Analytical target cascading (ATC) is an effective decomposition approach used for engineering design optimization problems that have hierarchical structures. With ATC, the overall system is split into subsystems, which are solved separately and coordinated via target/response consistency constraints. As parallel computing becomes more common, it is desirable to have separable subproblems in ATC so that each subproblem can be solved concurrently to increase computational throughput. In this paper, we first examine existing ATC methods, providing an alternative to existing nested coordination schemes by using the block coordinate descent method (BCD). Then we apply diagonal quadratic approximation (DQA) by linearizing the cross term of the augmented Lagrangian function to create separable subproblems. Local and global convergence proofs are described for this method. To further reduce overall computational cost, we introduce the truncated DQA (TDQA) method, which limits the number of inner loop iterations of DQA. These two new methods are empirically compared to existing methods using test problems from the literature. Results show that computational cost of nested loop methods is reduced by using BCD, and generally the computational cost of the truncated methods is superior to the nested loop methods with lower overall computational cost than the best previously reported results.
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e-mail: yanjingl@stanford.edu
e-mail: zhaosong@sfu.ca
e-mail: jmichalek@cmu.edu
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Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading
Yanjing Li,
Yanjing Li
Ph.D. Candidate
Department of Electrical Engineering and Computer Science,
e-mail: yanjingl@stanford.edu
Stanford University
, Stanford, CA 94305
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Zhaosong Lu,
Zhaosong Lu
Assistant Professor
Department of Mathematics,
e-mail: zhaosong@sfu.ca
Simon Fraser University
, Burnaby, British Columbia V5A 1S6 Canada
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Jeremy J. Michalek
Jeremy J. Michalek
Assistant Professor
Department of Mechanical Engineering, and Department of Engineering and Public Policy,
e-mail: jmichalek@cmu.edu
Carnegie Mellon University
, Pittsburgh, PA 15213
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Yanjing Li
Ph.D. Candidate
Department of Electrical Engineering and Computer Science,
Stanford University
, Stanford, CA 94305e-mail: yanjingl@stanford.edu
Zhaosong Lu
Assistant Professor
Department of Mathematics,
Simon Fraser University
, Burnaby, British Columbia V5A 1S6 Canadae-mail: zhaosong@sfu.ca
Jeremy J. Michalek
Assistant Professor
Department of Mechanical Engineering, and Department of Engineering and Public Policy,
Carnegie Mellon University
, Pittsburgh, PA 15213e-mail: jmichalek@cmu.edu
J. Mech. Des. May 2008, 130(5): 051402 (11 pages)
Published Online: March 25, 2008
Article history
Received:
October 13, 2006
Revised:
June 26, 2007
Published:
March 25, 2008
Citation
Li, Y., Lu, Z., and Michalek, J. J. (March 25, 2008). "Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading." ASME. J. Mech. Des. May 2008; 130(5): 051402. https://doi.org/10.1115/1.2838334
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