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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Bibliographic Details
Published in:Optimization and engineering Vol. 11; no. 3; pp. 355 - 379
Main Authors: Yonekura, Kazuo, Kanno, Yoshihiro
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2010
Springer Nature B.V
Subjects:
Control
Cross sections
Engineering
Environmental Management
Financial Engineering
Mathematical models
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Programming
Systems Theory
Topology
Trusses
Uncertainty
Topology optimization
Semidefinite program
Global optimization
Robust optimization
Branch-and-bound method
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary: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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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-010-9107-1