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Technical Briefs

Cutting Plane Methods for Analytical Target Cascading With Augmented Lagrangian Coordination

[+] Author and Article Information
Wenshan Wang

Research Assistant
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: wenshaw@clemson.edu

Vincent Y. Blouin

Assistant Professor
School of Materials Science and Engineering,
Clemson University,
Clemson, SC 29634
e-mail: vblouin@clemson.edu

Melissa K. Gardenghi

Associate Professor
Division of Mathematical Sciences,
Bob Jones University,
Greenville, SC 29614
e-mail: mgardeng@bju.edu

Georges M. Fadel

Professor
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634
e-mail: fgeorge@clemson.edu

Margaret M. Wiecek

Professor
e-mail: wmalgor@clemson.edu

Benjamin C. Sloop

Research Assistant
e-mail: bsloop@clemson.edu
Department of Mathematical Sciences,
Clemson University,
Clemson, SC 29634

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received November 17, 2011; final manuscript received May 14, 2013; published online August 7, 2013. Assoc. Editor: Wei Chen.

J. Mech. Des 135(10), 104502 (Aug 07, 2013) (6 pages) Paper No: MD-11-1471; doi: 10.1115/1.4024847 History: Received November 17, 2011; Revised May 14, 2013

Analytical target cascading (ATC), a hierarchical, multilevel, multidisciplinary coordination method, has proven to be an effective decomposition approach for large-scale engineering optimization problems. In recent years, augmented Lagrangian relaxation methods have received renewed interest as dual update methods for solving ATC decomposed problems. These problems can be solved using the subgradient optimization algorithm, the application of which includes three schemes for updating dual variables. To address the convergence efficiency disadvantages of the existing dual update schemes, this paper investigates two new schemes, the linear and the proximal cutting plane methods, which are implemented in conjunction with augmented Lagrangian coordination for ATC-decomposed problems. Three nonconvex nonlinear example problems are used to show that these two cutting plane methods can significantly reduce the number of iterations and the number of function evaluations when compared to the traditional subgradient update methods. In addition, these methods are also compared to the method of multipliers and its variants, showing similar performance.

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References

Figures

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Fig. 1

Decomposition structures

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Fig. 2

Example 1: number of iterations and number of function evaluations versus solution error

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Fig. 3

Example 2: number of iterations and number of function evaluations versus solution error

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Fig. 4

Example 3: number of iterations and number of function evaluations versus solution error

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Fig. 5

CPU time versus solution error

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