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A Global Optimization Algorithm for Sum of Linear Ratios Problem

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  • Yuelin Gao
  • Siqiao Jin

Abstract

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

Suggested Citation

  • Yuelin Gao & Siqiao Jin, 2013. "A Global Optimization Algorithm for Sum of Linear Ratios Problem," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, June.
    • Handle: RePEc:hin:jnljam:276245
    DOI: 10.1155/2013/276245
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    Cited by:

    1. M. N. Yarahmadi & S. A. MirHassani & F. Hooshmand, 2023. "A heuristic method to find a quick feasible solution based on the ratio programming," Operational Research, Springer, vol. 23(3), pages 1-19, September.
    2. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. 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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