A new deterministic global computing algorithm for solving a kind of linear fractional programming

This paper investigates a class of linear fractional programming (LFP) problem, which minimizes the sum of a finite number of linear fractional functions over a polyhedral region. Firstly, the equivalence problem (EP) of the LFP problem is given by a new two-stage transformation method. Secondly, co...

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Bibliographic Details
Published in:Optimization Vol. 72; no. 6; pp. 1485 - 1513
Main Authors: Zhang, Bo, Gao, YueLin, Liu, Xia, Huang, XiaoLi
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.06.2023
Taylor & Francis LLC
Subjects:
Algorithms
branch and bound
Global optimization
linear fractional programming
Mathematical programming
Optimization
output-space
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:This paper investigates a class of linear fractional programming (LFP) problem, which minimizes the sum of a finite number of linear fractional functions over a polyhedral region. Firstly, the equivalence problem (EP) of the LFP problem is given by a new two-stage transformation method. Secondly, considering the characteristics that the branch-and-bound algorithm can guarantee the global optimality of the solution to an optimization problem, and then based on the EP, we discuss the bounding operation, branching operation, pruning operation and rectangle-region reduction technique of this algorithm. After that, the convergence of the algorithm is proved and its computational complexity is deduced from the worst case. Finally, some experiments are reported to verify the effectiveness, feasibility and other performance of the proposed algorithm.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2027940