Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.

1.
Gu
,
L.
, 2001, “
A Comparison of Polynomial Based Regression Models in Vehicle Safety Analysis
,”
Proceedings 2001 ASME Design Engineering Technical Conferences—Design Automation Conference
,
A.
Diaz
, ed.,
ASME
, Pittsburgh, PA, September
9
12
, DAC-21063.
2.
Koch
,
P. N.
,
Simpson
,
T. W.
,
Allen
,
J. K.
, and
Mistree
,
F.
, 1999, “
Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size
,”
J. Aircr.
0021-8669,
36
(
1
), pp.
275
286
.
3.
Barthelemy
,
J. F. M.
, and
Haftka
,
R.
, 1993, “
Approximation Concepts for Optimal Structural Design—A Review
,”
Struct. Optim.
0934-4373,
5
, pp.
129
144
.
4.
Haftka
,
R. T.
,
Scott
,
E. P.
, and
Cruz
,
J. R.
, 1998, “
Optimization and Experiments: A Survey
,”
Appl. Mech. Rev.
0003-6900,
51
(
7
), pp.
435
448
.
5.
Simpson
,
T. W.
,
Peplinski
,
J.
,
Koch
,
P. N.
, and
Allen
,
J. K.
, 2001, “
Metamodels for Computer-Based Engineering Design: Survey and Recommendations
,”
Eng. Comput.
0177-0667,
17
(
2
), pp.
129
150
.
6.
Simpson
,
T. W.
,
Booker
,
A. J.
,
Ghosh
,
D.
,
Giunta
,
A. A.
,
Koch
,
P. N.
, and
Yang
,
R. J.
, 2004, “
Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion
,”
Struct. Multidiscip. Optim.
1615-147X,
27
, pp.
302
313
.
7.
Ullman
,
D. G.
, 2002, “
Toward the Ideal Mechanical Engineering Design Support System
,”
Res. Eng. Des.
0934-9839,
13
, pp.
55
64
.
8.
Myers
,
R. H.
, and
Montgomery
,
D.
, 1995,
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
,
Wiley
, Toronto.
9.
Chen
,
W.
, 1995, “
A Robust Concept Exploration Method for Configuring Complex System
,” Ph.D. dissertation thesis, Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA.
10.
Mitchell
,
T. J.
, 1974, “
An Algorithm for the Construction of “D-Optimal” Experimental Designs
,”
Technometrics
0040-1706,
16
(
2
), pp.
203
210
.
11.
Giunta
,
A. A.
,
Balabanov
,
V.
,
Haim
,
D.
,
Grossman
,
B.
,
Mason
,
W. H.
,
Watson
,
L. T.
, and
Haftka
,
R. T.
, 1997, “
Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments Theory and Response Surface Modeling
,”
Aeronaut. J.
0001-9240,
101
(
1008
), pp.
347
356
.
12.
Sacks
,
J.
,
Welch
,
W. J.
,
Mitchell
,
T. J.
, and
Wynn
,
H. P.
, 1989, “
Design and Analysis of Computer Experiments
,”
Stat. Sci.
0883-4237,
4
(
4
), pp.
409
435
.
13.
Jin
,
R.
,
Chen
,
W.
, and
Simpson
,
T. W.
, 2001, “
Comparative Studies of Metamodeling Techniques Under Multiple Modeling Criteria
,”
Struct. Multidiscip. Optim.
1615-147X,
23
(
1
), pp.
1
13
.
14.
Koehler
,
J. R.
, and
Owen
,
A.
, 1996, “
Computer Experiments
,”
Handbook of Statistics
,
S.
Ghosh
and
C. R.
Rao
, eds.,
Elsevier Science
, New York, pp.
261
308
.
15.
Currin
,
C.
,
Mitchell
,
T. J.
,
Morris
,
M. D.
, and
Ylvisaker
,
D.
, 1991, “
Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments
,”
J. Am. Stat. Assoc.
0162-1459,
86
(
416
), pp.
953
963
.
16.
Johnson
,
M. E.
,
Moore
,
L. M.
, and
Ylvisaker
,
D.
, 1990, “
Minimax and Maximin Distance Designs
,”
J. Stat. Plan. Infer.
0378-3758,
26
(
2
), pp.
131
148
.
17.
Taguchi
,
G.
,
Yokoyama
,
Y.
, and
Wu
,
Y.
, 1993,
Taguchi Methods: Design of Experiments
,
American Supplier Institute
, Allen Park, MI.
18.
Owen
,
A.
, 1992, “
Orthogonal Arrays for Computer Experiments, Integration, and Visualization
,”
Stat. Sin.
1017-0405,
2
, pp.
439
452
.
19.
Hedayat
,
A. S.
,
Sloane
,
N. J. A.
, and
Stufken
,
J.
, 1999,
Orthogonal Arrays: Theory and Applications
,
Springer
, New York.
20.
McKay
,
M. D.
,
Bechman
,
R. J.
, and
Conover
,
W. J.
, 1979, “
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code
,”
Technometrics
0040-1706,
21
(
2
), pp.
239
245
.
21.
Iman
,
R. L.
, and
Conover
,
W. J.
, 1980, “
Small Sensitivity Analysis Techniques for Computer Models With an Application to Risk Assessment
,”
Commun. Stat: Theory Meth.
0361-0926,
A9
(
17
), pp.
1749
1842
.
22.
Tang
,
B.
, 1993, “
Orthogonal Array-based Latin Hypercubes
,”
J. Am. Stat. Assoc.
0162-1459,
88
(
424
), pp.
1392
1397
.
23.
Park
,
J. S.
, 1994, “
Optimal Latin-hypercube Designs for Computer Experiments
,”
J. Stat. Plan. Infer.
0378-3758,
39
, pp.
95
111
.
24.
Ye
,
K. Q.
,
Li
,
W.
, and
Sudjianto
,
A.
, 2000, “
Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs
,”
J. Stat. Plan. Infer.
0378-3758,
90
,
145
159
.
25.
Kalagnanam
,
J. R.
, and
Diwekar
,
U. M.
, 1997, “
An Efficient Sampling Technique for Off-Line Quality Control
,”
Technometrics
0040-1706,
39
(
3
), pp.
308
319
.
26.
Meckesheimer
,
M.
,
Booker
,
A. J.
,
Barton
,
R. R.
, and
Simpson
,
T. W.
, 2002, “
Computationally Inexpensive Metamodel Assessment Strategies
,”
AIAA J.
0001-1452,
40
(
10
), pp.
2053
2060
.
27.
Fang
,
K. T.
,
Lin
,
D. K. J.
,
Winker
,
P.
, and
Zhang
,
Y.
, 2000, “
Uniform Design: Theory and Application
,”
Technometrics
0040-1706,
39
(
3
), pp.
237
248
.
28.
Chen
,
V. C. P.
,
Tsui
,
K.-L.
,
Barton
,
R. R.
, and
Meckesheimer
,
M.
, 2006, “
A Review on Design, Modeling and Applications of Computer Experiments
,”
IIE Trans.
0740-817X,
38
, pp.
273
291
.
29.
Simpson
,
T. W.
,
Lin
,
D. K. J.
, and
Chen
,
W.
, 2001, “
Sampling Strategies for Computer Experiments: Design and Analysis
,”
Int. J. Reliab. Appl.
1598-0073,
2
(
3
), pp.
209
240
.
30.
Au
,
S. K.
, and
Beck
,
J. L.
, 1999, “
A New Adaptive Importance Sampling Scheme for Reliability Calculations
,”
Struct. Safety
0167-4730,
21
, pp.
135
158
.
31.
Zou
,
T.
,
Mourelatos
,
Z.
,
Mahadevan
,
S.
, and
Tu
,
J.
, 2003, “
An Indicator Response Surface-Based Monte Carlo Method for Efficient Component and System Reliability Analysis
,”
Proceedings ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Chicago, IL, September 2–6, DAC-48708.
32.
Zou
,
T.
,
Mahadevan
,
S.
,
Mourelatos
,
Z.
, and
Meernik
,
P.
, 2002, “
Reliability Analysis of Automotive Body-Door Subsystem
,”
Reliab. Eng. Syst. Saf.
0951-8320,
78
, pp.
315
324
.
33.
Kloess
,
A.
,
Mourelatos
,
Z.
, and
Meernik
,
P.
, 2004, “
Probabilistic Analysis of An Automotive Body-Door System
,”
Int. J. Veh. Des.
0143-3369,
34
(
2
), pp.
101
125
.
34.
Ditlevsen
,
O.
,
Olesen
,
R.
, and
Mohr
,
G.
, 1987, “
Solution of A Class of Load Combination Problems by Directional Simulation
,”
Struct. Safety
0167-4730,
4
, pp.
95
109
.
35.
Walker
,
J. R.
, 1986, “
Practical Application of Variance Reduction Techniques in Probabilistic Assessments
,”
Proceedings 2nd International Conference on Radioactive Waste Management
, Winnipeg, Manitoba, Canada, September 7–11.
36.
Nie
,
J.
, and
Ellingwood
,
B. R.
, 2005, “
Finite Element-Based Structural Reliability Assessment Using Efficient Directional Simulation
,”
J. Eng. Mech.
0733-9399,
131
(
3
), pp.
259
267
.
37.
Wang
,
L.
,
Shan
,
S.
, and
Wang
,
G. G.
, 2004, “
Mode-Pursuing Sampling Method for Global Optimization on Expensive Black-box Functions
,”
Eng. Optimiz.
0305-215X,
36
(
4
), pp.
419
438
.
38.
Shan
,
S.
, and
Wang
,
G. G.
, 2005, “
An Efficient Pareto Set Identification Approach for Multi-objective Optimization on Black-box Functions
,”
J. Mech. Des.
1050-0472,
127
, pp.
866
874
.
39.
Wang
,
G. G.
,
Wang
,
L.
, and
Shan
,
S.
, 2005, “
Reliability Assessment Using Discriminative Sampling and Metamodeling
,”
SAE Trans.
0096-736X, J. Passenger Cars—Mechanical Syst., pp.
291
300
.
40.
Fu
,
J. C.
, and
Wang
,
L.
, 2002, “
A Random-Discretization Based Monte Carlo Sampling Method and Its Applications
,”
Methodol. Comput. Appl. Probab.
1387-5841,
4
, pp.
5
25
.
41.
Lin
,
Y.
, 2004, “
An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design
,” Ph.D. dissertation thesis, Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA.
42.
Jin
,
R.
,
Chen
,
W.
, and
Sudjianto
,
A.
, 2005, “
An Efficient Algorithm for Constructing Optimal Design of Computer Experiments
,”
J. Stat. Plan. Infer.
0378-3758,
134
(
1
), pp.
268
287
.
44.
Sasena
,
M.
,
Parkinson
,
M.
,
Goovaerts
,
P.
,
Papalambros
,
P.
, and
Reed
,
M.
, 2002, “
Adaptive Experimental Design Applied to An Ergonomics Testing Procedure
,”
Proceedings ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference
,
ASME
, Montreal, Canada, September 29-October 2, DETC2002/DAC-34091.
45.
Wang
,
G. G.
, 2003, “
Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points
,”
J. Mech. Des.
1050-0472,
125
, pp.
210
220
.
46.
Wang
,
G. G.
, and
Simpson
,
T. W.
, 2004, “
Fuzzy Clustering Based Hierarchical Metamodeling for Space Reduction and Design Optimization
,”
Eng. Optimiz.
0305-215X,
36
(
3
), pp.
313
335
.
47.
Jin
,
R.
,
Chen
,
W.
, and
Sudjianto
,
A.
, 2002, “
On Sequential Sampling for Global Metamodeling for in Engineering Design
,”
Proceedings ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference
, Montreal, Canada, September 29–October 2, DETC2002/DAC-34092.
48.
Sacks
,
J.
,
Schiller
,
S. B.
, and
Welch
,
W. J.
, 1989, “
Designs for Computer Experiments
,”
Technometrics
0040-1706,
31
(
1
), pp.
41
47
.
49.
Cresssie
,
N.
, 1988, “
Spatial Prediction and Ordinary Kriging
,”
Math. Geol.
0882-8121,
20
(
4
), pp.
405
421
.
50.
Papadrakakis
,
M.
,
Lagaros
,
M.
, and
Tsompanakis
,
Y.
, 1998, “
Structural Optimization Using Evolution Strategies and Neural Networks
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
156
(
1–4
), pp.
309
333
.
51.
Dyn
,
N.
,
Levin
,
D.
, and
Rippa
,
S.
, 1986, “
Numerical Procedures for Surface Fitting of Scattered Data by Radial Basis Functions
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
7
(
2
), pp.
639
659
.
52.
Fang
,
H.
, and
Horstemeyer
,
M. F.
, 2006, “
Global Response Approximation With Radial Basis Functions
,”
Eng. Optimiz.
0305-215X,
38
(
4
), pp.
407
424
.
53.
Friedman
,
J. H.
, 1991, “
Multivariate Adaptive Regressive Splines
,”
Ann. Stat.
0090-5364,
19
(
1
), pp.
1
67
.
54.
De Boor
,
C.
, and
Ron
,
A.
, 1990, “
On Multivariate Polynomial Interpolation
,”
Constructive Approx.
0176-4276,
6
, pp.
287
302
.
55.
Langley
,
P.
, and
Simon
,
H. A.
, 1995, “
Applications of Machine Learning and Rule Induction
,”
Commun. ACM
0001-0782,
38
(
11
), pp.
55
64
.
56.
Varadarajan
,
S.
,
Chen
,
W.
, and
Pelka
,
C. J.
, 2000, “
Robust Concept Exploration of Propulsion Systems With Enhanced Model Approximation Capabilities
,”
Eng. Optimiz.
0305-215X,
32
(
3
), pp.
309
334
.
57.
Giunta
,
A. A.
, and
Watson
,
L. T.
, 1998, “
A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models
,”
Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization
, Vol.
1
,
American Institute of Aeronautics and Astronautics, Inc.
, St. Louis, MO, September 2–4, AIAA-98-4758.
58.
Simpson
,
T. W.
,
Mauery
,
T. M.
,
Korte
,
J. J.
, and
Mistree
,
F.
, 2001, “
Kriging Metamodels for Global Approximation in Simulation-based Multidisciplinary Design Optimization
,”
AIAA J.
0001-1452,
39
(
12
), pp.
2233
2241
.
59.
Wang
,
L.
,
Beeson
,
D.
,
Akkaram
,
S.
, and
Wiggs
,
G.
, 2005, “
Gaussian Process Metamodels for Efficient Probabilistic Design in Complex Engineering Design Spaces
,”
Proceedings ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Long Beach, CA, September 24–28, DETC2005-85406.
60.
Qian
,
Z.
,
Seepersad
,
C. C.
,
Joseph
,
V. R.
,
Wu
,
C. F. J.
, and
Allen
,
J. K.
, 2004, “
Building Surrogate Models Based on Detailed and Approximate Simulations
,”
Proceedings ASME 2004 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Salt Lake City, UT, September 28–October 2, DETC2004-57486.
61.
Martin
,
J. D.
, and
Simpson
,
T. W.
, 2005, “
Use of Kriging Models to Approximate Deterministic Computer Models
,”
AIAA J.
0001-1452,
43
(
4
), pp.
853
863
.
62.
Li
,
R.
, and
Sudjianto
,
A.
, 2003, “
Penalized Likelihood Kriging Model for Analysis of Computer Experiments
,”
Proceedings ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Chicago, IL, September 2–6, DETC2003/DAC-48758.
63.
Kleijnen
,
J. P. C.
, and
van Beers
,
W.
, 2003, “
Kriging for Interpolation in Random Simulation
,”
J. Oper. Res. Soc. Jpn.
0453-4514,
54
, pp.
255
262
.
64.
Daberkow
,
D. D.
, and
Mavris
,
D. N.
, 2002, “
An Investigation of Metamodeling Techniques for Complex Systems Design
,”
Proceedings 9th AIAA/USFA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Atlanta, GA, September 4–6, AIAA 2002–5457.
65.
Lophaven
,
S. N.
,
Nielsen
,
H. B.
, and
Søndergaard
,
J.
, 2002, DACE—A Matlab Kriging Toolbox—Version 2.0, Informatics and Mathematical Modelling,
Technical University of Denmark
, Kgs. Lyngby, Denmark, Rep. No. IMM-REP-2002-12.
66.
Clarke
,
S. M.
,
Griebsch
,
J. H.
, and
Simpson
,
T. W.
, 2005, “
Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses
,”
J. Mech. Des.
1050-0472,
127
(
6
), pp.
1077
1087
.
67.
Pérez
,
V. M.
,
Renaud
,
J. E.
, and
Watson
,
L. T.
, 2002, “
Adaptive Experimental Design for Construction of Response Surface Approximations
,”
AIAA J.
0001-1452,
40
(
12
), pp.
2495
2503
.
68.
Mullur
,
A. A.
, and
Messac
,
A.
, 2005, “
Extended Radial Basis Functions: More Flexible and Effective Metamodeling
,”
AIAA J.
0001-1452,
43
(
6
), pp.
1306
1315
.
69.
Turner
,
C. J.
, and
Crawford
,
R. H.
, 2005, “
Selecting an Appropriate Metamodel: The Case for NURBS Meamodels
,”
Proceedings ASME 2005 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Long Beach, CA, September 24–28, DETC2005-85043.
70.
Morris
,
M. D.
,
Mitchell
,
T. J.
, and
Ylvisaker
,
D.
, 1993, “
Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction
,”
Technometrics
0040-1706,
35
(
3
), pp.
243
255
.
71.
Koehler
,
J. R.
, 1997, “
Estimating the Response, Derivatives, and Transmitted Variance Using Computer Experiments
,”
Proceedings 1997 Symposium on the Interface of Computing Science and Statistics
, Houston, TX, May 14–17.
72.
Toropov
,
V. V.
, and
Filatov
,
A. A.
, 1993, “
Multi-parameter Structural Optimization Using FEM and Multipoint Approximation
,”
Struct. Multidiscip. Optim.
1615-147X,
6
, pp.
7
14
.
73.
Wang
,
L. P.
,
Grandhi
,
R. V.
, and
Canfield
,
R. A.
, 1996, “
Multivariate Hermite Approximation for Design Optimization
,”
Int. J. Numer. Methods Eng.
0029-5981,
39
, pp.
787
803
.
74.
Rasmussen
,
J.
, 1998, “
Nonlinear Programming by Cumulative Approximation Refinement
,”
Struct. Optim.
0934-4373,
15
, pp.
1
7
.
75.
Shin
,
Y. S.
, and
Grandhi
,
R. V.
, 2001, “
A Global Structural Optimization Technique Using an Interval Method
,”
Struct. Multidiscip. Optim.
1615-147X,
22
, pp.
351
363
.
76.
Huber
,
K. P.
,
Berthold
,
M. R.
, and
Szczerbicka
,
H.
, 1996, “
Analysis of Simulation Models with Fuzzy Graph Based Metamodeling
,”
Perform. Eval.
0166-5316,
27–28
, pp.
473
490
.
77.
Madu
,
C. N.
, 1995, “
A Fuzzy Theoretic Approach to Simulation Metamodeling
,”
Appl. Math. Lett.
0893-9659,
8
(
6
), pp.
35
41
.
78.
Kleijnen
,
J. P. C.
, 2004, “
Design and Analysis of Monte Carlo Experiments
,”
Handbook of Computational Statistics: Concepts and Fundamentals
,
J. E.
Gentle
,
W.
Haerdle
, and
Y.
Mori
, eds.,
Springer-Verlag
, Heidelberg, Germany.
79.
Giunta
,
A. A.
,
Dudley
,
J. M.
,
Narducci
,
R.
,
Grossman
,
B.
,
Haftka
,
R. T.
,
Mason
,
W. H.
, and
Watson
,
L. T.
, 1994, “
Noisy Aerodynamic Response and Smooth Approximations in HSCT Design
,”
Proceedings 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 7–9 Sept.
, Vol.
2
,
AIAA
, Panama City, FL.
80.
Madsen
,
J. I.
,
Shyy
,
W.
, and
Haftka
,
R.
, 2000, “
Response Surface Techniques for Diffuser Shape Optimization
,”
AIAA J.
0001-1452,
38
(
9
), pp.
1512
1518
.
81.
Jin
,
R.
,
Du
,
X.
, and
Chen
,
W.
, 2003, “
The Use of Metamodeling Techniques for Optimization Under Uncertainty
,”
Struct. Multidiscip. Optim.
1615-147X,
25
(
2
), pp.
99
116
.
82.
van Beers
,
W.
, and
Kleijnen
,
J. P. C.
, 2004, “
Kriging Interpolation in Simulation: A Survey
,”
Proceedings of the 2004 Winter Simulation Conference
,
R. G.
Ingalls
,
M. D.
Rossetti
,
J. S.
Smith
, and
B. A.
Peters
, eds., Washington, D.C., December 5–8, pp.
113
121
.
83.
Oberkampf
,
W. L.
, and
Trucano
,
T. G.
, 2000, “
Validation Methodology in Computational Fluid Dynamics
,”
Proceedings Fluids 2000
, Denver, CO, June 19–22, AIAA 2000–2549.
84.
Roache
,
P. J.
, 1998,
Verification and Validation in Computational Science and Engineering
,
Hermosa Publishers
, Albuquerque, NM.
85.
Meckesheimer
,
M.
, 2001, “
A Framework For Metamodel-Based Design: Subsystem Metamodel Assessment and Implementation Issues
,” Ph.D. dissertation thesis, Industrial Engineering, The Pennsylvania State University, University Park, PA.
86.
Mitchell
,
T. J.
, and
Morris
,
M. D.
, 1992, “
Bayesian Design and Analysis of Computer Experiments: Two Examples
,”
Stat. Sin.
1017-0405,
2
, pp.
359
379
.
87.
Montgomery
,
D.
, 1991,
Design and Analysis of Experiments
,
Wiley
, New York.
88.
Wong
,
P. C.
, and
Bergeron
,
R. D.
, 1997, “
30 Years of Multidimensional Multivariate Visualization
,”
Scientific Visualization—Overviews, Methodologies and Techniques
,
G. M.
Nielson
,
H.
Hagan
, and
H.
Muller
, eds.,
IEEE Computer Society Press
, Los Alamitos, CA, pp.
3
33
.
89.
Keim
,
D. A.
, and
Kriegel
,
H. P.
, 1996, “
Visualization Techniques for Mining Large Databases: A Comparison
,”
IEEE Trans. Knowl. Data Eng.
1041-4347,
8
(
6
), pp.
923
938
.
90.
Winer
,
E. H.
, and
Bloebaum
,
C. L.
, 2002, “
Development of Visual Design Steering as an Aid in Large-scale Multidisciplinary Design Optimization. Part II: Method Validation
,”
Struct. Multidiscip. Optim.
1615-147X,
23
(
6
), pp.
425
435
.
91.
Winer
,
E. H.
, and
Bloebaum
,
C. L.
, 2002, “
Development of Visual Design Steering as an Aid in Large-scale Multidisciplinary Design Optimization. Part I: Method Development
,”
Struct. Multidiscip. Optim.
1615-147X,
23
(
6
), pp.
412
424
.
92.
Eddy
,
J.
, and
Lewis
,
K. E.
, 2002, “
Visualization of Multi-dimensional Design and Optimization Data Using Cloud Visualization
,”
Proceedings ASME 2002 Design Engineering Technical Conference and Computers and Information in Engineering Conference
, Montreal, Canada, September 29–October 2, DETC2002/DAC-34130.
93.
Kodiyalam
,
S.
,
Yang
,
R. J.
, and
Gu
,
L.
, 2004, “
High Performance Computing and Surrogate Modeling for Rapid Visualization with Multidisciplinary Optimization
,”
AIAA J.
0001-1452,
42
(
11
), pp.
2347
2354
.
94.
Simpson
,
T. W.
, 2004, “
Multidisciplinary Design Optimization
,”
Aerosp. Am.
0740-722X,
12
, pp.
34
.
95.
Stump
,
G.
,
Simpson
,
T. W.
,
Yukish
,
M.
, and
Bennett
,
L.
, 2002, “
Multidimensional Design and Visualization and Its Application to a Design By Shopping Paradigm
,”
Proceedings 9th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
AIAA
, Atlanta, GA, September 4–6, AIAA-2002-5622.
96.
Eddy
,
J.
, and
Lewis
,
K. E.
, 2002, “
Multidimensional Design Visualization in Multiobjective Optimization
,”
Proceedings 9th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
AIAA
, Atlanta, GA, September 4–6, AIAA-2002-5621.
97.
Mattson
,
C. A.
, and
Messac
,
A.
, 2003, “
Concept Selection Using s-Pareto Frontiers
,”
AIAA J.
0001-1452,
41
(
6
), pp.
1190
1204
.
98.
Ligetti
,
C.
, and
Simpson
,
T. W.
, 2005, “
Metamodel-Driven Design Optimization Using Integrative Graphical Design Interfaces: Results From a Job-Shop Manufacturing Simulation Experiment
,” Transactions of the ASME,
J. Comput. Inf. Sci. Eng.
1530-9827,
5
(
1
), pp.
8
17
.
99.
Ligetti
,
C.
,
Simpson
,
T. W.
,
Frecker
,
M.
,
Barton
,
R. R.
, and
Stump
,
G.
, 2003, “
Assessing the Impact of Graphical Design Interfaces on Design Efficiency and Effectiveness
,” Transactions of the ASME,
J. Comput. Inf. Sci. Eng.
1530-9827,
3
(
2
), pp.
144
154
.
100.
Simpson
,
T. W.
,
Iyer
,
P. S.
,
Rothrock
,
L.
,
Frecker
,
M.
,
Barton
,
R. R.
,
Barron
,
K. A.
, and
Meckesheimer
,
M.
, 2005, “
Metamodel-Driven Interfaces for Engineering Design: Impact of Delay and Problem Size on User Performance
,”
Proceedings 1st AIAA Multidisciplinary Design Optimization Specialist Conference, 18–21 Apr.
,
AIAA
, Austin, TX, April 18–21, AIAA-2005-2060.
101.
Box
,
G. E. P.
, and
Draper
,
N. R.
, 1969,
Evolutionary Operation: A Statistical Method for Process Management
,
Wiley
, New York.
102.
Welch
,
W. J.
,
Buck
,
R. J.
,
Sacks
,
J.
,
Wynn
,
H. P.
,
Mitchell
,
T. J.
, and
Morris
,
M. D.
, 1992, “
Screening, Predicting, and Computer Experiments
,”
Technometrics
0040-1706,
34
(
1
), pp.
15
25
.
103.
Balabanov
,
V. O.
,
Giunta
,
A. A.
,
Golovidov
,
O.
,
Grossman
,
B.
,
Mason
,
W. H.
, and
Watson
,
L. T.
, 1999, “
Reasonable design space approach to response surface approximation
,”
J. Aircr.
0021-8669,
36
(
1
), pp.
308
315
.
104.
Chen
,
W.
,
Allen
,
J. K.
,
Schrage
,
D. P.
, and
Mistree
,
F.
, 1997, “
Statistical Experimentation Methods for Achieving Affordable Concurrent Systems Design
,”
AIAA J.
0001-1452,
35
(
5
), pp.
893
900
.
105.
Wujek
,
B. A.
, and
Renaud
,
J. E.
, 1998, “
New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 1
,”
AIAA J.
0001-1452,
36
(
10
), pp.
1911
1921
.
106.
Wujek
,
B. A.
, and
Renaud
,
J. E.
, 1998, “
New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2
,”
AIAA J.
0001-1452,
36
(
10
), pp.
1922
1934
.
107.
Toropov
,
V.
,
van Keulen
,
F.
,
Markine
,
V.
, and
de Doer
,
H.
, 1996, “
Refinements in the Multi-Point Approximation Method to Reduce the Effects of Noisy Structural Responses
,”
Proceedings 6th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Vol.
2
,
AIAA
, Bellevue, WA, September 4–6, AIAA-96-4087-CP.
108.
Alexandrov
,
N.
,
Dennis
,
J. E. J.
,
Lewis
,
R. M.
, and
Torczon
,
V.
, 1998, “
A Trust Region Framework for Managing the Use of Approximation Models in Optimization
,”
Struct. Optim.
0934-4373,
15
(
1
), pp.
16
23
.
109.
Rodríguez
,
J. F.
,
Renaud
,
J. E.
, and
Watson
,
L. T.
, 1998, “
Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization
,”
J. Mech. Des.
1050-0472,
120
, pp.
58
66
.
110.
Renaud
,
J. E.
, and
Gabriele
,
G. A.
, 1994, “
Approximation in Non-hierarchical System Optimization
,”
AIAA J.
0001-1452,
32
, pp.
198
205
.
111.
Wang
,
G. G.
,
Dong
,
Z.
, and
Aitchison
,
P.
, 2001, “
Adaptive Response Surface Method—A Global Optimization Scheme for Computation-Intensive Design Problems
,”
Eng. Optimiz.
0305-215X,
33
(
6
), pp.
707
734
.
112.
Shan
,
S.
, and
Wang
,
G. G.
, 2004, “
Space Exploration and Global Optimization for Computationally Intensive Design Problems: A Rough Set Based Approach
,”
Struct. Multidiscip. Optim.
1615-147X,
28
(
6
), pp.
427
441
.
113.
Wang
,
G. G.
, and
Shan
,
S.
, 2004, “
Design Space Reduction for Multi-objective Optimization and Robust Design Optimization Problems
,”
SAE Trans.
0096-736X, Journal of Materials & Manufacturing, pp.
101
110
.
114.
Li
,
B.
,
Shiu
,
B.-W.
, and
Lau
,
K.-J.
, 2001, “
Fixture Configuration Design for Sheet Metal Laser Welding With a Two-Stage Response Surface Methodology
,”
Proceedings ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Pittsburgh, PA, September 9–12, DETC2001/DAC-21096.
115.
Dennis
,
J. E.
, and
Torczon
,
V.
, 1996, “
Managing Approximation Models in Optimization
,”
Multidisciplinary Design Optimization: State of the Art
,
N.
Alexandrov
, and
M. Y.
Hussaini
, eds., Society for Industrial and Applied Mathematics,
Philadelphia.
116.
Osio
,
I. G.
, and
Amon
,
C. H.
, 1996, “
An Engineering Design Methodology With Multistage Bayesian Surrogates and Optimal Sampling
,”
Res. Eng. Des.
0934-9839,
8
(
4
), pp.
189
206
.
117.
Booker
,
A. J.
,
Dennis
,
J. E.
,
Frank
, Jr.,
P. D.
,
Serafini
,
D. B.
,
Torczon
,
V.
, and
Trosset
,
M. W.
, 1999, “
A Rigorous Framework for Optimization of Expensive Functions by Surrogates
,”
Struct. Optim.
0934-4373,
17
(
1
), pp.
1
13
.
118.
Rodríguez
,
J. F.
,
Pérez
,
V. M.
,
Padmanabhan
,
D.
, and
Renaud
,
J. E.
, 2001, “
Sequential Approximate Optimization Using Variable Fidelity Response Surface Approximations
,”
Struct. Multidiscip. Optim.
1615-147X,
22
, pp.
24
44
.
119.
Schonlau
,
M. S.
,
Welch
,
W. J.
, and
Jones
,
D. R.
, 1998, “
Global Versus Local Search in Constrained Optimization of Computer Models
,”
New Development and Applications in Experimental Design
,
N.
Flournoy
,
W. F.
Rosenberger
, and
W. K.
Wong
eds.,
Institute of Mathematical Statistics
,
Haywood, CA
, pp.
11
25
.
120.
Sasena
,
M.
,
Papalambros
,
P.
, and
Goovaerts
,
P.
, 2002, “
Global Optimization of Problems With Disconnected Feasible Regions Via Surrogate Modeling
,”
Proceedings 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
AIAA
, Atlanta, Ga, September, AIAA 2002-5573.
121.
Gelsey
,
A.
,
Schwabacher
,
M.
, and
Smith
,
D.
, 1998, “
Using Modeling Knowledge to Guide Design Space Search
,”
Artif. Intell.
0004-3702,
100
(
1-0
), pp.
1
27
.
122.
Shan
,
S.
, and
Wang
,
G. G.
, 2006, “
Failure Surface Frontier for Reliability Assessment on Expensive Performance Function
,”
J. Mech. Des.
1050-0472,
128
,
1227
1235
.
123.
Jones
,
D. R.
,
Schonlau
,
M.
, and
Welch
,
W. J.
, 1998, “
Efficient Global Optimization of Expensive Black Box Functions
,”
J. Global Optim.
0925-5001,
13
, pp.
455
492
.
124.
Hirokawa
,
N.
,
Fujita
,
K.
, and
Iwase
,
T.
, 2002, “
Voronoi Diagram Based Blending of Quadratic Response Surfaces for Cumulative Global Optimization
,”
Proceedings 9th AIAA/ISSMO Symposium on Multi-Disciplinary Analysis and Optimization
,
AIAA
, Atlanta, GA, September 4–6, AIAA-2002-5460.
125.
Hacker
,
K.
,
Eddy
,
J.
, and
Lewis
,
K. E.
, 2001, “
Tuning a Hybrid Optimization Algorithm by Determining the Modality of the Design Space
,”
Proceedings ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Pittsburgh, PA, September 9–12, DETC2001/DAC-21093.
126.
Ong
,
Y. S.
,
Nair
,
P. B.
, and
Keane
,
A. J.
, 2003, “
Evolutionary Optimization of Computationally Expensive Problems via Surrogate Modeling
,”
AIAA J.
0001-1452,
41
(
4
), pp.
687
696
.
127.
Tappeta
,
R. V.
, and
Rosenberger
,
W. F.
, 2001, “
Interactive Multiobjective Optimization Design Strategy for Decision Based Design
,”
J. Mech. Des.
1050-0472,
123
, pp.
205
215
.
128.
Wilson
,
B.
,
Cappelleri
,
D. J.
,
Simpson
,
T. W.
, and
Frecker
,
M. I.
, 2000, “
Efficient Pareto Frontier Exploration Using Surrogate Approximations
,”
Proceedings 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
AIAA
, Long Beach, CA, September 6–8, AIAA-2000-4895.
129.
Li
,
Y.
,
Fadel
,
G. M.
, and
Wiecek
,
M. M.
, 1998, “
Approximating Pareto Curves Using the Hyper-Ellipse
,”
Proceedings 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
AIAA
, St. Louis, AIAA-98-4961.
130.
Yang
,
B. S.
,
Yeun
,
Y. S.
, and
Ruy
,
W. S.
, 2003, “
Managing Approximation Models in Multiobjective Optimization
,”
Struct. Multidiscip. Optim.
1615-147X,
24
, pp.
141
156
.
131.
Zhang
,
J.
,
Wiecek
,
M. M.
, and
Chen
,
W.
, 2000, “
Local Approximation of the Efficient Frontier in Robust Design
,”
J. Mech. Des.
1050-0472,
122
, pp.
232
236
.
132.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K. L.
, and
Mistree
,
F.
, 1996, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
J. Mech. Des.
1050-0472,
118
, pp.
478
485
.
133.
Chen
,
W.
,
Fu
,
W.
,
Biggers
,
S. B.
, and
Latour
,
R. A.
, 2000, “
An Affordable Approach for Robust Design of Thick Laminated Composite Structure
,”
Optim. Eng.
1389-4420,
1
(
3
), pp.
305
322
.
134.
Booker
,
A. J.
,
Meckesheimer
,
M.
, and
Torng
,
T.
, 2004, “
Reliability Based Design Optimization Using Design Explorer
,”
Optim. Eng.
1389-4420,
5
, pp.
179
205
.
135.
Youn
,
B. D.
, and
Choi
,
K. K.
, 2004, “
Selecting Probabilistic Approaches for Reliability-Based Design Optimization
,”
AIAA J.
0001-1452,
42
(
1
), pp.
124
131
.
136.
Sobieszczanski-Sobieski
,
J.
, and
Haftka
,
R. T.
, 1997, “
Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments
,”
Struct. Optim.
0934-4373,
14
(
1
), pp.
1
23
.
137.
Golovidov
,
O.
,
Kodiyalam
,
S.
,
Marineau
,
P.
,
Wang
,
L.
, and
Rohl
,
P.
, 1999, “
A Flexible, Object-based Implementation of Approximation Models in an MDO Framework
,”
Design Optimization: Int. J. Product Process Improvement
,
1
(
4
), pp.
388
404
.
138.
Batill
,
S. M.
,
Stelmack
,
M. A.
, and
Sellar
,
R. S.
, 1999, “
Framework for Multidisciplinary Design Based on Response-Surface Approximations
,”
J. Aircr.
0021-8669,
36
(
1
), pp.
287
297
.
139.
Sobieski
,
I.
, and
Kroo
,
I.
, 2000, “
Collaborative Optimization Using Response Surface Estimation
,”
AIAA J.
0001-1452,
38
(
10
), pp.
1931
1938
.
140.
Wang
,
D.
, 2005, “
Multidisciplinary Design Optimization With Collaboration Pursuing and Domain Decomposition: Application to Aircraft Design
,” Ph.D. dissertation thesis, Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, Canada.
141.
Plackett
,
R. L.
, and
Burman
,
J. P.
, 1946, “
The Design of Optimum Multifactorial Experiments
,”
Biometrika
0006-3444,
33
(
4
), pp.
305
325
.
142.
Otto
,
J. C.
,
Landman
,
D.
, and
Patera
,
A. T.
, 1996, “
A Surrogate Approach to the Experimental Optimization of Multi-element Airfoils
,”
Proceedings 6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Bellevue Wa, September 4–6,
AIAA
96-4138 CP.
143.
Otto
,
J. C.
,
Paraschivoiu
,
M.
,
Yesilyurt
,
S.
, and
Patera
,
A. T.
, 1995, “
Computer Simulation Surrogates for Optimization: Application of Trapezoidal Ducts and Axisymmetric Bodies
,”
Proceedings ASME International Mechanical Engineering Conference and Exposition
,
ASME
, San Francisco, CA, November 12–17.
144.
Wang
,
D.
,
Naterer
,
G.
, and
Wang
,
G. G.
, 2003, “
Thermofluid Optimization of a Heated Helicopter Engine Cooling Bay Surface
,”
Can. Aeronautics Space J.
0008-2821,
49
(
2
), pp.
73
86
.
145.
Yang
,
R. J.
,
Wang
,
N.
,
Tho
,
C. H.
, and
Bobineau
,
J. P.
, 2001, “
Metamodeling Development for Vehicle Frontal Impact Simulation
,”
Proceedings ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Pittsburgh, PA, September 9–12, DETC2001/DAC-21012.
146.
Redhe
,
M.
,
Giger
,
M.
, and
Nilsson
,
L.
, 2004, “
An Investigation of Structural Optimization in Crashworthiness Design Using a Stochastic Approach
,”
Struct. Multidiscip. Optim.
1615-147X,
27
, pp.
446
459
.
147.
Giunta
,
A.
,
Balabanov
,
V.
,
Haim
,
D.
,
Grossman
,
B.
,
Mason
,
W. H.
,
Watson
,
L. T.
, and
Haftka
,
R.
, 1996, “
Wing Design for a High-Speed Civil Transport Using a Design of Experiments Methodology
,”
Proceedings 6th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Vol.
1
,
AIAA
, Bellevue, WA, September 4–6, AIAA-96-4001-CP.
148.
Wang
,
G. G.
, and
Dong
,
Z.
, 2000, “
Design Optimization of a Complex Mechanical System Using Adaptive Response Surface Method
,”
Trans. Can. Soc. Mech. Eng.
0315-8977,
24
(
1B
), pp.
295
306
.
149.
Ejakov
,
M.
,
Sudjianto
,
A.
, and
Pieprzak
,
J.
, 2004, “
Robustness and Performance Optimization of Engine Bearing System Using Computer Model and Surrogate Noise
,”
Proceedings ASME 2004 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
ASME
, Salt Lake City, Utah, September 28–October 2, DETC2004-57327.
150.
Srivastava
,
A.
,
Hacker
,
K.
,
Lewis
,
K. E.
, and
Simpson
,
T. W.
, 2004, “
A Method for Using Legacy Data for Metamodel-Based Design of Large-Scale Systems
,”
Struct. Multidiscip. Optim.
1615-147X,
28
, pp.
146
155
.
151.
Leary
,
S. J.
,
Bhaskar
,
A.
, and
Keane
,
A. J.
, 2003, “
A Knowledge-Based Approach To Response Surface Modelling in Multifidelity Optimization
,”
J. Global Optim.
0925-5001,
26
, pp.
297
319
.
152.
Farhang Mehr
,
A.
,
Li
,
G.
,
Azarm
,
S.
, and
Diaz
,
A.
, 2004, “
Meta-Modeling of Multi-Response Engineering Simulations
,”
Proceedings 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
, Albany, NY, Aug. 30–Sept. 1, AIAA-2004-4485.
153.
Sahin
,
K. H.
, and
Diwekar
,
U. M.
, 2004, “
Better Optimization of Nonlinear Uncertain Systems (Bonus): A New Algorithm for Stochastic Programming Using Reweighting Through Kernel Density Estimation
,”
Ann. Operat. Res.
0254-5330,
132
, pp.
47
68
.
154.
Ellman
,
T.
,
Keane
,
J.
,
Schwabacher
,
M.
, and
Yao
,
K. T.
, 1997, “
Multi-level Modeling for Engineering Design Optimization
,”
Artif. Intell. Eng. Des. Anal. Manuf.
0890-0604,
11
(
5
), pp.
1
36
.
155.
Leoni
,
N.
, and
Amon
,
C. H.
, 2000, “
Bayesian Surrogates for Integrating Numerical, Analytical and Experimental Data: Application to Inverse Heat Transfer in Wearable Computers
,”
IEEE Trans. Compon. Packag. Technol.
1521-3331,
23
(
1
), pp.
23
32
.
156.
Bakr
,
M. H.
,
Bandler
,
J. W.
,
Madsen
,
K.
, and
Sondergaard
,
J.
, 2000, “
Review of the Space Mapping Approach to Engineering Optimization and Modeling
,”
Optim. Eng.
1389-4420,
1
, pp.
241
276
.
157.
Campbell
,
M.
, 2006, “
Qualitative and Quantitative Sequential Sampling
,”
Proceedings of the ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
, ASME, Philadelphia, PA, September 10–13, DETC2006/DAC-99178.
158.
Romero
,
D. A.
, 2006, “
On Adaptive Sampling for Metamodels in Simulation-based Design and Optimization
,”
Proceedings of the ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
, ASME, Philadelphia, PA, September 10–13, DETC2006/DAC-99210.
159.
Koch
,
P. N.
,
Yang
,
R. J.
, and
Gu
,
L.
, 2004, “
Design for Six Sigma Through Robust Optimization
,”
Struct. Multidiscip. Optim.
1615-147X,
26
(
3–4
), pp.
235
248
.
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