IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i4p1366-1375.html
   My bibliography  Save this article

On the efficiency of chaos optimization algorithms for global optimization

Author

Listed:
  • Yang, Dixiong
  • Li, Gang
  • Cheng, Gengdong

Abstract

Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions.

Suggested Citation

  • Yang, Dixiong & Li, Gang & Cheng, Gengdong, 2007. "On the efficiency of chaos optimization algorithms for global optimization," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1366-1375.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1366-1375
    DOI: 10.1016/j.chaos.2006.04.057
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906004334
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.04.057?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Tang, Fang & Huang, De-Xian, 2005. "Improved particle swarm optimization combined with chaos," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1261-1271.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ivona Brajević & Jelena Ignjatović, 2019. "An upgraded firefly algorithm with feasibility-based rules for constrained engineering optimization problems," Journal of Intelligent Manufacturing, Springer, vol. 30(6), pages 2545-2574, August.
    2. Hossein Lotfi, 2022. "A Multiobjective Evolutionary Approach for Solving the Multi-Area Dynamic Economic Emission Dispatch Problem Considering Reliability Concerns," Sustainability, MDPI, vol. 15(1), pages 1-23, December.
    3. He, Qie & Wang, Ling & Liu, Bo, 2007. "Parameter estimation for chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 654-661.
    4. Adel Taieb & Moêz Soltani & Abdelkader Chaari, 2017. "Parameter Optimization of MIMO Fuzzy Optimal Model Predictive Control By APSO," Complexity, Hindawi, vol. 2017, pages 1-11, October.
    5. Mohamad Javad Alizadeh & Davoud Ahmadyar & Ali Afghantoloee, 2017. "Improvement on the Existing Equations for Predicting Longitudinal Dispersion Coefficient," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(6), pages 1777-1794, April.
    6. Hong, Wei-Chiang, 2010. "Application of chaotic ant swarm optimization in electric load forecasting," Energy Policy, Elsevier, vol. 38(10), pages 5830-5839, October.
    7. Jinn-Tong Chiu & Ching-Hai Lin, 2016. "A Modified Particle Swarm Optimization Based on Eagle Foraging Behavior," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 703-727, May.
    8. Li, Yuanmao & Liu, Guixiong & Deng, Wei & Li, Zuyu, 2024. "Comparative study on parameter identification of an electrochemical model for lithium-ion batteries via meta-heuristic methods," Applied Energy, Elsevier, vol. 367(C).
    9. Anouar Farah & Akram Belazi & Khalid Alqunun & Abdulaziz Almalaq & Badr M. Alshammari & Mohamed Bechir Ben Hamida & Rabeh Abbassi, 2021. "A New Design Method for Optimal Parameters Setting of PSSs and SVC Damping Controllers to Alleviate Power System Stability Problem," Energies, MDPI, vol. 14(21), pages 1-26, November.
    10. Peng, Bo & Liu, Bo & Zhang, Fu-Yi & Wang, Ling, 2009. "Differential evolution algorithm-based parameter estimation for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2110-2118.
    11. Alatas, Bilal & Akin, Erhan & Ozer, A. Bedri, 2009. "Chaos embedded particle swarm optimization algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1715-1734.
    12. Sadeghian, Hamidreza & Wang, Zhifang, 2020. "A novel impact-assessment framework for distributed PV installations in low-voltage secondary networks," Renewable Energy, Elsevier, vol. 147(P1), pages 2179-2194.
    13. Borghi, Giacomo & Grassi, Sara & Pareschi, Lorenzo, 2023. "Consensus based optimization with memory effects: Random selection and applications," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    14. Jui-Ho Chen & Her-Terng Yau & Weir Hung, 2014. "Design and Study on Sliding Mode Extremum Seeking Control of the Chaos Embedded Particle Swarm Optimization for Maximum Power Point Tracking in Wind Power Systems," Energies, MDPI, vol. 7(3), pages 1-15, March.
    15. Alfi, Alireza, 2012. "Chaos suppression on a class of uncertain nonlinear chaotic systems using an optimal H∞ adaptive PID controller," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 351-357.
    16. Lian, Zhigang & Gu, Xingsheng & Jiao, Bin, 2008. "A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 851-861.
    17. Arturo Valdivia-González & Daniel Zaldívar & Erik Cuevas & Marco Pérez-Cisneros & Fernando Fausto & Adrián González, 2017. "A Chaos-Embedded Gravitational Search Algorithm for the Identification of Electrical Parameters of Photovoltaic Cells," Energies, MDPI, vol. 10(7), pages 1-25, July.
    18. Hengliang Guo & Yanling Guo & Wenyu Zhang & Xiaohui He & Zongxi Qu, 2021. "Research on a Novel Hybrid Decomposition–Ensemble Learning Paradigm Based on VMD and IWOA for PM 2.5 Forecasting," IJERPH, MDPI, vol. 18(3), pages 1-19, January.
    19. Guedes, Priscila F.S. & Mendes, Eduardo M.A.M. & Nepomuceno, Erivelton, 2022. "Effective computational discretization scheme for nonlinear dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    20. Yu, Haiquan & Zhou, Jianxin & Si, Fengqi & Nord, Lars O., 2022. "Combined heat and power dynamic economic dispatch considering field operational characteristics of natural gas combined cycle plants," Energy, Elsevier, vol. 244(PA).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1366-1375. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.