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Mathematical Problems in Engineering
Volume 2008, Article ID 646205, 13 pages
Research Article

Global Optimization for Sum of Linear Ratios Problem Using New Pruning Technique

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
2College of Mechanical and Electric Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China
3Jiangsu Provincial Key Laboratory of Modern Agricultural Equipment and Technology, Jiangsu University, Zhenjiang 212013, China
4College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received 7 June 2008; Accepted 21 November 2008

Academic Editor: Alexander P. Seyranian

Copyright © 2008 Hongwei Jiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A global optimization algorithm is proposed for solving sum of general linear ratios problem (P) using new pruning technique. Firstly, an equivalent problem (P1) of the (P) is derived by exploiting the characteristics of linear constraints. Then, by utilizing linearization method the relaxation linear programming (RLP) of the (P1) can be constructed and the proposed algorithm is convergent to the global minimum of the (P) through the successive refinement of the linear relaxation of feasible region and solutions of a series of (RLP). Then, a new pruning technique is proposed, this technique offers a possibility to cut away a large part of the current investigated feasible region by the optimization algorithm, which can be utilized as an accelerating device for global optimization of problem (P). Finally, the numerical experiments are given to illustrate the feasibility of the proposed algorithm.