An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem

This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, b...

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Bibliographic Details
Published in:Mathematical problems in engineering Vol. 2021; pp. 1 - 10
Main Authors: Jia, Pujun, Jiao, Hongwei, Shi, Dongwei, Yin, Jingben
Format: Journal Article
Language:English
Published: New York Hindawi 27.11.2021
John Wiley & Sons, Inc
Subjects:
Algorithms
Lower bounds
Mathematical problems
Mathematical programming
Minimax technique
Optimization
Ratios
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary:This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2021/3584494