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A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition

Author

Listed:
  • Yan-Kuen Wu

    (Shaoxing Key Laboratory for Smart Society Monitoring, Prevention & Control, School of International Business, Zhejiang Yuexiu University, Shaoxing 312069, China)

  • Sy-Ming Guu

    (Graduate Institute of Business and Management, College of Management, Chang Gung University, Taoyuan 33302, Taiwan
    Department of Neurology, Chang Gung Memorial Hospital, Linkou 33305, Taiwan)

  • Ya-Chan Chang

    (Graduate Institute of Business and Management, College of Management, Chang Gung University, Taoyuan 33302, Taiwan)

Abstract

Min–max programming problems with addition–min constraints have been studied in the literature to model data transfer in BitTorrent-like peer-to-peer file-sharing systems. It is well known that the class of overlap functions contains various operators, including the “min” operator. The aim of this paper is to generalize the above min–max programming problem with addition–overlap function constraints. We demonstrate that this new optimization problem can be transformed into a simplified single-variable optimization problem, which makes it easier to find an optimal solution. The bisection method will be used to find this optimal solution. In addition, when the overlap function is explicitly specified, an iterative method is given to compute the optimal objective value with a polynomial time complexity. A numerical example is provided to illustrate the procedures.

Suggested Citation

  • Yan-Kuen Wu & Sy-Ming Guu & Ya-Chan Chang, 2024. "A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition," Mathematics, MDPI, vol. 12(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3183-:d:1496678
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    References listed on IDEAS

    as
    1. Gang Xiao & Khizar Hayat & Xiaopeng Yang, 2023. "Evaluation and its derived classification in a Server-to-Client architecture based on the fuzzy relation inequality," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 213-245, June.
    2. Ya-Ling Chiu & Sy-Ming Guu & Jiajun Yu & Yan-Kuen Wu, 2019. "A single-variable method for solving min–max programming problem with addition-min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 433-449, December.
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