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Research Papers

A Nonhierarchical Formulation of Analytical Target Cascading

[+] Author and Article Information
S. Tosserams

Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlandss.tosserams@tue.nl

M. Kokkolaras

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109mk@umich.edu

L. F. P. Etman

Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlandsl.f.p.etman@tue.nl

J. E. Rooda

Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlandsj.e.rooda@tue.nl

The alternating optimization approach is also known as “nonlinear Gauss–Seidel” or “block-coordinate descent” (28,30).

J. Mech. Des 132(5), 051002 (Apr 29, 2010) (13 pages) doi:10.1115/1.4001346 History: Received January 29, 2009; Revised December 08, 2009; Published April 29, 2010; Online April 29, 2010

Analytical target cascading (ATC) is a method developed originally for translating system-level design targets to design specifications for the components that comprise the system. ATC has been shown to be useful for coordinating decomposition-based optimal system design. The traditional ATC formulation uses hierarchical problem decompositions, in which coordination is performed by communicating target and response values between parents and children. The hierarchical formulation may not be suitable for general multidisciplinary design optimization (MDO) problems. This paper presents a new ATC formulation that allows nonhierarchical target-response coupling between subproblems and introduces system-wide functions that depend on variables of two or more subproblems. Options to parallelize the subproblem optimizations are also provided, including a new bilevel coordination strategy that uses a master problem formulation. The new formulation increases the applicability of the ATC to both decomposition-based optimal system design and MDO. Moreover, it belongs to the class of augmented Lagrangian coordination methods, having thus convergence properties under standard convexity and continuity assumptions. A supersonic business jet design problem is used to demonstrate the flexibility and effectiveness of the presented formulation.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Functional dependence structure of the original and proposed ATC formulations: The arrows indicate the flow of subproblem responses; the shaded boxes are used to represent the dependence of system-wide functions on subproblem variables

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Figure 2

Nonhierarchical target and response flow between subproblem j and its neighbors

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Figure 3

Illustration of coordination algorithms for the nonhierarchical ATC formulation. Each inner loop may be exact, inexact, or consist of only a single iteration.

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Figure 4

Target and response flow with intermediate responses r̂

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Figure 5

Functional dependencies of the business jet problem: single arrows indicate flow of responses; double arrows indicate shared variables

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Figure 6

Four different ATC formulations. Single arrows represent target-response coupling where the direction of the arrow indicates the direction of response flow. The response directions for the shared variables t/c, ARw, Λw, Sref, Sht, and ARht for all but the hierarchical ATC formulation are chosen arbitrarily. The dashed boxes annotated by “range constraint” in Fig. 6 and “range and total weight constraints” in Fig. 6 represent system-wide constraints.

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