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.

Figures/Tables 7

References 15

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

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Figures/Tables 7

References 15

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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

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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