A New branch-and-cut algorithm for linear sum-of-ratios problem based on SLO method and LO relaxation

Hezhi Luo (), Youmin Xu (), Huixian Wu () and Guoqiang Wang ()
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Hezhi Luo: Zhejiang Normal University
Youmin Xu: Zhejiang Normal University
Huixian Wu: Hangzhou Dianzi University
Guoqiang Wang: Shanghai University of Engineering Science

Computational Optimization and Applications, 2025, vol. 90, issue 1, No 9, 257-301

Abstract: Abstract We consider a linear sum-of-ratios fractional programming problem that arises from a broad range of applications and is known to be NP-hard. In this paper, we first develop a successive linear optimization (SLO) method for the linear sum-of-ratios problem and show that it converges to a KKT point of the underlying problem. Second, we propose a new branch-and-cut algorithm for globally solving the linear sum-of-ratios fractional program by integrating the SLO method, the linear optimization (LO) relaxation, branch-and-bound framework and branch-and-cut rule. We establish the global convergence of the algorithm and estimate its complexity. Numerical results are reported to illustrate the effectiveness of the proposed algorithm in finding a global optimal solution to large-scale instances of linear sum-of-ratios problem.

Keywords: Global optimization; Fractional programming; Sum-of-ratios; Successive linear optimization; Linear optimization relaxation; Branch-and-cut (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00622-3

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