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A Fuzzy Variable H Strategy Based Ripple-Spreading Algorithm to Find the k Shortest Paths

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  • Yingfei Zhang

    (College of Safety Science and Engineering, Civil Aviation University of China, Tianjin 300300, China)

  • Xiaobing Hu

    (College of Safety Science and Engineering, Civil Aviation University of China, Tianjin 300300, China
    School of Engineering, University of Warwick, Coventry CV4 7AL, UK
    Collaborative Innovation Center of Etourism, Beijing Union University, Beijing 100101, China)

  • Hang Li

    (College of Safety Science and Engineering, Civil Aviation University of China, Tianjin 300300, China)

  • Gongpeng Zhang

    (Collaborative Innovation Center of Etourism, Beijing Union University, Beijing 100101, China)

  • Chi Zhang

    (Beijing College of Politics and Law, Beijing 102628, China)

  • Mark S. Leeson

    (School of Engineering, University of Warwick, Coventry CV4 7AL, UK)

Abstract

Ripple-spreading Algorithm (RSA) is a relatively new, nature-inspired, multi-agent based method for path optimization. This paper demonstrates that by modifying the micro-level behaviors of nodes and ripples, RSA achieves good scalability for solving the k shortest paths problem ( k − SPP ). Initially, each node may generate k or more ripples to guarantee optimality. To improve computational efficiency for large-scale problems, we propose an approximate RSA (ARSA), where nodes generate no more than h ripples ( 1 ≤ h < k ). While this reduces optimality, it significantly improves efficiency. Further, we introduce a fuzzy variable H strategy, FVHSRSA, to strike a better balance between optimality and efficiency. The optimality/efficiency of ARSA may still suffer if it uses a constant h too small/large. This strategy allows nodes closer to the destination to generate more ripples, while nodes farther away use fewer ripples. By dynamically adjusting h , FVHSRSA achieves a better trade-off between optimality and efficiency. Comprehensive experiments on 4 common network categories validate the effectiveness and efficiency of FVHSRSA in solving the k − SPP .

Suggested Citation

  • Yingfei Zhang & Xiaobing Hu & Hang Li & Gongpeng Zhang & Chi Zhang & Mark S. Leeson, 2024. "A Fuzzy Variable H Strategy Based Ripple-Spreading Algorithm to Find the k Shortest Paths," Mathematics, MDPI, vol. 12(23), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3670-:d:1527728
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    References listed on IDEAS

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    1. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    2. Thomas, Barrett W. & White III, Chelsea C., 2007. "The dynamic shortest path problem with anticipation," European Journal of Operational Research, Elsevier, vol. 176(2), pages 836-854, January.
    3. Burghouwt, Guillaume & Hakfoort, Jacco & Ritsema van Eck, Jan, 2003. "The spatial configuration of airline networks in Europe," Journal of Air Transport Management, Elsevier, vol. 9(5), pages 309-323.
    4. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    5. Hu, Xiao-Bing & Zhang, Ming-Kong & Zhang, Qi & Liao, Jian-Qin, 2017. "Co-Evolutionary path optimization by Ripple-Spreading algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 411-432.
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