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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
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    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.
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    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 1-34, 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.

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