Full Text:   <2221>

Summary:  <1847>

CLC number: TP3-05

On-line Access: 2019-11-11

Received: 2019-03-19

Revision Accepted: 2019-08-21

Crosschecked: 2019-10-10

Cited: 0

Clicked: 5459

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yan Huang

http://orcid.org/0000-0003-3896-5636

-   Go to

Article info.
Open peer comments

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

http://doi.org/10.1631/FITEE.1900155


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.

@article{title="Unusual phenomenon of optimizing the Griewank function with the increase of dimension",
author="Yan Huang, Jian-ping Li, Peng Wang",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="20",
number="10",
pages="1344-1360",
year="2019",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1900155"
}

%0 Journal Article
%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
%V 20
%N 10
%P 1344-1360
%@ 2095-9184
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1900155

TY - JOUR
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
ER -
DOI - 10.1631/FITEE.1900155


Abstract: 
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.

Griewank函数优化过程中的独特现象研究

摘要:Griewank函数是一类由二次凸函数和振荡非凸函数构成的典型多模测试函数。这两个组成部分在不同维数下显示出不同的相对重要性。不同于其他多数测试函数,随着函数维数增加,Griewank函数在优化过程出现优化难度先变难、后变易的现象。本文首先通过结构分析、数学分析和量子分析,从方法论角度解释该现象。然后,通过频率变换和幅度变换对Griewank函数作一般化处理。运用具有量子隧道效应的多尺度量子谐振子算法验证Griewank函数特性。实验结果表明Griewank函数的双尺度结构是该现象的主要原因。本文所提量子隧道效应可用于多种群体优化算法中分析解的生成和变化。

关键词:Griewank;双尺度结构;多尺度量子谐振子算法;量子隧道效应

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

Reference

[1]Akay B, Karaboga D, 2012. A modified artificial bee colony algorithm for real-parameter optimization. Inform Sci, 192(1):120-142.

[2]Akbari R, Mohammadi A, Ziarati K, 2010. A novel bee swarm optimization algorithm for numerical function optimization. Commun Nonl Sci Numer Simul, 15(10):3142-3155.

[3]Chen DB, Zhao CX, 2009. Particle swarm optimization with adaptive population size and its application. Appl Soft Comput, 9(1):39-48.

[4]Cho H, Olivera F, Guikema SD, 2008. A derivation of the number of minima of the Griewank function. Appl Math Comput, 204(2):694-701.

[5]Gao WF, Liu SY, Huang LL, 2012. A global best artificial bee colony algorithm for global optimization. J Comput Appl Math, 236(11):2741-2753.

[6]Griewank AO, 1981. Generalized descent for global optimization. J Optim Theory Appl, 34(1):11-39.

[7]Karaboga D, Basturk B, 2007. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim, 39(3):459-471.

[8]Kirkpatrick S, Gelatt CDJr, Vecchi MP, 1983. Optimization by simulated annealing. Science, 220(4598):671-680.

[9]Ksikążek K, Połap D, Woźniak M, et al., 2017. Radiation heat transfer optimization by the use of modified ant lion optimizer. Proc IEEE Symp Series on Computational Intelligence.

[10]Liang JJ, Qu BY, Suganthan PN, 2013. Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-parameter Numerical Optimization. Technical Report No. 201311, Zhengzhou University, Zhengzhou, China.

[11]Locatelli M, 2003. A note on the Griewank test function. J Glob Optim, 25(2):169-174.

[12]Muthukrishnan S, Albash T, Lidar DA, 2016. Tunneling and speedup in quantum optimization for permutation-symmetric problems. Phys Rev X, 6(3):031010.

[13]Oftadeh R, Mahjoob MJ, Shariatpanahi M, 2010. A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search. Comput Math Appl, 60(7):2087-2098.

[14]Polap D, Woźniak M, 2017. Polar bear optimization algorithm: meta-heuristic with fast population movement and dynamic birth and death mechanism. Symmetry, 9(10), Article 203.

[15]Qin AK, Huang VL, Suganthan PN, 2009. Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput, 13(2):398-417.

[16]Rao RV, Savsani VJ, Vakharia DP, 2012. Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems. Inform Sci, 183(1):1-15.

[17]Shi Y, Eberhart RC, 1999. Empirical study of particle swarm optimization. Proc Congress on Evolutionary Computation, p.1945-1950.

[18]Tan Y, Zhu YC, 2010. Fireworks algorithm for optimization. Proc 1$^rm st$ Int Conf on Advances in Swarm Intelligence, p.355-364.

[19]Wang P, Huang Y, Ren C, et al., 2013. Multi-scale quantum harmonic oscillator for high-dimensional function global optimization algorithm. Acta Electron Sin, 41(12):2468-2473 (in Chinese).

[20]Wang P, Huang Y, An JX, et al., 2016. Performance analysis of multi-scale quantum harmonic oscillator global optimization algorithm in combinatorial optimization problems. J Univ Electron Sci Technol China, 45(3):469-474 (in Chinese).

[21]Wang P, Cheng K, Huang Y, et al., 2018a. Multiscale quantum harmonic oscillator algorithm for multimodal optimization. Comput Intell Neurosci, 2018:8430175.

[22]Wang P, Ye XG, Li B, et al., 2018b. Multi-scale quantum harmonic oscillator algorithm for global numerical optimization. Appl Soft Comput, 69:655-670.

[23]Wang P, Li B, Jin J, et al., 2018c. Multi-scale quantum harmonic oscillator algorithm with individual stabilization strategy. Proc 9th Int Conf on Swarm Intelligence, p.624-633.

[24]Wang PP, Chen DS, 1996. Continuous optimization by a variant of simulated annealing. Comput Optim Appl, 6(1):59-71.

[25]Woźniak M, Ksikąźek K, Marciniec J, et al., 2018. Heat production optimization using bio-inspired algorithms. Eng Appl Artif Intell, 76:185-201.

[26]Zambrano-Bigiarini M, Clerc M, Rojas R, 2013. Standard particle swarm optimisation 2011 at CEC-2013: a baseline for future PSO improvements. Proc IEEE Congress on Evolutionary Computation, p.2337-2344.

[27]Zhang LP, Yu HJ, Hu SX, 2003. A new approach to improve particle swarm optimization. Proc Genetic and Evolutionary Computation Conf, p.134-139.

[28]Zhou DD, Shi YH, Cheng S, 2012. Brain storm optimization algorithm with modified step-size and individual generation. Proc 3rd Int Conf on Advances in Swarm Intelligence, p.243-252.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE