IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v212y2023icp91-121.html
   My bibliography  Save this article

Convergence analysis of flow direction algorithm in continuous search space and its improvement

Author

Listed:
  • Ye, Wenwen
  • Li, Shengping

Abstract

The flow direction algorithm (FDA) is a new physics-based meta-heuristic optimization algorithm that is being used successfully in a variety of applications. However, FDA lacks theoretically rigorous convergency analysis and suffers from several drawbacks, such as premature convergence, lack of population diversity, and imbalance between exploitation and exploration. In this paper, the supermartingale convergence theorem is used to analyse the global convergence of FDA in a continuous search space. We first demonstrate that FDA’s global convergence is determined by the accumulation of the minimum probability (Pt∗) that the flow swarm fall into the global optimal region in each iteration. Then, an improved flow direction algorithm, namely, guided flow direction algorithm (GFDA), is proposed to increase the minimum probability by making full use of the neighbourhood information. Comprehensive experimental studies were conducted to test and validate the proposed GFDA. Twenty competitive meta-heuristic optimization algorithms, twenty-three classical benchmark functions, ten recently single objective bound constrained numerical optimization problems(CEC2020), and four constrained engineering problems were used. Finally, the experimental results and statistical tests (Friedman test and Wilcoxon test) demonstrate the superiority of GFDA compared to other algorithms.

Suggested Citation

  • Ye, Wenwen & Li, Shengping, 2023. "Convergence analysis of flow direction algorithm in continuous search space and its improvement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 91-121.
  • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:91-121
    DOI: 10.1016/j.matcom.2023.04.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423001751
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2023.04.020?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. Xu, Gang & Luo, Kun & Jing, Guoxiu & Yu, Xiang & Ruan, Xiaojun & Song, Jun, 2020. "On convergence analysis of multi-objective particle swarm optimization algorithm," European Journal of Operational Research, Elsevier, vol. 286(1), pages 32-38.
    2. Li, Yu & Yu, Xiaomei & Liu, Jingsen, 2023. "An opposition-based butterfly optimization algorithm with adaptive elite mutation in solving complex high-dimensional optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 498-528.
    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. Wang, Zheng-Xin & Jv, Yue-Qi, 2021. "A non-linear systematic grey model for forecasting the industrial economy-energy-environment system," Technological Forecasting and Social Change, Elsevier, vol. 167(C).
    2. Feilong Chang & Fahui Yuan & Zhixiong Lu, 2023. "A Multi-Objective Optimization Method for a Tractor Driveline Based on the Diversity Preservation Strategy of Gradient Crowding," Agriculture, MDPI, vol. 13(7), pages 1-16, June.
    3. Zhe Liu & Shurong Li, 2022. "A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm," Annals of Operations Research, Springer, vol. 311(2), pages 853-898, April.
    4. Page, Kenneth & Pérez, Juan & Telha, Claudio & García-Echalar, Andrés & López-Ospina, Héctor, 2021. "Optimal bundle composition in competition for continuous attributes," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1168-1187.
    5. Pan, Jeng-Shyang & Zhang, Zhen & Chu, Shu-Chuan & Zhang, Si-Qi & Wu, Jimmy Ming-Tai, 2024. "A parallel compact Marine Predators Algorithm applied in time series prediction of Backpropagation neural network (BNN) and engineering optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 65-88.
    6. Chih, Mingchang, 2023. "Stochastic stability analysis of particle swarm optimization with pseudo random number assignment strategy," European Journal of Operational Research, Elsevier, vol. 305(2), pages 562-593.
    7. Mubashir Rasool & Muhammad Adil Khan & Runmin Zou, 2023. "A Comprehensive Analysis of Online and Offline Energy Management Approaches for Optimal Performance of Fuel Cell Hybrid Electric Vehicles," Energies, MDPI, vol. 16(8), pages 1-33, April.

    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:matcom:v:212:y:2023:i:c:p:91-121. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.