With the increasing design dimensionality, it is more difficult to solve multidisciplinary design optimization (MDO) problems. Many MDO decomposition strategies have been developed to reduce the dimensionality. Those strategies consider the design problem as a black-box function. However, practitioners usually have certain knowledge of their problem. In this paper, a method leveraging causal graph and qualitative analysis is developed to reduce the dimensionality of the MDO problem by systematically modeling and incorporating the knowledge about the design problem into optimization. Causal graph is created to show the input–output relationships between variables. A qualitative analysis algorithm using design structure matrix (DSM) is developed to automatically find the variables whose values can be determined without resorting to optimization. According to the impact of variables, an MDO problem is divided into two subproblems, the optimization problem with respect to the most important variables, and the other with variables of lower importance. The novel method is used to solve a power converter design problem and an aircraft concept design problem, and the results show that by incorporating knowledge in form of causal relationship, the optimization efficiency is significantly improved.

References

References
1.
Shan
,
S.
, and
Wang
,
G. G.
,
2010
, “
Survey of Modeling and Optimization Strategies to Solve High-Dimensional Design Problems With Computationally-Expensive Black-Box Functions
,”
Struct. Multidiscip. Optim.
,
41
(
2
), pp.
219
241
.
2.
Sobieszczanski-Sobieski
,
J.
,
1988
, “
Optimization by Decomposition: A Step From Hierarchic to Non-Hierarchic Systems
,” National Aeronautics and Space Administration, Washington, DC, Report No. N89-25149,
3.
Braun
,
D. R.
,
1996
, “
Collaborative Optimization: An Architecture for Large-Scale Distributed Design
,” Ph.D. thesis, Stanford University, Stanford, CA.
4.
Sobieszczanski-Sobieski
,
J.
,
Agte
,
J. S.
, and
Sandusky
,
R.
,
2000
, “
Bi-Level Integrated System Synthesis
,”
AIAA J.
,
38
(
1
), pp.
164
172
.
5.
Balling
,
R.
, and
Rawlings
,
M. R.
,
2000
, “
Collaborative Optimization With Disciplinary Conceptual Design
,”
Struct. Multidiscip. Optim.
,
20
(
3
), pp.
232
241
.
6.
Hwang
,
J.
,
Lee
,
D. Y.
,
Cutler
,
J.
, and
Martins
,
J.
,
2013
, “
Large-Scale MDO of a Small Satellite Using a Novel Framework for the Solution of Coupled Systems and their Derivatives
,”
AIAA
Paper No. AIAA 2013-1599.
7.
Tedford
,
N. P.
, and
Martins
,
J. R. R. A.
,
2010
, “
Benchmarking Multidisciplinary Design Optimization Algorithms
,”
Optim. Eng.
,
11
(
1
), pp.
159
183
.
8.
Coatanea
,
E.
,
Roca
,
R.
,
Mokhtarian
,
H.
,
Mokammel
,
F.
, and
Ikkala
,
K.
,
2016
, “
A Conceptual Modeling and Simulation Framework for System Design
,”
Comput. Sci. Eng.
,
18
(
4
), pp.
42
52
.
9.
Steward
,
D. V.
,
1981
, “
The Design Structure System: A Method for Managing the Design of Complex Systems
,”
IEEE Trans. Eng. Manage.
,
EM-28
(
3
), pp.
71
74
.
10.
Warfield
,
J.
,
1973
, “
Binary Matrices in System Modeling
,”
IEEE Trans. Syst. Man. Cybern.
,
SMC-3
(
5
), pp.
441
449
.
11.
Morris
,
M. D.
, and
Mitchell
,
T. J.
,
1995
, “
Exploratory Designs for Computational Experiments
,”
J. Stat. Plan. Inference
,
43
(
3
), pp.
381
402
.
12.
Ding
,
C.
,
He
,
X.
,
Zha
,
H.
, and
Simon
,
H. D.
,
2002
, “
Adaptive Dimension Reduction for Clustering High Dimensional Data
,”
IEEE
International Conference on Data Mining, Maebashi City, Japan, Dec. 9–12, pp.
147
154
.
13.
Phadke
,
M. S.
,
1998
, “
Quality Engineering Using Design of Experiment
,”
Quality Control, Robust Design and Taguchi Method
,
Wadsworth
,
Los Angeles, CA
.
14.
Ghani
,
J.
,
Choudhury
,
I.
, and
Hassan
,
H.
,
2004
, “
Application of Taguchi Method in the Optimization of End Milling Parameters
,”
J. Mater. Process. Technol.
,
145
(
1
), pp.
84
92
.
15.
NASA MultiDisciplinary Optimization Branch
,
2018
, “
Test Suite Problem 2.5, POWER CONVERTER
,” NASA Langley Research Center, Hampton VA, accessed Jan. 2, 2019, http://www.eng.buffalo.edu/Research/MODEL/mdo.test.orig/class2prob5/descr.html
16.
Wang
,
D.
,
Wang
,
G.
, and
Naterer
,
G.
,
2007
, “
Collaboration Pursuing Method for MDO Problems
,”
AIAA J.
,
45
(
5
), pp.
1091
1103
.
17.
Wu
,
D.
,
Coatanea
,
E.
, and
Wang
,
G. G.
,
2017
, “
Dimension Reduction and Decomposition Using Causal Graph and Qualitative Analysis for Aircraft Concept Design Optimization
,”
ASME
Paper No. DETC2017-67601.
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