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An Output-Space Based Branch-and-Bound Algorithm for Sum-of-Linear-Ratios Problem

Author

Listed:
  • Bo Zhang

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P. R. China)

  • Yuelin Gao

    (Ningxia Province Cooperative Innovation, Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, P. R. China3Ningxia Province Key Laboratory of Intelligent Information and Data Processing, North Minzu University, Yinchuan 750021, P. R. China)

Abstract

Founded on the idea of subdividing the (p − 1)-dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm.

Suggested Citation

  • Bo Zhang & Yuelin Gao, 2023. "An Output-Space Based Branch-and-Bound Algorithm for Sum-of-Linear-Ratios Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(02), pages 1-23, April.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:02:n:s0217595922500105
    DOI: 10.1142/S0217595922500105
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