In decomposition-based design optimization strategies such as analytical target cascading (ATC), it is sometimes necessary to use reduced representations of highly discretized functional data exchanged among subproblems to enable efficient design optimization. However, the variables used by such reduced representation methods are often abstract, making it difficult to constrain them directly beyond simple bounds. This problem is usually addressed by implementing a penalty value-based heuristic that indirectly constrains the reduced representation variables. Although this approach is effective, it leads to many ATC iterations, which in turn yields an ill-conditioned optimization problem and an extensive runtime. To address these issues, this paper introduces a direct constraint management technique that augments the penalty value-based heuristic with constraints generated by support vector domain description (SVDD). A comparative ATC study between the existing and proposed constraint management methods involving electric vehicle design indicates that the SVDD augmentation is the most appropriate within decomposition-based design optimization.

References

References
1.
Kim
,
H. M.
, 2001, “
Target Cascading in Optimal System Design
,” Ph.D. Dissertation, University of Michigan, Ann Arbor, MI.
2.
Kim
,
H. M.
,
Michelena
,
N. M.
,
Papalambros
,
P. Y.
, and
Jiang
,
T.
, 2003, “
Target Cascading in Optimal System Design
,”
ASME J. Mech. Des.
,
125
(
3
), pp.
474
480
.
3.
Alexander
,
M. J.
, 2011, “
Management of Functional Data Variables in Decomposition-Based Design Optimization
,” Ph.D. Dissertation, University of Michigan, Ann Arbor, MI.
4.
Alexander
,
M. J.
,
Allison
,
J. T.
, and
Papalambros
,
P. Y.
, 2011, “
Reduced Representations of Vector-Valued Coupling Variables in Decomposition-Based Design Optimization
,”
Struct. Multidiscip. Optim.
5.
Kokkolaras
,
M.
,
Louca
,
L. S.
,
Delagrammatikas
,
D. J.
,
Michelena
,
N. F.
,
Filipi
,
Z. S.
,
Papalambros
,
P. Y.
,
Stein
,
J. L.
, and
Assanis
,
D. N.
, 2004, “
Simulation-Based Optimal Design of Heavy Trucks by Model-Based Decomposition: An Extensive Analytical Target Cascading Case Study
,”
Int. J. Heavy Vehicle Syst.
,
11
(
3/4
), pp.
402
431
.
6.
Wagner
,
T. C.
, and
Papalambros
,
P. Y.
, 1993, “
A General Framework for Decomposition Analysis in Optimal Design
,”
ASME Adv. Des. Autom.
,
65
, pp.
315
325
.
7.
Sirovich
,
L.
, 1987, “
Turbulence and the Dynamics of Coherent Structures. I—Coherent Structures. II—Symmetries and Transformations. III—Dynamics and Scaling
,”
Q. Appl. Math.
,
43
, pp.
561
–571, 573–
590
.
8.
Lucia
,
D. J.
,
Beran
,
P. S.
, and
Silva
,
W. A.
, 2004, “
Reduced Order Modeling: New Approaches for Computational Physics
,”
Prog. Aerosp. Sci.
,
40
, pp.
51
117
.
9.
Alexander
,
M. J.
,
Allison
,
J. T.
,
Papalambros
,
P. Y.
, and
Gorsich
,
D. J.
, 2010, “
Constraint Management of Reduced Representation Variables in Decomposition-Based Design Optimization
,”
Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, DETC 2010-28788.
10.
Tarassenko
,
L.
,
Hayton
,
P.
,
Cerneaz
,
N.
, and
Brady
,
M.
, 1995, “
Novelty Detection for the Identification of Masses in Mammograms
,”
Proceedings of the 4th International Conference on Artificial Neural Networks
, pp.
442
447
.
11.
Barber
,
C. B.
,
Dobkin
,
D. P.
, and
Huhdanpaa
,
H. T.
, 1996, “
The Quickhull Algorithm for Convex Hulls
,”
ACM Trans. Math. Softw.
,
22
(
4
), pp.
469
483
.
12.
Basudhar
,
A.
, and
Missoum
,
S.
, 2010, “
An Improved Adaptive Sampling Scheme for the Construction of Explicit Boundaries
,”
Struct. Multidiscip. Optim.
,
42
(
4
), pp.
517
529
.
13.
Basudhar
,
A.
, and
Missoum
,
S.
, 2009, “
A Sampling-Based Approach for Probabilistic Design With Random Fields
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
47/48
), pp.
3647
3655
.
14.
Tax
,
D. M. J.
, and
Duin
,
R. P. W.
, 1999, “
Data Domain Description Using Support Vectors
,”
Proceedings of the European Symposium on Artificial Neural Networks
, pp.
251
256
.
15.
Tax
,
D. M. J.
, and
Duin
,
R. P. W.
, 1999, “
Support Vector Domain Description
,”
Pattern Recogn. Lett.
,
20
, pp.
1191
1199
.
16.
Malak
,
R. J.
, 2008, “
Using Parameterized Efficient Sets to Model Alternatives for Systems Design Decisions
,” Ph.D. Dissertation, Georgia Institute of Technology, Atlanta, GA.
17.
Malak
,
R. J.
, and
Paredis
,
C. J. J.
, 2010, “
Using Support Vector Machines to Formalize the Valid Input Domain of Predictive Models in Systems Design Problems
,”
ASME J. Mech. Des.
,
132
(
10
), p.
101001
.
18.
Karhunen
,
K.
, 1946, “
Zur spektral theorie stochastischer prozesse
,”
Ann. Acad. Sci. Fennicae Ser
,
34
.
19.
Loeve
,
M.
, 1945, “
Functions aleatorie de second ordre
,”
C. R. Acad. des Sci.
, p.
220
.
20.
Ahmed
,
N.
, and
Goldstein
,
M. H.
, 1975,
Orthogonal Transforms for Digital Signal Processing
,
Springer
,
Berlin
.
21.
Toal
,
D. J. J.
,
Bressloff
,
N. W.
, and
Keane
,
A. J.
, 2008, “
Geometric Filtration Using POD for Aerodynamic Design Optimization
,”
Proceedings of the 26th AIAA Applied Aerodynamics Conference
, AIAA 2008-6584.
22.
Bui-Thanh
,
T.
,
Damodaran
,
M.
, and
Wilcox
,
K.
, 2004, “
Aerodynamic Reconstruction and Inverse Design Using Proper Orthogonal Decomposition
,”
AIAA J.
,
42
(
8
), pp.
1505
1516
.
23.
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
, pp.
176
189
.
24.
MATLAB® function Reference, The MathWorks, Inc., Natick, MA.
25.
Vapnik
,
V.
, 1995,
The Nature of Statistical Learning Theory
,
Springer
,
New York
.
26.
Scholkopf
,
B.
, and
Smola
,
J. A.
, 2002,
Learning With Mercer Kernels
,
MIT
,
Cambridge, MA
.
27.
Allison
,
J. T.
, 2008, “
Optimal Partitioning and Coordination Decisions in Decomposition-based Design Optimization
,” Ph.D. Dissertation, University of Michigan, Ann Arbor, MI.
28.
Alexander
,
M. J.
,
Allison
,
J. T.
, and
Papalambros
,
P. Y.
, 2011, “
Decomposition-Based Design Optimization of Electric Vehicle Powertrains Using Proper Orthogonal Decomposition
,”
Int. J. Powertrains
,
1
(
1
), pp.
72
92
.
29.
Abramson
,
M.
, 2007,
NOMADm Version 4.5 User’s Guide
,
Air Force Institute of Technology
,
Wright Patterson AFB
.
30.
Sendur
,
P.
,
Stein
,
J. L.
, and
Peng
,
H.
, 2002, “
A Model Accuracy and Validity Algorithm
,”
Proceedings of the 2002 ASME International Mechanical Engineering Congress and Exposition
, IMECE2002-DSC-34284.
31.
Alexander
,
M. J.
, and
Papalambros
,
P. Y.
, 2010, “
An Accuracy Assessment Method for Two-Dimensional Functional Data in Simulation Models
,”
Proceedings of the 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference
, AIAA 2010-9134.
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