IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i9p828-d264916.html
   My bibliography  Save this article

Optimal Randomness in Swarm-Based Search

Author

Listed:
  • Jiamin Wei

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
    School of Engineering, University of California, Merced, 5200 Lake Road, Merced, CA 95343, USA)

  • YangQuan Chen

    (School of Engineering, University of California, Merced, 5200 Lake Road, Merced, CA 95343, USA)

  • Yongguang Yu

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Yuquan Chen

    (School of Engineering, University of California, Merced, 5200 Lake Road, Merced, CA 95343, USA
    Department of Automation, University of Science and Technology of China, Hefei 230027, China)

Abstract

Lévy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that Lévy flights can maximize the efficiency of resource searching in uncertain environments and also the movements of many foragers and wandering animals have been shown to follow a Lévy distribution. The reason mainly comes from the fact that the Lévy distribution has an infinite second moment and hence is more likely to generate an offspring that is farther away from its parent. However, the investigation into the efficiency of other different heavy-tailed probability distributions in swarm-based searches is still insufficient up to now. For swarm-based search algorithms, randomness plays a significant role in both exploration and exploitation or diversification and intensification. Therefore, it is necessary to discuss the optimal randomness in swarm-based search algorithms. In this study, cuckoo search (CS) is taken as a representative method of swarm-based optimization algorithms, and the results can be generalized to other swarm-based search algorithms. In this paper, four different types of commonly used heavy-tailed distributions, including Mittag-Leffler distribution, Pareto distribution, Cauchy distribution, and Weibull distribution, are considered to enhance the searching ability of CS. Then four novel CS algorithms are proposed and experiments are carried out on 20 benchmark functions to compare their searching performances. Finally, the proposed methods are used to system identification to demonstrate the effectiveness.

Suggested Citation

  • Jiamin Wei & YangQuan Chen & Yongguang Yu & Yuquan Chen, 2019. "Optimal Randomness in Swarm-Based Search," Mathematics, MDPI, vol. 7(9), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:828-:d:264916
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/9/828/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/9/828/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    2. Zhao, Xuejing & Wang, Chen & Su, Jinxia & Wang, Jianzhou, 2019. "Research and application based on the swarm intelligence algorithm and artificial intelligence for wind farm decision system," Renewable Energy, Elsevier, vol. 134(C), pages 681-697.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed T. Hachemi & Fares Sadaoui & Abdelhakim Saim & Mohamed Ebeed & Hossam E. A. Abbou & Salem Arif, 2023. "Optimal Operation of Distribution Networks Considering Renewable Energy Sources Integration and Demand Side Response," Sustainability, MDPI, vol. 15(24), pages 1-32, December.
    2. Qi Xiong & Xinman Zhang & Shaobo He & Jun Shen, 2021. "A Fractional-Order Chaotic Sparrow Search Algorithm for Enhancement of Long Distance Iris Image," Mathematics, MDPI, vol. 9(21), pages 1-17, November.

    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. Ren, Jinfu & Liu, Yang & Liu, Jiming, 2023. "Chaotic behavior learning via information tracking," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Wang, Lei & Chen, Yi-Ming, 2020. "Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    4. Fendzi Donfack, Emmanuel & Nguenang, Jean Pierre & Nana, Laurent, 2020. "On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    6. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    7. Kailai Ni & Jianzhou Wang & Guangyu Tang & Danxiang Wei, 2019. "Research and Application of a Novel Hybrid Model Based on a Deep Neural Network for Electricity Load Forecasting: A Case Study in Australia," Energies, MDPI, vol. 12(13), pages 1-30, June.
    8. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    9. Boeing, Geoff, 2017. "Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction," SocArXiv c7p43, Center for Open Science.
    10. Md Tariqul Islam & M. J. Hossain, 2023. "Artificial Intelligence for Hosting Capacity Analysis: A Systematic Literature Review," Energies, MDPI, vol. 16(4), pages 1-33, February.
    11. Wafaa S. Sayed & Moheb M. R. Henein & Salwa K. Abd-El-Hafiz & Ahmed G. Radwan, 2017. "Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems," Complexity, Hindawi, vol. 2017, pages 1-17, February.
    12. Meng, Anbo & Zhu, Zibin & Deng, Weisi & Ou, Zuhong & Lin, Shan & Wang, Chenen & Xu, Xuancong & Wang, Xiaolin & Yin, Hao & Luo, Jianqiang, 2022. "A novel wind power prediction approach using multivariate variational mode decomposition and multi-objective crisscross optimization based deep extreme learning machine," Energy, Elsevier, vol. 260(C).
    13. Jianzhou Wang & Chunying Wu & Tong Niu, 2019. "A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network," Sustainability, MDPI, vol. 11(2), pages 1-34, January.
    14. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    15. Das, Saptarshi & Pan, Indranil & Das, Shantanu, 2016. "Effect of random parameter switching on commensurate fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 157-173.
    16. Yu, Qiang & Turner, Ian & Liu, Fawang & Vegh, Viktor, 2022. "The application of the distributed-order time fractional Bloch model to magnetic resonance imaging," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    17. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    18. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    19. Runzi Luo & Haipeng Su, 2018. "The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output," Complexity, Hindawi, vol. 2018, pages 1-8, November.
    20. Ibrahim Mohamed Diaaeldin & Mahmoud A. Attia & Amr K. Khamees & Othman A. M. Omar & Ahmed O. Badr, 2023. "A Novel Multiobjective Formulation for Optimal Wind Speed Modeling via a Mixture Probability Density Function," Mathematics, MDPI, vol. 11(6), pages 1-19, March.

    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:gam:jmathe:v:7:y:2019:i:9:p:828-:d:264916. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.