An efficient algorithm and complexity result for solving the sum of general affine ratios problem
In this paper, with the unique hypothesis that the denominator is not equal to 0, an efficient outer space rectangle branch-and-bound algorithm is presented to globally solve the sum of general affine ratios problem. By using equivalent transformation and the characteristics of general single ratio...
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| Veröffentlicht in: | Chaos, solitons and fractals Jg. 164; S. 112701 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.11.2022
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| ISSN: | 0960-0779, 1873-2887 |
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| Abstract | In this paper, with the unique hypothesis that the denominator is not equal to 0, an efficient outer space rectangle branch-and-bound algorithm is presented to globally solve the sum of general affine ratios problem. By using equivalent transformation and the characteristics of general single ratio function, a linear program relaxation problem is constructed for computing the lower bound of the global minimum value of the original problem. Moreover, to enhance the running speed of the presented algorithm, we design an outer space accelerating technic for deleting the entire outer space rectangle or a part of the entire examined outer space rectangle, in which there contains no the global minimum point of the equivalent problem. Furthermore, through the complexity analysis of the presented algorithm, we estimate its maximum iteration times. In addition, we prove the global convergence of the presented algorithm, report and analyze the numerical computational results for indicating the validity of the presented algorithm. Finally, two practical problems from power transportation and production planning are solved to verify the usefulness of the presented algorithm.
•We present a novel outer space branch-and-bound algorithm for the SGAR.•The algorithm economizes the required computations by dividing space.•The main calculation involves solving a series of linear programming problems.•We give the complexity analysis of the algorithm for the first time.•The computing efficiency is significantly higher than the existing algorithms. |
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| AbstractList | In this paper, with the unique hypothesis that the denominator is not equal to 0, an efficient outer space rectangle branch-and-bound algorithm is presented to globally solve the sum of general affine ratios problem. By using equivalent transformation and the characteristics of general single ratio function, a linear program relaxation problem is constructed for computing the lower bound of the global minimum value of the original problem. Moreover, to enhance the running speed of the presented algorithm, we design an outer space accelerating technic for deleting the entire outer space rectangle or a part of the entire examined outer space rectangle, in which there contains no the global minimum point of the equivalent problem. Furthermore, through the complexity analysis of the presented algorithm, we estimate its maximum iteration times. In addition, we prove the global convergence of the presented algorithm, report and analyze the numerical computational results for indicating the validity of the presented algorithm. Finally, two practical problems from power transportation and production planning are solved to verify the usefulness of the presented algorithm.
•We present a novel outer space branch-and-bound algorithm for the SGAR.•The algorithm economizes the required computations by dividing space.•The main calculation involves solving a series of linear programming problems.•We give the complexity analysis of the algorithm for the first time.•The computing efficiency is significantly higher than the existing algorithms. |
| ArticleNumber | 112701 |
| Author | Jiao, Hongwei Ma, Junqiao |
| Author_xml | – sequence: 1 givenname: Hongwei surname: Jiao fullname: Jiao, Hongwei email: jiaohongwei2022@163.com organization: School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China – sequence: 2 givenname: Junqiao surname: Ma fullname: Ma, Junqiao organization: School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China |
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| Cites_doi | 10.1016/j.chaos.2022.112682 10.1080/00207160.2021.1909727 10.1023/A:1011233805045 10.1080/1055678031000105242 10.1016/j.ejor.2015.01.039 10.1016/j.apm.2012.02.023 10.1016/j.cam.2022.114784 10.1016/j.cie.2019.106234 10.1186/s13660-018-1651-9 10.1007/s10589-012-9488-5 10.1007/BF01096535 10.1080/02331934.2019.1632250 10.1023/A:1008314922240 10.1051/ro/2022061 10.1016/j.cam.2018.10.038 10.1016/j.cam.2008.04.032 10.1016/j.ejor.2019.03.014 10.1023/A:1023274721632 10.1016/j.cor.2013.03.012 10.1016/j.ejor.2006.08.036 10.1007/BF00120666 10.1155/2013/276245 10.1023/A:1008312714792 10.1023/B:JOTA.0000026129.07165.5a 10.3390/math7090867 10.1007/BF00138693 10.1023/A:1013807129844 |
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| Keywords | 90C32 Branch-and-bound Sum of general affine ratios Complexity analysis Global optimization 90C26 Accelerating technic |
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| Title | An efficient algorithm and complexity result for solving the sum of general affine ratios problem |
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