一类新的无参数的填充打洞函数法

doi:10.15960/j.cnki.issn.1007-6093.2025.02.017

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (2): 214-220.doi: 10.15960/j.cnki.issn.1007-6093.2025.02.017

一类新的无参数的填充打洞函数法

袁柳洋¹^,²^,*(), 汤梦瑶¹^,², 迟晓妮³

1. 武汉科技大学理学院, 湖北武汉 430065
2. 冶金工业过程系统科学湖北省重点实验室 (武汉科技大学), 湖北武汉 430081
3. 桂林电子科技大学数学与计算科学学院, 广西桂林 541004

收稿日期:2022-01-10 出版日期:2025-06-15 发布日期:2025-06-12
通讯作者: 袁柳洋 E-mail:yangly0601@126.com
基金资助:
湖北省教育厅科学技术研究项目(Q20211111);湖北省冶金工业过程系统科学重点实验室开放基金(Y201905);国家自然科学基金(12361064);广西自然科学基金(2021GXNSFAA220034)

A new class of parameter-free filled tunnel function methods

Liuyang YUAN¹^,²^,*(), Mengyao TANG¹^,², Xiaoni CHI³

1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, Hubei, China
2. Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology), Wuhan 430081, Hubei, China
3. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China

Received:2022-01-10 Online:2025-06-15 Published:2025-06-12
Contact: Liuyang YUAN E-mail:yangly0601@126.com

摘要/Abstract

摘要：

自填充函数算法被提出以来, 参数被视为制约算法效率的主要因素, 因此构造无参数的填充函数显得极为重要。为了提高算法效率, 本文构造了一类新的无参数的填充打洞函数, 分析并讨论了该函数的性质。基于新的填充打洞函数, 提出了一个新的全局优化算法, 并对算法进行了数值实验, 数值实验结果表明该算法可行且有效。

关键词: 填充函数法, 打洞函数法, 全局优化算法, 局部极小点, 全局极小点

Abstract:

Since the filled function algorithm is proposed, parameters have been regarded as the main factor restricting the efficiency of the algorithm. So it is particularly important to construct a filled function without parameters. In order to improve the efficiency and accuracy of the algorithm, a new class of parameter-free filled tunnel functions is constructed in this paper. Some properties of the new class of filled tunnel functions are analyzed. Based on the filled tunnel functions, a new global optimization algorithm is proposed, and numerical experiments are carried out on the algorithm. The numerical experiment results show that the algorithm is feasible and effective.

Key words: filled function methods, tunnel function methods, global optimization algorithm, local minimizer, global minimizer

中图分类号:

O221.2

袁柳洋, 汤梦瑶, 迟晓妮. 一类新的无参数的填充打洞函数法[J]. 运筹学学报（中英文）, 2025, 29(2): 214-220.

Liuyang YUAN, Mengyao TANG, Xiaoni CHI. A new class of parameter-free filled tunnel function methods[J]. Operations Research Transactions, 2025, 29(2): 214-220.

图/表 2

表1

表2

参考文献 16

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No.	$ n $	iter	$ T $-mean/s	SR
1	2	1.0	1.054 7	3/8
2	2	1.5	0.976 6	4/8
3	2	1.6	1.453 1	7/8
	3	1.2	1.640 7	6/8
	5	2.2	2.992 2	5/8
	7	1.3	3.625 0	7/8
	10	1.7	6.464 9	7/8
4	2	8.9	3.347 7	8/8
	3	4.8	2.084 0	8/8
	5	4.5	3.796 9	6/8
	7	1.0	3.560 6	2/8
	10	6.5	9.078 1	8/8

No.	$ n $	算法A			文献[8]算法			文献[13]算法
No.	$ n $	$ f $-best	$ f $-mean	SR	$ f $-best	$ f $-mean	SR	$ f $-best	$ f $-mean	SR
1	2	$ 1.077\,9\times 10^{-15} $	$ 1.077\,9\times 10^{-15} $	3/8	—	—	0/8	—	—	0/8
2	2	$ -1.878 9 $	$ -1.727 5 $	4/8	$ -1.878 9 $	0.240 3	4/8	$ -1.878 9 $	$ -1.878 9 $	2/8
3	2	$ 1.421 1\times 10^{-13} $	0.710 7	7/8	0.995 0	7.587 2	8/8	0.995 0	2.363 0	8/8
	3	1.989 9	11.641 0	6/8	1.989 9	12.213 1	7/8	1.989 9	10.945 4	6/8
	5	1.989 9	7.362 7	5/8	1.989 9	18.655 4	4/8	1.989 9	7.794 7	5/8
	7	20.894 0	33.994 2	7/8	26.863 8	41.645 9	7/8	22.884 0	33.331 0	6/8
	10	2.984 9	28.000 9	7/8	19.899 2	44.488 7	7/8	15.919 3	36.481 7	6/8
4	2	$ -0.749 3 $	$ -0.749 3 $	8/8	0.196 8	11.179 3	8/8	0.196 8	5.817 9	8/8
	3	3.882 3	13.591 3	8/8	3.883 2	13.591 3	8/8	2.095 6	12.785 1	8/8
	5	2.266 2	15.536 4	6/8	2.266 0	12.392 7	6/8	10.320 4	16.878 7	6/8
	7	2.315 1	7.103 7	2/8	2.315 1	2.315 1	1/8	—	—	0/8
	10	1.980 3	9.211 2	8/8	1.980 3	9.206 0	8/8	1.980 3	8.161 6	8/8

[1]	王伟祥, 尚有林, 王朵. 求解带箱子集约束的非光滑全局优化问题的填充函数方法[J]. 运筹学学报, 2019, 23(1): 28-34.
[2]	刘牧华, 尚有林, 李璞. 基于不等式约束的一类新的增广lagrangian函数[J]. 运筹学学报, 2011, 15(4): 115-123.

一类新的无参数的填充打洞函数法

A new class of parameter-free filled tunnel function methods

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