全局优化问题的一个新的无参数填充函数

doi:10.15960/j.cnki.issn.1007-6093.2021.01.008

Abstract

Abstract:

Since the filled function algorithm for global optimization problems has been proposed, the selection and adjustment of parameters have always been the factors that restrict the effectiveness of the algorithm. How to select appropriate parameters in the actual calculation process directly affects and determines the operation speed and efficiency. Therefore, constructing a filled function without parameters is extremely important. This paper proposes a new parameterless filled function, and gives the corresponding filled function algorithm.Through numerical experiments and comparison with existing literature, numerical experiments verify the effectiveness of the algorithm.

Key words: global optimization, filled function, parameterless, deterministic algorithm

CLC Number:

O221.2

Deqiang QU, Youlin SHANG, Yue ZHAN, Dan WU. A new parameterless filled function for global optimization problems[J]. Operations Research Transactions, 2021, 25(1): 89-95.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.ort.shu.edu.cn/EN/10.15960/j.cnki.issn.1007-6093.2021.01.008

https://www.ort.shu.edu.cn/EN/Y2021/V25/I1/89

Figures/Tables 7

1	Ge R P . A filled function method for finding a global minimizer ofa function of several variables[J]. Mathematical Programming, 1990, 46 (1): 191- 204.
2	Ge R P , Qin Y F . A class of filled function for finding globalminimizers of a function of several variables[J]. Journal ofOptimization Theory and Applications, 1987, 54 (2): 241- 252. doi: 10.1007/BF00939433
3	Ge R P , Huang H . A continuous approach to nonlinear integer programming[J]. Applied Mathematics and Computation, 1989, 34, 39- 60. doi: 10.1016/0096-3003(89)90005-2
4	Liu X . Finding global minima with a computable filled function[J]. Journal of global Optimization, 2001, 19 (2): 151- 161. doi: 10.1023/A:1008330632677
5	Liu X . Several filled functions with mitigators[J]. Applied Mathematics and Computation, 2002, 133 (2-3): 375- 387. doi: 10.1016/S0096-3003(01)00248-X
6	李博, 鲁殿军. 一个新的单参数填充函数算法[J]. 工程数学学报, 2015, 32 (2): 269- 270. doi: 10.3969/j.issn.1005-3085.2015.02.011
7	LIN Hongwei , LI Huirong . A new filled function with one parameter to solve global optimization[J]. Open Journal of Optimization, 2015, 4, 10- 20. doi: 10.4236/ojop.2015.41002
8	尚有林. 非线性全局优化中填充函数方法的研究[D]. 上海: 上海大学, 2005.
9	Zhang Y , Zhang L , Xu Y . New filled functions for nonsmooth global optimization[J]. Applied Mathematical Modelling, 2009, 33 (7): 3114- 3129. doi: 10.1016/j.apm.2008.10.015
10	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 (01): 28- 34.
11	石礼堂, 陈伟. 非线性无约束优化问题的滤子填充函数算法[J]. 运筹学学报, 2017, 24 (1): 35- 44.
12	茅嘉, 杨永建. 一个无参数的填充函数算法[J]. 应用数学与计算数学学报, 2010, 21 (01): 55- 64.
13	吴波, 高岳林. 全局优化问题的一个无参数填充函数算法[J]. 数学的实践与认识, 2017, 47 (4): 170- 174.
14	胡铨, 王薇. 求解带箱式约束全局优化问题的滤子填充函数方法[J]. 运筹学学报, 2016, 20 (3): 57- 67.
15	Lin H , Gao Y , Wang X , et al. A filled function which has thesame local minimizer of the objective function[J]. Optimization Letters, 2019, 13 (1): 761- 776.

k	x_k	x_k^*	f(x_k^* )
1	(0.5, 0.5)	(0.089 8, 0.712 7)	-6.573 073×10^-1
2	(0.419 8, 0.712 7)	(-0.089 8, -0.712 7)	3.173 728×10^-1
3	(0.089 8, 1.042 7)	(0.089 8, 0.712 7)	-6.048 199×10^-1
4	(-0.240 2, 0.712 7)	(0.089 8, 0.712 7)	-5.021 703×10^-1
5	(0.089 8, 0.382 7)	(0.089 8, 0.712 7)	-1.031 628

k	x_k	x_k^*	f(x_k^* )
1	(0.5, 0.5)	(-2, 0)	3.037 112×10^-1
2	(-1.67, 0)	(-2, 0)	1.089×10^-1
3	(-2, 0.33)	(-2, 0)	5.912 071×10^-1
4	(-2.33, 0)	(-2, 0)	1.089×10^-1
5	(-2, -0.33)	(-2, 0)	3.553 869×10^-15

k	x_k	x_k^*	f(x_k^*)
1	(0.5, 0.5)	(-0.131 4×10^-7, -0.164 0×10^-7)	2.055 631×10^-1
2	(0.33, 0)	(-0.093 9×10^-7, -0.198 3×10^-7)	1.089×10^-1
3	(0, 0.33)	(0.131 4×10^-7, 0.164 0×10^-7)	2.055 631×10^-1
4	(-0.33, 0)	(0.093 9×10^-7, 0.198 3×10^-7)	1.089×10^-1
5	(0, -0.33)	(-0.114 8×10^-7, -0.092 8×10^-7)	2.431 368×10^-16

k	x_k	x_k ^*	f(x_k^* )
1	(0.5, 0.5)	(1, 1)	4.045 035×10^-1
2	(1.33, 1)	(1, 1)	5.444 996×10^-2
3	(1, 1.33)	(1, 1)	2.607 556×10^-1
4	(0.67, 1)	(1, 1)	5.445 004×10^-2
5	(1, 0.67)	(1, 1)	3.868 840×10^-14

k	x_k	x_k ^*	f(x_k^* )
1	(3, 3)	(0, 6.132 6)	4.493 61×10⁸
2	(0.33, 6.432 7)	(0, 6.934 6)	2.598 926×10^-3
3	(0, 6.753 7)	(0, 5.470 7)	4.493 61×10^{8}
4	(-0.33, 6.423 7)	(0, 5.928 1)	2.677 228×10^-3
5	(0, 6.093 7)	(0, 6.423 7)	5.083 155×10^-7

A new parameterless filled function for global optimization problems

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 7

Related Articles 15

Recommended Articles

Metrics

Comments

算法	算例1	算例2	算例3	算例4	算例5
文献[10]	-	-	-	-	31.221 9
文献[13]	10.926 1	16.963 8	10.690 5	13.511 1	-
本文算法	8.740 9	13.571 0	8.552 4	10.808 9	28.099 7

[1]	WEI Jiazhen, BIAN Wei. A survey on research advances in consensus-based optimization algorithm [J]. Operations Research Transactions, 2026, 30(1): 1-23.
[2]	Bo ZHANG, Hongyu WANG, Yuelin GAO. A D.C. relaxation based branch-and-bound algorithm for sum-of-linear-products programming problems [J]. Operations Research Transactions, 2025, 29(4): 159-174.
[3]	Suxia MA, Yuelin GAO, Hongwei LIN, Bo ZHANG. A new non parameter-filled function method for global optimization [J]. Operations Research Transactions, 2025, 29(2): 141-157.
[4]	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.
[5]	Fusheng BAI, Mi LAN. An adaptive surrogate optimization method for expensive black-box problems with hidden constraints [J]. Operations Research Transactions, 2024, 28(1): 89-100.
[6]	Xiaoli HUANG, Yuelin GAO, Bo ZHANG, Xia LIU. An adaptive global optimization algorithm for solving quadratically constrained quadratic programming problems [J]. Operations Research Transactions, 2022, 26(2): 83-100.
[7]	Fusheng BAI, Dan FENG, Ke ZHANG. Combined response surface method with adaptive sampling for expensive black-box global optimization [J]. Operations Research Transactions, 2021, 25(2): 1-14.
[8]	Jiali CHEN, Ying ZHANG, Shenggang WANG, Xiaoying XIE. A new filled function and its application in data fitting problems [J]. Operations Research Transactions, 2021, 25(1): 81-88.
[9]	ZHAO Dan, GAO Yuelin. Non-parameter filled function method for nonlinear integer programming [J]. Operations Research Transactions, 2020, 24(4): 63-73.
[10]	CHEN Yong, WANG Wei, XU Yifan. An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion [J]. Operations Research Transactions, 2020, 24(1): 88-100.
[11]	WANG Weixiang, SHANG Youlin, WANG Duo. Filled function method for solving non-smooth box constrained global optimization problems [J]. Operations Research Transactions, 2019, 23(1): 28-34.
[12]	TIAN Mingyu, YANG Yongjian. A global optimization algorithm for polynomial programming [J]. Operations Research Transactions, 2018, 22(4): 79-88.
[13]	WU Peipei, GAO Yuelin. A new single parameter filled function method for nonlinear integer programming [J]. Operations Research Transactions, 2017, 21(3): 111-118.
[14]	ZHENG Yue, ZHUANG Daoyuan, WAN Zhongping. A global optimization method for solving the weak linear bilevel programming problems [J]. Operations Research Transactions, 2017, 21(3): 86-94.
[15]	SHI Litang, CHEN Wei. A filled-filter function algorithm for solving unconstrained nonlinear optimization [J]. Operations Research Transactions, 2017, 21(1): 55-64.

算法	算例1	算例2	算例3	算例4	算例5
文献[10]	-	-	-	-	11024
文献[13]	11267	4465	13014	4713	-
本文算法	10140	4019	11713	4478	9922