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Technical Briefs

A Note on the Convergence of Analytical Target Cascading With Infinite Norms

[+] Author and Article Information
Jeongwoo Han

 Argonne National Laboratory, 9700 S. 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(3), 034502 (Mar 01, 2010) (6 pages) doi:10.1115/1.4001001 History: Received January 14, 2009; Revised December 18, 2009; Published March 01, 2010; Online March 01, 2010

Analytical target cascading (ATC) is a multidisciplinary design optimization method for multilevel hierarchical systems. To improve computational efficiency, especially for problems under uncertainty or with strong monotonicity, a sequential linear programming (SLP) algorithm was previously employed as an alternate coordination strategy to solve ATC and probabilistic ATC problems. The SLP implementation utilizes L norms to maintain the linearity of SLP subsequences. This note offers a proof that there exists a set of weights such that the ATC algorithm converges when L norms are used. Examples are also provided to illustrate the effectiveness of using L norms as a penalty function to maintain the formulation linear and differentiable. The examples show that the proposed method provides more robust results for linearized ATC problems due to the robustness of the linear programming solver.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Nonhierarchical and (b) hierarchical decompositions

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Figure 2

General forest in the problem hierarchy covering all nodes and edges from level i=p to s (adapted from Ref. 22)

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Figure 3

Example problem structure

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Figure 4

Pareto surface of the linearized problem at zif0

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Figure 5

Pareto surface of the linearized problem at zf0

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