Design of complex products with several interacting subsystems or disciplinary analyses poses substantive challenges to both analysis and optimization, necessitating specialized solution techniques. A product or system may qualify as complex due to large scale or due to strong interactions. Single-level strategies for complex system optimization centralize decision-making authority, while multilevel strategies distribute the decision-making process. This article studies important differences between two popular single-level formulations: multidisciplinary feasible (MDF) and individual disciplinary feasible (IDF). Results presented aim at aiding practitioners in selecting between formulations. Specifically, while IDF incurs some computational overhead, it may find optima hidden to MDF and is more efficient computationally for strongly coupled problems; further, MDF is sensitive to variations in coupling strength, while IDF is not. Conditions that lead to failure of MDF are described. Two new reproducible design examples are introduced to illustrate these findings and to provide test problems for other investigations.

1.
Wagner
,
T. C.
, 1993, “
General Decomposition Methodology For Optimal System Design
,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
2.
Rogers
,
J. L.
, and
Bloebaum
,
C. L.
, 1994, “
Ordering Design Tasks Based on Coupling Strengths
,”
5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL
, Sept. 7–9, Paper No. AIAA-1994-4326.
3.
Haftka
,
R.
,
Sobieszczanski-Sobieski
,
J.
, and
Padula
,
S. L.
, 1992, “
On Options for Interdisciplinary Analysis and Design Optimization
,”
Struct. Optim.
0934-4373,
4
(
2
), pp.
65
74
.
4.
Alyaqout
,
S. F.
,
Papalambros
,
P. Y.
, and
Ulsoy
,
A. G.
, 2005, “
Quantification and Use of System Coupling in Decomposed Design Optimization Problems
,”
Proceedings of International Mechanical Engineering Congress and Exposition
, Nov. 5–11, Paper No. IMECE2005-81364.
5.
Sosa
,
M. E.
,
Eppinger
,
S. D.
, and
Rowles
,
C. M.
, 2003, “
Identifying Modular and Integrative Systems and Their Impact on Design Team Interactions
,”
ASME J. Mech. Des.
1050-0472,
125
, pp.
240
252
.
6.
Sosa
,
M. E.
,
Eppinger
,
S. D.
, and
Rowles
,
C. M.
, 2004, “
The Misalignment of Product Architecture and Organizational Structure in Complex Product Development
,”
Manage. Sci.
0025-1909,
50
(
12
), pp.
1674
1689
.
7.
Chanron
,
V.
, and
Lewis
,
K.
, 2004, “
Convergence and Stability in Distributed Design of Large Systems
,”
ASME Design Engineering Technical Conference
, Sept. 28–Oct. 2, Paper No. DETC2004-57344.
8.
Bertsekas
,
D. P.
, 1999,
Nonlinear Programming
,
2nd ed.
,
Athena Scientific
, Nashua, NH.
9.
Cramer
,
E. J.
,
Dennis
,
J. E.
Jr.
,
Frank
,
P. D.
,
Lewis
,
R. M.
, and
Shubin
,
G. R.
, 1994, “
Problem Formulation for Multidisciplinary Optimization
,”
SIAM J. Optim.
1052-6234,
4
(
4
), pp.
754
776
.
10.
Allison
,
J. T.
, 2004, “
Complex System Optimization: A Review of Analytical Target Cascading, Collaborative Optimization, and Other Formulations
,” MS’s thesis, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.
11.
Allison
,
J. T.
,
Kokkolaras
,
M.
,
Zawislak
,
M.
, and
Papalambros
,
P. Y.
, 2005, “
On the Use of Analytical Target Cascading and Collaborative Optimization for Complex System Design
,”
6th World Conference on Structural and Multidisciplinary Optimization
, May 30–June 3.
12.
Balling
,
R. J.
, and
Sobieszczanski-Sobieski
,
J.
, 1996, “
Optimization of Coupled Systems: A Critical Overview of Approaches
,”
AIAA J.
0001-1452,
34
(
1
), pp.
6
17
.
13.
Balling
,
R. J.
, and
Wilkinson
,
C. A.
, 1997, “
Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems
,”
AIAA J.
0001-1452,
35
, pp.
178
186
.
14.
Hulme
,
K. F.
, and
Bloebaum
,
C. L.
, 2000, “
Simulation-Based Comparison of Multidisciplinary Design Optimization Solution Strategies Using Cascade
,”
Struct. Multidiscip. Optim.
1615-147X,
19
(
1
), pp.
17
35
.
15.
Sobieszczanski-Sobieski
,
J.
, and
Haftka
,
R. T.
, 1997, “
Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments
,”
Struct. Optim.
0934-4373,
14
(
1
),
1
23
.
16.
Braun
,
R. D.
, 1996, “
Collaborative Optimization: An Architecture for Large-Scale Distributed Design
,” Ph.D. thesis, Stanford University, Stanford, CA.
17.
Alexandrov
,
N. M.
, and
Lewis
,
R. M.
, 2000, “
Algorithmic Perspective on Problem Formulations in MDO
,”
8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Sept. 6–8.
18.
Thareja
,
R.
, and
Haftka
,
R.
, 1986, “
Numerical Difficulties Associated With Using Equality Constraints to Achieve Multilevel Decomposition in Structural Optimization
,”
AIAA/ASME/ASCE/AHS 27th Structures, Structural Dynamics and Materials Conference. Part 1: Structures and Materials
.
19.
Chapra
,
S. C.
, and
Canale
,
R. P.
, 1998,
Numerical Methods for Engineers
,
3rd ed.
,
McGraw-Hill
, New York.
20.
Hildebrand
,
F. B.
, 1974,
Introduction to Numerical Analysis
,
2nd ed.
,
McGraw-Hill
, New York.
21.
Kim
,
H. M.
, 2001, “
Target Cascading in Optimal System Design
,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
22.
Wells Manufacturing Corp.
, 1999, “
Making Sense of Engine Airflow
,” Counterpoint: The Electronic Diagnostic and Driveability Resource, Vol.
3
(
3
), pp.
1
3
.
23.
Papalambros
,
P. Y.
, and
Wilde
,
D. J.
, 2000,
Principles of Optimal Design: Modeling and Computation
,
2nd ed.
,
Cambridge University Press
, New York.
24.
University of Michigan, Aerospace Engineering display, François-Xavier Bagnoud Building, April, 2006.
25.
Incropera
,
F. P.
, and
DeWitt
,
D. P.
, 2002,
Introduction to Heat Transfer
,
John Wiley and Sons, Inc.
, New York.
26.
MATWEB Material Property Data, http://www.matweb.com/http://www.matweb.com/, accessed April 9, 2004.
You do not currently have access to this content.