An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems
In this study, we propose an effective algorithm for globally solving the sum of linear ratios problems. Firstly, by introducing new variables, we transform the initial problem into an equivalent nonconvex programming problem. Secondly, by utilizing direct relaxation, the linear relaxation programmi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2017/8138975 |
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| _version_ | 1850237886938480640 |
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| author | Hongwei Jiao Lei Cai Zhisong Hou Chunyang Bai |
| author_facet | Hongwei Jiao Lei Cai Zhisong Hou Chunyang Bai |
| author_sort | Hongwei Jiao |
| collection | DOAJ |
| description | In this study, we propose an effective algorithm for globally solving the sum of linear ratios problems. Firstly, by introducing new variables, we transform the initial problem into an equivalent nonconvex programming problem. Secondly, by utilizing direct relaxation, the linear relaxation programming problem of the equivalent problem can be constructed. Thirdly, in order to improve the computational efficiency of the algorithm, an out space pruning technique is derived, which offers a possibility of pruning a large part of the out space region which does not contain the optimal solution of the equivalent problem. Fourthly, based on out space partition, by combining bounding technique and pruning technique, a new out space branch-and-bound algorithm for globally solving the sum of linear ratios problems (SLRP) is designed. Finally, numerical experimental results are presented to demonstrate both computational efficiency and solution quality of the proposed algorithm. |
| format | Article |
| id | doaj-art-1dca0e4bde4841818fee7933bf2a7a0a |
| institution | OA Journals |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-1dca0e4bde4841818fee7933bf2a7a0a2025-08-20T02:01:39ZengWileyJournal of Control Science and Engineering1687-52491687-52572017-01-01201710.1155/2017/81389758138975An Effective Algorithm for Globally Solving Sum of Linear Ratios ProblemsHongwei Jiao0Lei Cai1Zhisong Hou2Chunyang Bai3School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, ChinaSchool of Information Engineering, Henan Institute of Science and Technology, Xinxiang 453003, ChinaSchool of Information Engineering, Henan Institute of Science and Technology, Xinxiang 453003, ChinaSchool of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, ChinaIn this study, we propose an effective algorithm for globally solving the sum of linear ratios problems. Firstly, by introducing new variables, we transform the initial problem into an equivalent nonconvex programming problem. Secondly, by utilizing direct relaxation, the linear relaxation programming problem of the equivalent problem can be constructed. Thirdly, in order to improve the computational efficiency of the algorithm, an out space pruning technique is derived, which offers a possibility of pruning a large part of the out space region which does not contain the optimal solution of the equivalent problem. Fourthly, based on out space partition, by combining bounding technique and pruning technique, a new out space branch-and-bound algorithm for globally solving the sum of linear ratios problems (SLRP) is designed. Finally, numerical experimental results are presented to demonstrate both computational efficiency and solution quality of the proposed algorithm.http://dx.doi.org/10.1155/2017/8138975 |
| spellingShingle | Hongwei Jiao Lei Cai Zhisong Hou Chunyang Bai An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems Journal of Control Science and Engineering |
| title | An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems |
| title_full | An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems |
| title_fullStr | An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems |
| title_full_unstemmed | An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems |
| title_short | An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems |
| title_sort | effective algorithm for globally solving sum of linear ratios problems |
| url | http://dx.doi.org/10.1155/2017/8138975 |
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