数形式较为复杂时，填充函数随之变复杂。填充函数中参数越多，计算时越难调节，导致计算量增加。针对此问题，在无不等式约束条件下，构建一个连续可微的单参数填充函数，并从理论上讨论该函数的相关性质。分析认为，通过极小化该填充函数，可以跳出目标函数当前局部极小点，找到一个更好的局部极小点。结合序列二次规划算法和拟牛顿算法设计新的填充算法，并选择实例进行数值试验，计算结果表明，提出的填充函数算法有效可行。研究结果可为求解非线性全局优化问题提供一种形式简单、参数容易调节的有效算法。

关键词:填充函数;非线性全局优化;局部极小点

doi:10.16186/j.cnki.1673-9787.2020100055

基金项目:国家自然科学基金资助项目（U1504104）

收稿日期:2020/10/23

修回日期:2021/03/10

出版日期:2022/11/25

A filled function algorithm for solving nonlinear global optimization problems

JING Shujie, DUAN Xiaohui, NIU Haifeng

School of Mathematics and Information Science，Henan Polytechnical University，Jiaozuo 454000，Henan，China

Abstract:Since the filled function is a composite function of the objective function，the corresponding filled function becomes more complex when the objective function is complex.In addition，the more parameters are contained in the filled function，the more difficult it is to adjust during calculation，which will increase the amount of calculation.To solve this problem，a continuously differentiable single parameter filled function was proposed under the condition of no inequality constraints，and the related properties of the function were discussed theoretically.By minimizing the filled function，the current local minimum could be jumped out and a better local minimum could be found.Finally，a new filled algorithm was designed combining SQP algorithm and BFGS algorithm，and examples were selected for numerical experiments.The calculation results showed that the algorithm was effective and feasible was provided，and an efficient filled function algorithm with simple form and easy adjustment of parameters for solving nonlinear global optimization problems.

Key words:filled function;nonlinear global optimization;local minimizer

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