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An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem
- Source :
- Mathematical Problems in Engineering, Vol 2021 (2021)
- Publication Year :
- 2021
- Publisher :
- Hindawi Limited, 2021.
-
Abstract
- 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.
- Subjects :
- Sequence
Article Subject
Branch and bound
Computer science
General Mathematics
medicine.medical_treatment
General Engineering
Engineering (General). Civil engineering (General)
Minimax
Upper and lower bounds
Linear-fractional programming
Engineering optimization
QA1-939
medicine
Applied mathematics
Relaxation (approximation)
TA1-2040
Mathematics
Relaxation technique
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2021
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....180b557a00cdf4221c03a2c3b208c06b