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CLC number: TP3-05

On-line Access: 2019-11-11

Received: 2019-03-19

Revision Accepted: 2019-08-21

Crosschecked: 2019-10-10

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Citations:  Bibtex RefMan EndNote GB/T7714


Yan Huang


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Frontiers of Information Technology & Electronic Engineering  2019 Vol.20 No.10 P.1344-1360


Unusual phenomenon of optimizing the Griewank function with the increase of dimension

Author(s):  Yan Huang, Jian-ping Li, Peng Wang

Affiliation(s):  School of Computer Science and Technology, Huaiyin Normal University, Huai'an 223000, China; more

Corresponding email(s):   hep128@qq.com, jpli2222@uestc.edu.cn, qhoalab@163.com

Key Words:  Griewank, Two-scale structure, Multi-scale quantum harmonic oscillator algorithm, Quantum tunnel effect

Yan Huang, Jian-ping Li, Peng Wang. Unusual phenomenon of optimizing the Griewank function with the increase of dimension[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1344-1360.

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author="Yan Huang, Jian-ping Li, Peng Wang",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

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%T Unusual phenomenon of optimizing the Griewank function with the increase of dimension
%A Yan Huang
%A Jian-ping Li
%A Peng Wang
%J Frontiers of Information Technology & Electronic Engineering
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%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900155

T1 - Unusual phenomenon of optimizing the Griewank function with the increase of dimension
A1 - Yan Huang
A1 - Jian-ping Li
A1 - Peng Wang
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 20
IS - 10
SP - 1344
EP - 1360
%@ 2095-9184
Y1 - 2019
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1900155

The griewank function is a typical multimodal benchmark function, composed of a quadratic convex function and an oscillatory nonconvex function. The comparative importance of griewank’s two major parts alters in different dimensions. Different from most test functions, an unusual phenomenon appears when optimizing the griewank function. The griewank function first becomes more difficult and then becomes easier to optimize with the increase of dimension. In this study, from the methodology perspective, this phenomenon is explained by structural, mathematical, and quantum analyses. Furthermore, frequency transformation and amplitude transformation are implemented on the griewank function to make a generalization. The multi-scale quantum harmonic oscillator algorithm (MQHOA) with quantum tunnel effect is used to verify its characteristics. Experimental results indicate that the griewank function’s two-scale structure is the main reason for this phenomenon. The quantum tunneling mechanism mentioned in this paper is an effective method which can be generalized to analyze the generation and variation of solutions for numerous swarm optimization algorithms.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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