Global optimization of robust truss topology via mixed integer semidefinite programming
This paper discusses a global optimization method of robust truss topology under the load uncertainties and slenderness constraints of the member cross-sectional areas. We consider a non-stochastic uncertainty of the external load, and attempt to minimize the maximum compliance corresponding to the...
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| Vydané v: | Optimization and engineering Ročník 11; číslo 3; s. 355 - 379 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer US
01.09.2010
Springer Nature B.V |
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| ISSN: | 1389-4420, 1573-2924 |
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| Abstract | This paper discusses a global optimization method of robust truss topology under the load uncertainties and slenderness constraints of the member cross-sectional areas. We consider a non-stochastic uncertainty of the external load, and attempt to minimize the maximum compliance corresponding to the most critical load. A design-dependent uncertainty model in the external load is proposed in order to consider the variation of truss topology rigorously. It is shown that this optimization problem can be formulated as a 0–1 mixed integer semidefinite programming (0–1MISDP) problem. We propose a branch-and-bound method for computing the global optimal solution of the 0–1MISDP. Numerical examples illustrate that the topology of robust optimal truss depends on the magnitude of uncertainty. The presented method can provide global optimal solutions for benchmark examples, which can be used for evaluating the performance of any other local optimization method for robust structural optimization. |
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| AbstractList | This paper discusses a global optimization method of robust truss topology under the load uncertainties and slenderness constraints of the member cross-sectional areas. We consider a non-stochastic uncertainty of the external load, and attempt to minimize the maximum compliance corresponding to the most critical load. A design-dependent uncertainty model in the external load is proposed in order to consider the variation of truss topology rigorously. It is shown that this optimization problem can be formulated as a 0-1 mixed integer semidefinite programming (0-1MISDP) problem. We propose a branch-and-bound method for computing the global optimal solution of the 0-1MISDP. Numerical examples illustrate that the topology of robust optimal truss depends on the magnitude of uncertainty. The presented method can provide global optimal solutions for benchmark examples, which can be used for evaluating the performance of any other local optimization method for robust structural optimization. This paper discusses a global optimization method of robust truss topology under the load uncertainties and slenderness constraints of the member cross-sectional areas. We consider a non-stochastic uncertainty of the external load, and attempt to minimize the maximum compliance corresponding to the most critical load. A design-dependent uncertainty model in the external load is proposed in order to consider the variation of truss topology rigorously. It is shown that this optimization problem can be formulated as a 0-1 mixed integer semidefinite programming (0-1MISDP) problem. We propose a branch-and-bound method for computing the global optimal solution of the 0-1MISDP. Numerical examples illustrate that the topology of robust optimal truss depends on the magnitude of uncertainty. The presented method can provide global optimal solutions for benchmark examples, which can be used for evaluating the performance of any other local optimization method for robust structural optimization.[PUBLICATION ABSTRACT] |
| Author | Yonekura, Kazuo Kanno, Yoshihiro |
| Author_xml | – sequence: 1 givenname: Kazuo surname: Yonekura fullname: Yonekura, Kazuo organization: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo – sequence: 2 givenname: Yoshihiro surname: Kanno fullname: Kanno, Yoshihiro email: kanno@mist.i.u-tokyo.ac.jp organization: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo |
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| Cites_doi | 10.1016/0899-8248(92)90005-S 10.1007/s10957-006-9102-z 10.1016/S0045-7949(03)00322-5 10.1007/s00158-006-0074-2 10.1016/j.cma.2007.03.003 10.1016/j.compstruc.2007.05.026 10.1007/s10589-007-9138-5 10.1137/S1052623495291951 10.1016/S0045-7949(99)00173-X 10.1007/s00158-004-0480-2 10.1016/j.compstruc.2004.10.007 10.1007/s10589-007-9152-7 10.1080/10556789908805766 10.1023/A:1018952429396 10.1061/(ASCE)0733-9445(1998)124:3(318) 10.2140/jomms.2008.3.213 10.1137/S1052623496297097 10.1007/BF01742459 10.1137/1.9780898718829 |
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| Keywords | Topology optimization Semidefinite program Global optimization Robust optimization Branch-and-bound method |
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