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
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.
[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>