JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (7): 80-87.doi: 10.6040/j.issn.1671-9352.0.2022.344

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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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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

CLC Number: 

  • TP301

Fig.1

Illustration of the new filled function method"

Table 1

Results of the HSFF algorithm"

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

Table 2

Comparison results of the three filled function algorithms"

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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