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Survey of Lévy Flight-Based Metaheuristics for Optimization

Author

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  • Juan Li

    (School of Artificial Intelligence, Wuchang University of Technology, Wuhan 430223, China
    Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China)

  • Qing An

    (School of Artificial Intelligence, Wuchang University of Technology, Wuhan 430223, China)

  • Hong Lei

    (School of Artificial Intelligence, Wuchang University of Technology, Wuhan 430223, China)

  • Qian Deng

    (School of Artificial Intelligence, Wuchang University of Technology, Wuhan 430223, China)

  • Gai-Ge Wang

    (Department of Computer Science and Technology, Ocean University of China, Qingdao 266100, China
    Intelligent Information Systems Institute, Wenzhou University, Wenzhou 325035, China
    Key Laboratory of Intelligent Image Processing and Analysis, Wenzhou 325035, China)

Abstract

Lévy flight is a random walk mechanism which can make large jumps at local locations with a high probability. The probability density distribution of Lévy flight was characterized by sharp peaks, asymmetry, and trailing. Its movement pattern alternated between frequent short-distance jumps and occasional long-distance jumps, which can jump out of local optimal and expand the population search area. The metaheuristic algorithms are inspired by nature and applied to solve NP-hard problems. Lévy flight is used as an operator in the cuckoo algorithm, monarch butterfly optimization, and moth search algorithms. The superiority for the Lévy flight-based metaheuristic algorithms has been demonstrated in many benchmark problems and various application areas. A comprehensive survey of the Lévy flight-based metaheuristic algorithms is conducted in this paper. The research includes the following sections: statistical analysis about Lévy flight, metaheuristic algorithms with a Lévy flight operator, and classification of Lévy flight used in metaheuristic algorithms. The future insights and development direction in the area of Lévy flight are also discussed.

Suggested Citation

  • Juan Li & Qing An & Hong Lei & Qian Deng & Gai-Ge Wang, 2022. "Survey of Lévy Flight-Based Metaheuristics for Optimization," Mathematics, MDPI, vol. 10(15), pages 1-27, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2785-:d:881515
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    References listed on IDEAS

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    Cited by:

    1. Jiahua Zhang & Xuemei Liu & Beikun Zhang, 2024. "Mathematical modelling and a discrete cuckoo search particle swarm optimization algorithm for mixed model sequencing problem with interval task times," Journal of Intelligent Manufacturing, Springer, vol. 35(8), pages 3837-3856, December.
    2. Chen, Jinbao & Zeng, Quan & Zou, Yidong & Li, Shaojie & Zheng, Yang & Liu, Dong & Xiao, Zhihuai, 2024. "Intelligent robust control for nonlinear complex hydro-turbine regulation system based on a novel state space equation and dynamic feedback linearization," Energy, Elsevier, vol. 302(C).

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