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.
Improving the Performance of the Augmented Lagrangian Coordination: Decomposition Variants and Dual Residuals
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.
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Xu, M., Fadel, G., and Wiecek, M. M. (January 6, 2017). "Improving the Performance of the Augmented Lagrangian Coordination: Decomposition Variants and Dual Residuals." ASME. J. Mech. Des. March 2017; 139(3): 031401. https://doi.org/10.1115/1.4035501
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