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

Abstract

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

CLC Number:

O221.2

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.

Figures/Tables 2

References 16

1	Ge R P . A filled function method for finding a global minimizer of a function of several variables[J]. Mathematical Programming, 1990, 46 (1): 191- 204.
2	朱文兴. 整数规划的一类填充函数算法[J]. 应用数学学报, 2000, 23 (4): 481- 487.
3	吴波, 高岳林. 求无约束连续全局优化问题的单参数填充函数法[J]. 宁夏大学学报(自然科学版), 2017, 38 (3): 221- 223.
4	张玉琴, 冯向东, 张建亮. 一个求解无约束优化的单参数填充函数算法[J]. 计算机技术与发展, 2020, 30 (7): 38- 41.
5	王倩. 一个求解无约束优化的单参数填充函数方法[J]. 数字通信世界, 2021 (3): 269- 270.
6	张玉琴, 冯向东, 张建亮. 一种无约束优化的无参数填充函数算法[J]. 计算机科学, 2020, 47 (S1): 54- 57.
7	Pandiya R , Widodo W , Salmah , et al. Non parameter-filled function for global optimization[J]. Applied Mathematics and Computation, 2021, 391, 1- 13.
8	Ahmed A I . A new parameter free filled function for solving unconstrained global optimization problems[J]. International Journal of Computer Mathematics, 2020, 98 (1): 1- 14.
9	Levy A V , Montalvo A . The tunneling algorithm for the global minimization of functions[J]. SIAM Journal on Scientific and Statistical Computing, 1985, 6 (1): 15- 29.
10	Yao Y . Dynamic tunneling algorithm for global optimization[J]. IEEE Transactions on Systems, Man and Cybernetics, 1989, 19 (5): 1222- 1230.
11	Oblow E M . SPT: A stochastic tunneling algorithm for global optimization[J]. Journal of Global Optimization, 2001, 20 (2): 191- 208. doi: 10.1023/A%3A1011265010691
12	李忠豪. 全局优化的填充函数和变形打洞函数法[D]. 上海: 上海大学, 2012.
13	Li J R , Shang Y L , Han P . New tunnel-filled method for discrete global optimization[J]. Journal of the Operations Research Society of China, 2017, 5 (2): 1- 10.
14	Wang C J , Yang Y J , Li J . A new filled function method for unconstrained global optimization[J]. Journal of Computational and Applied Mathematics, 2008, 225 (1): 68- 79.
15	Li S , Shang Y L , Qu D Q . A novel parameter-free filled function and its application in least square method[J]. Chinese Quarterly Journal of Mathematics, 2021, 36 (3): 1- 12.
16	Yang Y J , Bai F S . An integral function and vector sequence method for unconstrained global optimization[J]. Journal of Global Optimization, 2011, 50 (2): 293- 311. doi: 10.1007/s10898-010-9581-1

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

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A new class of parameter-free filled tunnel function methods

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