Global optimization for max-plus linear systems and applications in distributed systems
This paper considers the global optimization of max-plus linear systems with affine equality constraints. For both the cases that the variables are real and non-negative, the necessary and sufficient conditions for the existence and uniqueness of globally optimal solutions are given, respectively. T...
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| Vydáno v: | Automatica (Oxford) Ročník 119; s. 109104 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.09.2020
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | This paper considers the global optimization of max-plus linear systems with affine equality constraints. For both the cases that the variables are real and non-negative, the necessary and sufficient conditions for the existence and uniqueness of globally optimal solutions are given, respectively. The proposed approaches are constructive and yield two polynomial algorithms for checking the solvabilities of the global optimization problems and finding all globally optimal solutions, in which the analytic expressions of general solutions are presented. The global optimization is then applied in the load scheduling of distributed systems with different processor capacities. The optimal allocation scheme is designed to minimize the completion time of the overall task. Some illustrative examples are presented to demonstrate the results. |
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| AbstractList | This paper considers the global optimization of max-plus linear systems with affine equality constraints. For both the cases that the variables are real and non-negative, the necessary and sufficient conditions for the existence and uniqueness of globally optimal solutions are given, respectively. The proposed approaches are constructive and yield two polynomial algorithms for checking the solvabilities of the global optimization problems and finding all globally optimal solutions, in which the analytic expressions of general solutions are presented. The global optimization is then applied in the load scheduling of distributed systems with different processor capacities. The optimal allocation scheme is designed to minimize the completion time of the overall task. Some illustrative examples are presented to demonstrate the results. |
| ArticleNumber | 109104 |
| Author | Tao, Yuegang Wang, Cailu |
| Author_xml | – sequence: 1 givenname: Yuegang surname: Tao fullname: Tao, Yuegang email: yuegangtao@hebut.edu.cn organization: School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, PR China – sequence: 2 givenname: Cailu surname: Wang fullname: Wang, Cailu email: cailu_wang@163.com organization: School of Automation, Beijing Institute of Technology, Beijing 100081, PR China |
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| Cites_doi | 10.1002/rnc.4285 10.1109/TAC.2016.2604562 10.1109/TAC.1985.1103925 10.1109/TASE.2017.2729894 10.1016/j.cam.2016.11.027 10.1016/j.automatica.2016.07.002 10.1016/j.sysconle.2016.07.005 10.1016/j.automatica.2015.01.002 10.1016/0377-2217(90)90419-C 10.1016/S0098-1354(00)00581-0 10.1016/S0024-3795(96)00407-7 10.1137/S036301299528534X 10.1016/j.automatica.2015.10.030 10.1016/0024-3795(88)90145-0 10.1007/s10898-007-9141-5 10.1016/j.laa.2012.04.051 10.1007/s10626-014-0205-7 10.1016/S0005-1098(01)00054-1 10.1002/rnc.1309 10.1016/j.automatica.2004.05.013 10.1016/0167-6911(94)00062-Z 10.1016/j.laa.2016.05.019 |
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| Keywords | Global optimization Distributed system General solution Polynomial algorithm Max-plus linear system |
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