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Research Papers: Design Automation

Improving the Performance of the Augmented Lagrangian Coordination: Decomposition Variants and Dual Residuals

[+] Author and Article Information
Meng Xu

Mem. ASME
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29631
e-mail: xu7@g.clemson.edu

Georges Fadel

Mem. ASME
Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29631
e-mail: fgeorge@clemson.edu

Margaret M. Wiecek

Department of Mathematical Sciences,
Clemson University,
Clemson, SC 29631
e-mail: wmalgor@clemson.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 25, 2016; final manuscript received December 12, 2016; published online January 6, 2017. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 139(3), 031401 (Jan 06, 2017) (11 pages) Paper No: MD-16-1392; doi: 10.1115/1.4035501 History: Received May 25, 2016; Revised December 12, 2016

The augmented Lagrangian coordination (ALC), as an effective coordination method for decomposition-based optimization, offers significant flexibility by providing different variants when solving nonhierarchically decomposed problems. In this paper, these ALC variants are analyzed with respect to the number of levels and multipliers, and the resulting advantages and disadvantages are explored through numerical tests. The efficiency, accuracy, and parallelism of three ALC variants (distributed ALC, centralized ALC, and analytical target cascading (ATC) extended by ALC) are discussed and compared. Furthermore, the dual residual theory for the centralized ALC is extended to the distributed ALC, and a new flexible nonmonotone weight update is proposed and tested. Numerical tests show that the proposed update effectively improves the accuracy and robustness of the distributed ALC on a benchmark engineering test problem.

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Figures

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Fig. 1

A problem decomposed into a four-node network structure

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Fig. 2

Four different ALC-structures to solve the problem depicted in Fig. 1: (a) distributed ALC, (b) centralized ALC, (c) ATC-2 level, and (d) ATC-3 level

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Fig. 3

Five-subproblem partition of example 1

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Fig. 4

Four ALC-structures (distributed ALC, centralized ALC, and ATC) to solve example 1: (a) distributed ALC, (b) centralized ALC, (c) ATC-2 level, and (d) ATC-3 level

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Fig. 5

Partition of example 2 [22]

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Fig. 6

Three ALC-structures (distributed ALC, centralized ALC, and ATC) to solve example 2: (a) distributed ALC, (b) centralized ALC, and (c) ATC-2 level

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Fig. 7

Comparison of the KKT conditions for the distributed ALC before and after the decomposition

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