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.
Issue Section:
Design Automation
References
1.
Braun
, R. D.
, 1996
, “Collaborative Optimization: An Architecture for Large-Scale Distributed Design
,” Doctoral dissertation, Stanford University, Stanford, CA.2.
Braun
, R. D.
, Moore
, A. A.
, and Kroo
, I. M.
, 1997
, “Collaborative Approach to Launch Vehicle Design
,” J. Spacecr. Rockets
, 34
(4
), pp. 478
–486
.3.
Sobieszczanski-Sobieski
, J.
, 1989
, “Optimization by Decomposition: A Step From Hierarchic to Non-Hierarchic Systems
,” Second NASA Air Force Symposium on Advances in Multidisciplinary Analysis and Optimization
, Hampton, VA, Paper No. N89-25149.4.
Sobieszczanski-sobieski
, J.
, Agte
, J. S.
, and Sandusky
, R. R.
, 2000
, “Bi-Level Integrated System Synthesis (BLISS)
,” AIAA J.
, 38
(1
), pp. 164
–172
.5.
Kim
, H.
, 2001
, “Target Cascading in Optimal System Design
,” Doctoral dissertation, University of Michigan, Ann Arbor, MI.6.
Michelena
, N.
, Park
, H.
, and Papalambros
, P. Y.
, 2003
, “Convergence Properties of Analytical Target Cascading
,” AIAA J.
, 41
(5
), pp. 897
–905
.7.
Kim
, H. M.
, Kokkolaras
, M.
, Louca
, L. S.
, Delagrammatikas
, G. J.
, Michelena
, N. F.
, Filipi
, Z. S.
, Papalambros
, P. Y.
, Stein
, J. L.
, and Assanis
, D. N.
, 2002
, “Target Cascading in Vehicle Redesign Class VI Truck Study
,” Int. J. Veh. Des.
, 29
(3
), pp. 199
–225
.8.
Lassiter
, J. B.
, Wiecek
, M. M.
, and Andrighetti
, K. R.
, 2005
, “Lagrangian Coordination and Analytical Target Cascading: Solving ATC-Decomposed Problems With Lagrangian Duality
,” Optim. Eng.
, 6
(3
), pp. 361
–381
.9.
Guarneri
, P.
, Leverenz
, J. T.
, Wiecek
, M. M.
, and Fadel
, G.
, 2013
, “Optimization of Nonhierarchically Decomposed Problems
,” J. Comput. Appl. Math.
, 246
, pp. 312
–319
.10.
Tosserams
, S.
, Etman
, L. F. P.
, Papalambros
, P. Y.
, and Rooda
, J. E.
, 2006
, “An Augmented Lagrangian Relaxation for Analytical Target Cascading Using the Alternating Direction Method of Multipliers
,” Struct. Multidiscip. Optim.
, 31
(3
), pp. 176
–189
.11.
Wang
, W.
, 2012
, “Network Target Coordination for Design Optimization of Decomposed Systems
,” Doctoral dissertation, Clemson University, Clemson, SC.12.
Wang
, W.
, Xu
, M.
, Guarneri
, P.
, Fadel
, G.
, and Blouin
, V.
, 2012
, “A Consensus Optimization Via Alternating Direction Method of Multipliers for Network Target Coordination
,” 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
, Indianapolis, IN, Paper No. AIAA 2012-5552.13.
Wang
, W.
, Guarneri
, P.
, Fadel
, G.
, and Blouin
, V.
, 2012
, “Network Target Coordination for Optimal Design of Decomposed Systems With Consensus Optimization
,” ASME
Paper No. DETC2012-70333. 14.
Xu
, M.
, Wang
, W.
, Guarneri
, P.
, and Fadel
, G.
, 2013
, “CADMM Applied to Hybrid Network Decomposition
,” Tenth World Congress on Structural and Multidisciplinary Optimization
, Orlando, FL, May 19–24, Paper No. 5455.15.
Tosserams
, S.
, Kokkolaras
, M.
, Etman
, L. F. P.
, and Rooda
, J. E.
, 2010
, “A Nonhierarchical Formulation of Analytical Target Cascading
,” ASME J. Mech. Des.
, 132
(5
), p. 051002
.16.
Tosserams
, S.
, Etman
, L. F. P.
, and Rooda
, J. E.
, 2009
, “Multi-Modality in Augmented Lagrangian Coordination for Distributed Optimal Design
,” Struct. Multidiscip. Optim.
, 40
(1–6
), pp. 329
–352
.17.
Blouin
, V. Y.
, Lassiter
, J. B.
, Wiecek
, M. M.
, and Fadel
, M.
, 2005
, “Augmented Lagrangian Coordination for Decomposed Design Problems
,” Sixth World Congress on Structural and Multidisciplinary Optimization
, Rio de Janeiro, Brazil, May 30–June 3.18.
Kim
, H. M.
, Chen
, W.
, and Wiecek
, M. M.
, 2006
, “Lagrangian Coordination for Enhancing The Convergence of Analytical Target Cascading
,” AIAA J.
, 44
(10
), pp. 2197
–2207
.19.
Bertsekas
, D. P.
, 2003
, Nonlinear Programming
, 2nd ed., Athena Scientific
, Belmont, MA
.20.
Tosserams
, S.
, Etman
, L. F. P.
, and Rooda
, J. E.
, 2007
, “An Augmented Lagrangian Decomposition Method for Quasi-Separable Problems in MDO
,” Struct. Multidiscip. Optim.
, 34
(3
), pp. 211
–227
.21.
Tosserams
, S.
, Etman
, L. F. P.
, and Rooda
, J. E.
, 2008
, “Augmented Lagrangian Coordination for Distributed Optimal Design in MDO
,” Int. J. Numer. Methods Eng.
, 73
(13
), pp. 1885
–1910
.22.
Tosserams
, S.
, Etman
, L. F. P.
, and Rooda
, J. E.
, 2008
, “Block-Separable Linking Constraints in Augmented Lagrangian Coordination
,” Struct. Multidiscip. Optim.
, 37
(5
), pp. 521
–527
.23.
Tosserams
, S.
, Etman
, L. F. P.
, and Rooda
, J. E.
, 2010
, “A Micro-Accelerometer MDO Benchmark Problem
,” Struct. Multidiscip. Optim.
, 41
(2
), pp. 255
–275
.24.
Tosserams
, S.
, 2008
, “Distributed Optimization for Systems Design: An Augmented Lagrangian Coordination Method
,” Doctoral dissertation, Eindhoven University of Technology, Eindhoven, The Netherlands.25.
Xu
, M.
, Fadel
, G.
, and Wiecek
, M. M.
, 2014
, “Dual Residual in Augmented Lagrangian Coordination for Decomposition-Based Optimization
,” ASME
Paper No. DETC2014-35103. 26.
Xu
, M.
, Fadel
, G.
, and Wiecek
, M. M.
, 2015
, “Dual Residual for Centralized Augmented Lagrangian Coordination Based on Optimality Conditions
,” ASME J. Mech. Des.
, 137
(6
), p. 061401
.27.
Xu
, M.
, Fadel
, G.
, and Wiecek
, M. M.
, 2014
, “Solving Structure for Network-Decomposed Problems Optimized With Augmented Lagrangian Coordination
,” ASME
Paper No. DETC2014-35121. 28.
Xu
, M.
, Fadel
, G.
, and Wiecek
, M. M.
, 2015
, “Dual Residual for Distributed ALC Based on Optimality Conditions
,” ASME
Paper No. DETC2015-47002. Copyright © 2017 by ASME
You do not currently have access to this content.
