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A spatial branch-reduction-bound algorithm for solving generalized linear fractional problems globally

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  • Hou, Zhisong
  • Liu, Sanyang

Abstract

In various engineering applications, the generalized linear fractional problem (GLFP) is an essential model that has many challenges in both theoretical and practical aspects. Therefore, the main work of this paper is to design an effective spatial algorithm for solving the GLFP efficiently. We start with equivalently converting the GLFP into an equivalent problem (EP) by transforming each fractional equation into one new variable. Next, applying the second-order cone relaxation to the constraint functions and executing a double-layer relaxation on the objective function of the EP, the second-order cone relaxed problem is constructed to underestimate the EP. Then, integrating some region reduction methods, we implement a spatial branch-reduction-bound algorithm. Furthermore, we verified the convergence of the proposed algorithm. Equally important, the maximum iterations of the proposed algorithm in the worst scenario are evaluated by the complexity analysis of the proposed algorithm. Finally, by comparing some algorithms in the current literature, numerical results confirm the feasibility, robustness, and efficiency of the proposed algorithm.

Suggested Citation

  • Hou, Zhisong & Liu, Sanyang, 2023. "A spatial branch-reduction-bound algorithm for solving generalized linear fractional problems globally," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010457
    DOI: 10.1016/j.chaos.2023.114144
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    References listed on IDEAS

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    1. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
    2. Nesterov, Y. & Nemirovskii, A., 1995. "An interior-point method for generalized linear-fractional programming," LIDAM Reprints CORE 1168, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    4. X. Liu & Y.L. Gao & B. Zhang & F.P. Tian, 2019. "A New Global Optimization Algorithm for a Class of Linear Fractional Programming," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
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    Cited by:

    1. Huang, Bingdi & Shen, Peiping, 2024. "An efficient branch and bound reduction algorithm for globally solving linear fractional programming problems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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