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Research Papers

A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading

[+] Author and Article Information
Jeongwoo Han

 Argonne National Laboratory, 9700 South Cass Avenue, Building 362, Argonne, IL 60439jhan@anl.gov

Panos Y. Papalambros

Department of Mechanical Engineering, University of Michigan, 2250 GG Brown Building, Ann Arbor, MI 48104pyp@umich.edu

J. Mech. Des 132(2), 021003 (Jan 14, 2010) (8 pages) doi:10.1115/1.4000758 History: Received November 24, 2008; Revised November 20, 2009; Published January 14, 2010; Online January 14, 2010

Decomposition-based strategies, such as analytical target cascading (ATC), are often employed in design optimization of complex systems. Achieving convergence and computational efficiency in the coordination strategy that solves the partitioned problem is a key challenge. A new convergent strategy is proposed for ATC that coordinates interactions among subproblems using sequential linearizations. The linearity of subproblems is maintained using infinity norms to measure deviations between targets and responses. A subproblem suspension strategy is used to suspend temporarily inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. An individual subproblem trust region method is introduced for faster convergence. The proposed strategy is intended for use in design optimization problems where sequential linearizations are typically effective, such as problems with extensive monotonicities, a large number of constraints relative to variables, and propagation of probabilities with normal distributions. Experiments with test problems show that, relative to standard ATC coordination, the number of subproblem evaluations is reduced considerably while the solution accuracy depends on the degree of monotonicity and nonlinearity.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Example of index notation for a hierarchically partitioned design problem

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Figure 2

Information flow for ATC subproblem LPij of Eq. 7

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Figure 3

Flowchart of the SLP coordination strategy for ATC (modified from Ref. 24)

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Figure 4

Flowchart of the SLP coordination strategy for ATC with a suspension strategy and individual subproblem trust regions

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Figure 5

Examples of the unsuspended and suspended ATC hierarchies

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Figure 6

Example 1 computational cost versus solution accuracy

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Figure 7

Three-bar two-rod structural design problem

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Figure 8

Example 2 computational cost and through versus solution accuracy

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