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《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

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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

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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
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