An Effective Branch and Bound Algorithm for Minimax Linear Fractional Programming

An effective branch and bound algorithm is proposed for globally solving minimax linear fractional programming problem (MLFP). In this algorithm, the lower bounds are computed during the branch and bound search by solving a sequence of linear relaxation programming problems (LRP) of the problem (MLF...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2014-01, Vol.2014 (2014), p.772-779-068
Main Authors: Jiao, Hong-Wei, Chen, Yong-Qiang, Wang, Feng-Hui
Format: Article
Language:English
Subjects:
Algorithms
Feasibility
Heuristic
Lower bounds
Mathematical models
Mathematical research
Mathematics
Minimax technique
Optimization
Optimization algorithms
Programming
Science
Simplex method
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Summary:An effective branch and bound algorithm is proposed for globally solving minimax linear fractional programming problem (MLFP). In this algorithm, the lower bounds are computed during the branch and bound search by solving a sequence of linear relaxation programming problems (LRP) of the problem (MLFP), which can be derived by using a new linear relaxation bounding technique, and which can be effectively solved by the simplex method. The proposed branch and bound algorithm is convergent to the global optimal solution of the problem (MLFP) through the successive refinement of the feasible region and solutions of a series of the LRP. Numerical results for several test problems are reported to show the feasibility and effectiveness of the proposed algorithm.
ISSN:1110-757X
1687-0042
DOI:10.1155/2014/160262