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Research Papers

An Alternative Formulation of Collaborative Optimization Based on Geometric Analysis

[+] Author and Article Information
Xiang Li1

 School of Aerospace Engineering,Beijing Institute of Technology, Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing 100081, China e-mail: Lixiang_0504@yahoo.com

Changan Liu

 Xi’an Aerospace Propulsion Institute, Xi’an 710100, China e-mail: anchangliu@163.com

Weiji Li

 School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China e-mail: Lx_0207@sina.com

Teng Long

 School of Aerospace Engineering, Beijing Institute of Technology, Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing 100081, China e-mail: Ly_cd@163.com

1

Corresponding author.

J. Mech. Des 133(5), 051005 (Jun 06, 2011) (11 pages) doi:10.1115/1.4003919 History: Received September 08, 2010; Revised March 30, 2011; Published June 06, 2011; Online June 06, 2011

Collaborative optimization (CO) is a multidisciplinary design optimization (MDO) method with bilevel computational structure, which decomposes the original optimization problem into one system-level problem and several subsystem problems. The strategy of decomposition in CO is a useful way for solving large engineering design problems. However, the computational difficulties caused by the system-level consistency equality constraints hinder the development of CO. In this paper, an alternative formulation of CO called CO with combination of linear approximations (CLA-CO) is presented based on the geometric analysis of CO, which is more intuitive and direct than the previous algebraic analysis. In CLA-CO, the consistency equality constraints in CO are replaced by linear approximations to the subsystem responses. As the iterative process goes on, more linear approximations are added into the system level. Consequently, the combination of these linear approximations makes the system-level problem gradually approximate the original problem. In CLA-CO, the advantages of the decomposition strategy are maintained while the computational difficulties of the conventional CO are avoided. However, there are still difficulties in applying the presented CLA-CO to problems with nonconvex constraints. The application of CLA-CO to three optimization problems, a numerical test problem, a composite beam design problem, and a gear reducer design problem, illustrates the capabilities and limitations of CLA-CO.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Geometry of the subsystem optimizations

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Figure 2

Construction of the linear approximations

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Figure 3

Computational structure of CLA-CO

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Figure 4

Comparison of the computational structures of CO and CLA-CO

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Figure 5

Geometry of subsystem with more than one constraint

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Figure 6

Geometry of problem 14

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Figure 7

Sketch of the composite beam design

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Figure 8

Geometries of the two subsystems

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Figure 9

Sketch of the gear reducer

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Figure 10

Comparison of CLA-CO and CO

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