您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (7): 80-87.doi: 10.6040/j.issn.1671-9352.0.2022.344

•   • 上一篇    下一篇

求解全局优化问题的一个新的填充函数算法

刘海燕*(),拓守恒   

  1. 西安邮电大学计算机学院, 陕西 西安 710121
  • 收稿日期:2022-06-23 出版日期:2023-07-20 发布日期:2023-07-05
  • 通讯作者: 刘海燕 E-mail:hyliu83@126.com
  • 作者简介:刘海燕(1983—)，女，博士，讲师，研究方向为优化建模、进化算法、大规模全局优化算法. E-mail：hyliu83@126.com
  • 基金资助:
    国家自然科学基金资助项目(62002289)

A new filled function method for global optimization

Haiyan LIU*(),Shouheng TUO   

  1. School of Computer Science and Technology, Xi'an University of Posts and Telecommunications, Xi'an 710121, Shaanxi, China
  • Received:2022-06-23 Online:2023-07-20 Published:2023-07-05
  • Contact: Haiyan LIU E-mail:hyliu83@126.com

RichHTML

1

PDF (PC)

442

摘要：

构造了一个新的单参数且连续可微的填充函数，并将其与进化算法相结合提出了一个新的填充函数算法。该算法通过不断跳出局部最优解进入更优解所在区域的方式来提高优化效率，通过设置进化算法中种群均匀分布、增加种群多样性的方式增加了算法的全局寻优性能，并将该算法在标准测试集上进行了测试。结果表明, 该算法简单有效，并且随着优化问题维度的提高而表现稳定。

关键词: 填充函数, 全局优化, 局部搜索, 进化算法, 多峰函数

Abstract:

A new hybrid single-parameter filled function is proposed which is also continuous and differentiable. Combined with an evolutionary algorithm, a new filled function algorithm is proposed. The new filled function algorithm can improve the efficiency of the optimization by repeatedly escaping from current local optimum to better areas with better solutions. To enhance the explore ability of the proposed algorithm, we use uniform distribution to make better population diversity. Numerical experiments show the simplicity and efficiency of the proposed algorithm.

Key words: filled function, global optimization, local search, evolutionary algorithm, multimodal function

中图分类号: 

  • TP301

图1

新的填充函数方法的图像"

表1

HSFF的数值实验结果"

No n Iter FEs a Rate/%
1 2 4.20 312.00 0.43 93.33
2 2(c=0.2) 4.53 236.80 0.30 100.00
2(c=0.5) 3.53 181.47 0.30 86.67
2(c=0.05) 5.20 257.67 0.30 100.00
3 2 2.53 117.53 0.30 100.00
4 2 2.67 126.80 0.30 100.00
5 2 3.73 173.27 0.30 100.00
6 2 5.27 402.67 0.94 100.00
7 2 3.40 186.47 0.30 100.00
3 4.00 315.93 0.30 100.00
5 4.93 692.93 0.30 100.00
7 4.73 1 090.53 0.30 100.00
10 6.60 2 541.20 0.30 100.00

表2

3个填充函数的对比结果"

No n 文献[1]的填充函数方法 文献[7]的填充函数方法 HSFF
Iter Ff Fg Iter Ff Fg Iter Ff Fg
1 2 4 21 276 460 2 315 0 4.20 312.00 0
2 2 15 27 500 942 2 778 0 4.53 236.80 0
34 54 505 2 500 2 310 0 3.53 181.47 0
35 38 424 1 940 3 977 0 5.20 257.67 0
3 2 32 92 498 2 203 2 577 0 2.53 117.53 0
4 2 44 35 171 2 319 2 303 0 2.67 126.80 0
5 2 14 15 759 671 2 265 0 3.73 173.27 0
6 2 20 103 988 1 861 3 635 0 5.27 402.67 0
7 2 22 107 899 2 445 3 549 0 3.40 186.47 0
3 6 248 407 3 976 2 1 283 0 4.00 315.93 0
5 16 1 229 860 13 644 2 5 291 0 4.93 692.93 0
7 21 1 443 686 16 661 2 12 793 0 4.73 1 090.53 0
10 16 1 829 898 23 955 2 33 810 0 6.60 2 541.20 0
1 GE Renpu . A filled function method for finding a global minimizer of a function of several variables[J]. Mathematical Programming, 1990, 46 (1): 191- 204.
2 LIU Xian . Finding global minima with a computable filled function[J]. Journal of Global Optimization, 2001, 19 (2): 151- 161.
doi: 10.1023/A:1008330632677
3 WANG Weixiang , SHANG Youlin , ZHANG Liansheng . A filled function method with one parameter for box constrained global optimization[J]. Applied Mathematics and Computation, 2007, 194 (1): 54- 66.
doi: 10.1016/j.amc.2007.04.011
4 ZHANG Ying , XU Yingtao . A one-parameter filled function method applied to nonsmooth constrained global optimization[J]. Computers & Mathematics with Applications, 2009, 58 (6): 1230- 1238.
5 HE Suxiang , CHEN Weilai , WANG Hui . A new filled function algorithm for constrained global optimization problems[J]. Applied Mathematics and Computation, 2011, 217 (12): 5853- 5859.
doi: 10.1016/j.amc.2010.12.070
6 李忠豪, 张连生, 杨永健. 不等式约束全局优化的填充函数法[J]. 中国海洋大学学报(自然科学版), 2013, 43 (11): 117- 120.
doi: 10.16441/j.cnki.hdxb.2013.11.017
LI Zhonghao , ZHANG Liansheng , YANG Yongjian . Filling function method for global optimization with inequality constraints[J]. Journal of Ocean University of China(Natural Science), 2013, 43 (11): 117- 120.
doi: 10.16441/j.cnki.hdxb.2013.11.017
7 EL-GINDY T M , SALIM M S , AHMED A I . A new filled function method applied to unconstrained global optimization[J]. Applied Mathematics and Computation, 2016, 273, 1246- 1256.
doi: 10.1016/j.amc.2015.08.091
8 LIU Xian , XU Wilsun . A new filled function applied to global optimization[J]. Computers & Operations Research, 2004, 31 (1): 61- 80.
doi: 10.3969/j.issn.1001-3695.2004.01.018
9 ZHANG Liansheng , NG Chikong , LI Duan , et al. A new filled function method for global optimization[J]. Journal of Global Optimization, 2004, 28 (1): 17- 43.
doi: 10.1023/B:JOGO.0000006653.60256.f6
10 YANG Yongjian , SHANG Youlin . A new filled function method for unconstrained global optimization[J]. Applied Mathematics and Computation, 2006, 173 (1): 501- 512.
doi: 10.1016/j.amc.2005.04.046
11 WANG Chengjun , YANG Yongjian , LI Jing . A new filled function method for unconstrained global optimization[J]. Journal of Computational and Applied Mathematics, 2009, 225 (1): 68- 79.
doi: 10.1016/j.cam.2008.07.001
12 GAO Yuelin , YANG Yongjian , YOU Mi . A new filled function method for global optimization[J]. Applied Mathematics and Computation, 2015, 268, 685- 695.
doi: 10.1016/j.amc.2015.06.090
13 LIU Xian . A class of continuously differentiable filled functions for global optimization[J]. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 2008, 38 (1): 38- 47.
doi: 10.1109/TSMCA.2007.909554
14 ZHANG Ying , ZHANG Liansheng , XU Yingtao . New filled functions for nonsmooth global optimization[J]. Applied Mathematical Modelling, 2009, 33 (7): 3114- 3129.
doi: 10.1016/j.apm.2008.10.015
15 LIN Hongwei , WANG Yuping , FAN Lei . A filled function method with one parameter for unconstrained global optimization[J]. Applied Mathematics and Computation, 2011, 218 (7): 3776- 3785.
doi: 10.1016/j.amc.2011.09.022
16 WEI Fei , WANG Yuping . A new filled function method with one parameter for global optimization[J]. Mathematical Problems in Engineering, 2013, (2013): 532325.
17 WEI Fei , WANG Yuping , LIN Hongwei . A new filled function method with two parameters for global optimization[J]. Journal of Optimization Theory and Applications, 2014, 163 (2): 510- 527.
doi: 10.1007/s10957-013-0515-1
18 LIU Haiyan , WANG Yuping , GUAN Shiwei , et al. A new filled function method for unconstrained global optimization[J]. International Journal of Computer Mathematics, 2017, 94 (12): 2283- 2296.
doi: 10.1080/00207160.2017.1283021
19 LIU Haiyan , WANG Yuping , GAO Xiaozhi , et al. A parameter free filled function method for global optimization[J]. Pacific Journal of Optimization, 2018, 14 (4): 567- 580.
20 PANDIYA R , WIDODO W , ENDRAYANTO I . Non parameter-filled function for global optimization[J]. Applied Mathematics and Computation, 2021, 391, 125642.
doi: 10.1016/j.amc.2020.125642
21 屈德强, 尚有林, 詹悦, 等. 全局优化问题的一个新的无参数填充函数[J]. 运筹学学报, 2021, 25 (1): 89- 95.
doi: 10.15960/j.cnki.issn.1007-6093.2021.01.008
QU Deqiang , SHANG Youlin , ZHAN Yue , et al. A new parameterless filled function for the global optimization problems[J]. Operations Research Transactions, 2021, 25 (1): 89- 95.
doi: 10.15960/j.cnki.issn.1007-6093.2021.01.008
[1] 曲滨鹏, 王智昊. 基于粒子群优化的适应Memetic算法分析[J]. 山东大学学报（理学版）, 2014, 49(08): 118-124.
[2] 王开荣,马琳. 广义几何规划的加速全局优化算法[J]. J4, 2013, 48(1): 72-77.
[3] 李彬1,2,李贻斌1,荣学文1. ELM-RBF神经网络的智能优化策略[J]. J4, 2010, 45(5): 48-51.
[4] 宋乐辉,陈月辉,潘 萌 . 动态系统的演化建模[J]. J4, 2008, 43(11): 27-30 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 杨军. 金属基纳米材料表征和纳米结构调控[J]. 山东大学学报（理学版）, 2013, 48(1): 1 -22 .
[2] 董伟伟. 一种具有独立子系统的决策单元DEA排序新方法[J]. J4, 2013, 48(1): 89 -92 .
[3] 张京友,张培爱,钟海萍. 进化图论在知识型企业组织结构设计中的应用[J]. J4, 2013, 48(1): 107 -110 .
[4] 赵君1,赵晶2,樊廷俊1*,袁文鹏1,3,张铮1,丛日山1. 水溶性海星皂苷的分离纯化及其抗肿瘤活性研究[J]. J4, 2013, 48(1): 30 -35 .
[5] 杨永伟1,2,贺鹏飞2,李毅君2,3. BL-代数的严格滤子[J]. 山东大学学报（理学版）, 2014, 49(03): 63 -67 .
[6] 李敏1,2,李歧强1. 不确定奇异时滞系统的观测器型滑模控制器[J]. 山东大学学报（理学版）, 2014, 49(03): 37 -42 .
[7] 廖明哲. 哥德巴赫的两个猜想[J]. J4, 2013, 48(2): 1 -14 .
[8] 赵同欣1,刘林德1*,张莉1,潘成臣2,贾兴军1. 紫藤传粉昆虫与花粉多型性研究[J]. 山东大学学报（理学版）, 2014, 49(03): 1 -5 .
[9] 王开荣,高佩婷. 建立在DY法上的两类混合共轭梯度法[J]. 山东大学学报（理学版）, 2016, 51(6): 16 -23 .
[10] 唐风琴1,白建明2. 一类带有广义负上限相依索赔额的风险过程大偏差[J]. J4, 2013, 48(1): 100 -106 .
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发