A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients
A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the opti...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/490297 |
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| _version_ | 1832550468295852032 |
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| author | Hongwei Jiao Yongqiang Chen |
| author_facet | Hongwei Jiao Yongqiang Chen |
| author_sort | Hongwei Jiao |
| collection | DOAJ |
| description | A new linearizing method is presented for globally solving sum
of linear ratios problem with coefficients. By using the linearizing method, linear relaxation
programming (LRP) of the sum of linear ratios problem with coefficients is established,
which can provide the reliable lower bound of the optimal value of the initial problem. Thus,
a branch and bound algorithm for solving the sum of linear ratios problem with coefficients
is put forward. By successively partitioning the linear relaxation of the feasible region and
solving a series of the LRP, the proposed algorithm is convergent to the global optimal
solution of the initial problem. Compared with the known methods, numerical experimental
results show that the proposed method has the higher computational efficiency in finding the
global optimum of the sum of linear ratios problem with coefficients. |
| format | Article |
| id | doaj-art-1527ffcf662a4316a6d4c4b69a6f3f08 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1527ffcf662a4316a6d4c4b69a6f3f082025-02-03T06:06:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/490297490297A New Linearizing Method for Sum of Linear Ratios Problem with CoefficientsHongwei Jiao0Yongqiang Chen1School of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, ChinaDepartment of Mathematics, Henan Normal University, Xinxiang 453007, ChinaA new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.http://dx.doi.org/10.1155/2014/490297 |
| spellingShingle | Hongwei Jiao Yongqiang Chen A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients Journal of Applied Mathematics |
| title | A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients |
| title_full | A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients |
| title_fullStr | A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients |
| title_full_unstemmed | A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients |
| title_short | A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients |
| title_sort | new linearizing method for sum of linear ratios problem with coefficients |
| url | http://dx.doi.org/10.1155/2014/490297 |
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