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A refined branch and bound algorithm for solving the sum of linear ratios programming

Author

Listed:
  • Yue, Hongwei
  • Li, Hou
  • Shen, Peiping
  • Deng, Yaping

Abstract

A refined branch and bound algorithm is introduced to efficiently solve the sum of linear ratios (SLR) programming. Initially, an equivalent problem of (SLR) is established through a two-stage transformation process, and then this equivalent problem is relaxed into a linear programming problem. Subsequently, under the criterion of minimal integral area, we characterize the relaxation gaps of the two components in the relaxation problem, and determine the corresponding optimal branching points. Based on these obtained points, we develop a refined branch rule. This rule guarantees that the lower bound for the optimal value of the original problem is effectively updated. To further enhance the efficiency of algorithm, a region tightening technique is incorporated to eliminate redundant calculations. Ultimately, the convergence and complexity of the algorithm are analyzed. Numerical experiments indicate that the algorithm has advantages in term of efficiency for the test instances.

Suggested Citation

  • Yue, Hongwei & Li, Hou & Shen, Peiping & Deng, Yaping, 2026. "A refined branch and bound algorithm for solving the sum of linear ratios programming," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 210-224.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:210-224
    DOI: 10.1016/j.matcom.2026.03.012
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