Griewank函数优化过程中的独特现象研究

黄焱; 李建平; 王鹏

doi:10.1631/FITEE.1900155

Your Location：

Home >

Browse articles >

Griewank函数优化过程中的独特现象研究

常规文章 | Updated：2022-05-19

- Griewank函数优化过程中的独特现象研究
- Unusual phenomenon of optimizing the Griewank function with the increase of dimension
- 信息与电子工程前沿（英文） 2019年20卷第10期页码：1344-1360
- Affiliations：
  
  School of Computer Science and Technology, Huaiyin Normal University, Huaioan 223000, China
  School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
  Jiangsu Key Laboratory of Media Design and Software Technology, Jiangnan University, Wuxi 214122, China
  School of Computer Science and Technology, Southwest Minzu University, Chengdu 610225, China
- Author bio：
  
  [ "Yan HUANG, E-mail: hep128@qq.com" ]
  Jian-ping LI, jpli2222@uestc.edu.cn
  [ "Peng WANG, qhoalab@163.com" ]
- Funds：
  
  Project supported by the Natural Science Foundation of Huaioan, China (No. HAB201828), the Fundamental Research Funds for the Central Universities of China (No. 2019NYB22), and the Open Foundation of Jiangsu Key Laboratory of Media Design and Software Technology, China (Nos. 19ST0204 and 18ST0203)
- DOI：10.1631/FITEE.1900155
  中图分类号： TP3-05
- 收稿：2019-03-19，
  
  修回：2019-10-10，
  
  纸质出版：2019-10
- Accepted：
Scan QR Code
黄焱, 李建平, 王鹏. Griewank函数优化过程中的独特现象研究[J]. 信息与电子工程前沿（英文）, 2019,20(10):1344-1360.

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.
黄焱, 李建平, 王鹏. Griewank函数优化过程中的独特现象研究[J]. 信息与电子工程前沿（英文）, 2019,20(10):1344-1360. DOI： 10.1631/FITEE.1900155.

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. DOI： 10.1631/FITEE.1900155.

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。

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 Griewankos 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 functionos 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.

关键词

Keywords

references

B Akay , , , D Karaboga . . A modified artificial bee colony algorithm for real-parameter optimization . . Inform Sci , , 2012 . . 192 ( ( 1 ): ): 120 - - 142 . . DOI: 10.1016/j.ins.2010.07.015 http://doi.org/10.1016/j.ins.2010.07.015 . .

R Akbari , , , A Mohammadi , , , K Ziarati . . A novel bee swarm optimization algorithm for numerical function optimization . . Commun Nonl Sci Numer Simul , , 2010 . . 15 ( ( 10 ): ): 3142 - - 3155 . . DOI: 10.1016/j.cnsns.2009.11.003 http://doi.org/10.1016/j.cnsns.2009.11.003 . .

DB Chen , , , CX Zhao . . Particle swarm optimization with adaptive population size and its application . . Appl Soft Comput , , 2009 . . 9 ( ( 1 ): ): 39 - - 48 . . DOI: 10.1016/j.asoc.2008.03.001 http://doi.org/10.1016/j.asoc.2008.03.001 . .

H Cho , , , F Olivera , , , SD Guikema . . A derivation of the number of minima of the Griewank function . . Appl Math Comput , , 2008 . . 204 ( ( 2 ): ): 694 - - 701 . . DOI: 10.1016/j.amc.2008.07.009 http://doi.org/10.1016/j.amc.2008.07.009 . .

WF Gao , , , SY Liu , , , LL Huang . . A global best artificial bee colony algorithm for global optimization . . J Comput Appl Math , , 2012 . . 236 ( ( 11 ): ): 2741 - - 2753 . . DOI: 10.1016/j.cam.2012.01.013 http://doi.org/10.1016/j.cam.2012.01.013 . .

AO Griewank . . Generalized descent for global optimization . . J Optim Theory Appl , , 1981 . . 34 ( ( 1 ): ): 11 - - 39 . . DOI: 10.1007/BF00933356 http://doi.org/10.1007/BF00933356 . .

D Karaboga , , , B Basturk . . A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm . . J Glob Optim , , 2007 . . 39 ( ( 3 ): ): 459 - - 471 . . DOI: 10.1007/s10898-007-9149-x http://doi.org/10.1007/s10898-007-9149-x . .

S Kirkpatrick , , , CDJr Gelatt , , , MP Vecchi . . Optimization by simulated annealing . . Science , , 1983 . . 220 ( ( 4598 ): ): 671 - - 680 . . DOI: 10.1126/science.220.4598.671 http://doi.org/10.1126/science.220.4598.671 . .

K Książek , , , D Połap , , , M Woźniak , , , 等 . . Radiation heat transfer optimization by the use of modified ant lion optimizer . . Proc IEEE Symp Series on Computational Intelligence , , 1981 . . DOI: 10.1109/SSCI.2017.8280853 http://doi.org/10.1109/SSCI.2017.8280853 . .

JJ Liang , , , BY Qu , , , PN Suganthan . . 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 , , 2013 . . .

M Locatelli . . A note on the Griewank test function . . J Glob Optim , , 2003 . . 25 ( ( 2 ): ): 169 - - 174 . . DOI: 10.1023/A:1021956306041 http://doi.org/10.1023/A:1021956306041 . .

S Muthukrishnan , , , T Albash , , , DA Lidar . . Tunneling and speedup in quantum optimization for permutation-symmetric problems . . Phys Rev X , , 2016 . . 6 ( ( 3 ): ): 031010 DOI: 10.1103/PhysRevX.6.031010 http://doi.org/10.1103/PhysRevX.6.031010 . .

R Oftadeh , , , MJ Mahjoob , , , M Shariatpanahi . . A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search . . Comput Math Appl , , 2010 . . 60 ( ( 7 ): ): 2087 - - 2098 . . DOI: 10.1016/j.camwa.2010.07.049 http://doi.org/10.1016/j.camwa.2010.07.049 . .

D Połap , , , M Woźniak . . Polar bear optimization algorithm: meta-heuristic with fast population movement and dynamic birth and death mechanism . . Symmetry , , 2017 . . 9 ( ( 10 ): ): Article 203 DOI: 10.3390/sym9100203 http://doi.org/10.3390/sym9100203 . .

AK Qin , , , VL Huang , , , PN Suganthan . . Differential evolution algorithm with strategy adaptation for global numerical optimization . . IEEE Trans Evol Comput , , 2009 . . 13 ( ( 2 ): ): 398 - - 417 . . DOI: 10.1109/TEVC.2008.927706 http://doi.org/10.1109/TEVC.2008.927706 . .

RV Rao , , , VJ Savsani , , , DP Vakharia . . Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems . . Inform Sci , , 2012 . . 183 ( ( 1 ): ): 1 - - 15 . . DOI: 10.1016/j.ins.2011.08.006 http://doi.org/10.1016/j.ins.2011.08.006 . .

Y Shi , , , RC Eberhart . . Empirical study of particle swarm optimization . . Proc Congress on Evolutionary Computation , , 1999 . . 1945 - - 1950 . . DOI: 10.1109/CEC.1999.785511 http://doi.org/10.1109/CEC.1999.785511 . .

Y Tan , , , YC Zhu . . Fireworks algorithm for optimization . . Proc 1 st Int Conf on Advances in Swarm Intelligence , , 2010 . . 355 - - 364 . . DOI: 10.1007/978-3-642-13495-1_44 http://doi.org/10.1007/978-3-642-13495-1_44 . .

P Wang , , , Y Huang , , , C Ren , , , 等 . . Multi-scale quantum harmonic oscillator for high-dimensional function global optimization algorithm . . Acta Electron Sin , , 2013 . . 41 ( ( 12 ): ): 2468 - - 2473 . . DOI: 10.3969/j.issn.0372-2112.2013.12.023 http://doi.org/10.3969/j.issn.0372-2112.2013.12.023 . .

P Wang , , , Y Huang , , , JX An , , , 等 . . Performance analysis of multi-scale quantum harmonic oscillator global optimization algorithm in combinatorial optimization problems . . J Univ Electron Sci Technol China , , 2016 . . 45 ( ( 3 ): ): 469 - - 474 . . DOI: 10.3969/j.issn.1001-0548.2016.02.027 http://doi.org/10.3969/j.issn.1001-0548.2016.02.027 . .

P Wang , , , K Cheng , , , Y Huang , , , 等 . . Multiscale quantum harmonic oscillator algorithm for multimodal optimization . . Comput Intell Neurosci , , 2018a . . 2018 8430175 DOI: 10.1155/2018/8430175 http://doi.org/10.1155/2018/8430175 . .

P Wang , , , XG Ye , , , B Li , , , 等 . . Multi-scale quantum harmonic oscillator algorithm for global numerical optimization . . Appl Soft Comput , , 2018b . . 69 655 - - 670 . . DOI: 10.1016/j.asoc.2018.05.005 http://doi.org/10.1016/j.asoc.2018.05.005 . .

P Wang , , , B Li , , , J Jin , , , 等 . . Multi-scale quantum harmonic oscillator algorithm with individual stabilization strategy . . Proc 9 th Int Conf on Swarm Intelligence , , 2018c . . 624 - - 633 . . DOI: 10.1007/978-3-319-93815-8_59 http://doi.org/10.1007/978-3-319-93815-8_59 . .

PP Wang , , , DS Chen . . Continuous optimization by a variant of simulated annealing . . Comput Optim Appl , , 1996 . . 6 ( ( 1 ): ): 59 - - 71 . . DOI: 10.1007/BF00248009 http://doi.org/10.1007/BF00248009 . .

M Woźniak , , , K Książek , , , J Marciniec , , , 等 . . Heat production optimization using bio-inspired algorithms . . Eng Appl Artif Intell , , 2018 . . 76 185 - - 201 . . DOI: 10.1016/j.engappai.2018.09.003 http://doi.org/10.1016/j.engappai.2018.09.003 . .

M Zambrano-Bigiarini , , , M Clerc , , , R Rojas . . Standard particle swarm optimisation 2011 at CEC-2013: a baseline for future PSO improvements . . Proc IEEE Congress on Evolutionary Computation , , 2013 . . 2337 - - 2344 . . DOI: 10.1109/CEC.2013.6557848 http://doi.org/10.1109/CEC.2013.6557848 . .

LP Zhang , , , HJ Yu , , , SX Hu . . A new approach to improve particle swarm optimization . . Proc Genetic and Evolutionary Computation Conf , , 2003 . . 134 - - 139 . . DOI: 10.1007/3-540-45105-6_12 http://doi.org/10.1007/3-540-45105-6_12 . .

DD Zhou , , , YH Shi , , , S Cheng . . Brain storm optimization algorithm with modified step-size and individual generation . . Proc 3 rd Int Conf on Advances in Swarm Intelligence , , 2012 . . 243 - - 252 . . DOI: 10.1007/978-3-642-30976-2_29 http://doi.org/10.1007/978-3-642-30976-2_29 . .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

暂无数据