This paper addresses the critical issue of effectiveness and efficiency in simulation-based optimization using surrogate models as predictive models in engineering design. Specifically, it presents a novel clustering-based multilocation search (CMLS) procedure to iteratively improve the fidelity and efficacy of Kriging models in the context of design decisions. The application of this approach will overcome the potential drawback in surrogate-model-based design optimization, namely, the use of surrogate models may result in suboptimal solutions due to the possible smoothing out of the global optimal point if the sampling scheme fails to capture the critical points of interest with enough fidelity or clarity. The paper details how the problem of smoothing out the best (SOB) can remain unsolved in multimodal systems, even if a sequential model updating strategy has been employed, and lead to erroneous outcomes. Alternatively, to overcome the problem of SOB defect, this paper presents the CMLS method that uses a novel clustering-based methodical procedure to screen out distinct potential optimal points for subsequent model validation and updating from a design decision perspective. It is embedded within a genetic algorithm setup to capture the buried, transient, yet inherent data pattern in the design evolution based on the principles of data mining, which are then used to improve the overall performance and effectiveness of surrogate-model-based design optimization. Four illustrative case studies, including a 21bar truss problem, are detailed to demonstrate the application of the CMLS methodology and the results are discussed.

1.
Hazelrigg
,
G. A.
, 1999, “
On the Role and Use of Mathematical Models in Engineering Design
,”
ASME J. Mech. Des.
1050-0472,
121
(
33
), pp.
336
341
.
2.
Gu
,
L.
, 2001, “
A Comparison of Polynomial Based Regression Models in Vehicle Safety Analysis
,”
Proceedings of ASME 2001 Design Engineering Technical Conferences
,
Pittsburgh, PA
, Sept. 9–12, Paper No. DETC2001/DAC-21063.
3.
Shao
,
T.
, and
Krishnamurty
,
S.
2006, “
Modeling Implications in Simulation-Based Design of Stents
,”
Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Philadelphia, PA
, Sept. 2–6, Paper No. DETC2006-99493.
4.
Booker
,
A. J.
,
Dennis
,
J. E.
,
Frank
,
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
.
5.
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
(
5
), pp.
302
313
.
6.
Wang
,
G. G.
, and
Shan
,
S.
, 2007, “
Review of Metamodeling Techniques in Support of Engineering Design Optimization
,”
ASME J. Mech. Des.
1050-0472,
129
(
4
), pp.
370
380
.
7.
Jones
,
D. R.
,
Schonlau
,
M.
, and
Welch
,
W. J.
, 1998, “
Efficient Global Optimization of Expensive Black-Box Functions
,”
J. Global Optim.
0925-5001,
13
(
4
), pp.
455
492
.
8.
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
.
9.
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
.
10.
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
.
11.
Chandrashekar
,
N.
, and
Krishnamurty
,
S.
, 2002, “
Bayesian Evaluation of Engineering Models
,”
Proceedings of ASME 2002 Design Engineering Technical Conference
,
Montreal, Canada
, Sept. 29–Oct. 2, Paper No. DETC2002/DAC-34141.
12.
Doraiswamy
,
S.
,
Krishnamurty
,
S.
, and
Grosse
,
I. R.
, 2000, “
Bayesian Analysis in Engineering Model Assessment
,”
Proceedings of ASME 2000 Design Engineering Technical Conferences
,
Baltimore, MD
, Sept. 10–13, Paper No. DETC2000/DTM-14546.
13.
Krishnamurty
,
S.
, and
Wilmes
,
G.
, 2004, “
Preference-Based Updating of Kriging Surrogate Models
,”
Proceedings of the Tenth AIAA/ISSMO Multidisciplinary Analysis
,
Albany, NY
, Aug. 30–Sept. 1, Paper No. AIAA-2004-4484.
14.
Simpson
,
T. W.
,
Peplinski
,
J. D.
,
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
.
15.
Kleijnen
,
J. P. C.
, and
van Beers
,
W. C. M.
, 2004, “
Application-Driven Sequential Designs for Simulation Experiments: Kriging Metamodelling
,”
J. Oper. Res. Soc.
,
55
(
9
), pp.
876
883
.
16.
Qian
,
Z.
,
Seepersad
,
C. C.
,
Joseph
,
V. R.
,
Allen
,
J. K.
, and
Wu
,
C. F. J.
, 2006, “
Building Surrogate Models Based on Detailed and Approximate Simulations
,”
ASME J. Mech. Des.
1050-0472,
128
(
4
), pp.
668
677
.
17.
Chen
,
W.
,
Jin
,
R.
, and
Sudjianto
,
A.
, 2005, “
Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty
,”
ASME J. Mech. Des.
1050-0472,
127
(
5
), pp.
875
886
.
18.
Hamza
,
K.
, and
Saitou
,
K.
, 2005, “
Design Optimization of Vehicle Structures for Crashworthiness Using Equivalent Mechanism Approximations
,”
ASME J. Mech. Des.
1050-0472,
127
(
3
), pp.
485
492
.
19.
Yang
,
R. J.
,
Wang
,
N.
,
Tho
,
C. H.
,
Bobineau
,
J. P.
, and
Wang
,
B. P.
, 2005, “
Metamodeling Development for Vehicle Frontal Impact Simulation
,”
ASME J. Mech. Des.
1050-0472,
127
(
5
), pp.
1014
1020
.
20.
Shao
,
T.
, and
Krishnamurty
,
S.
, 2006, “
Surrogate Model Updating Using Clustering in a Genetic Algorithm Setup
,”
Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Philadelphia, PA
, Sept. 2–6, Paper No. DETC2006-99491.
21.
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
.
22.
Sacks
,
J.
,
Schiller
,
S. B.
, and
Welch
,
W. J.
, 1989, “
Design for Computer Experiments
,”
Technometrics
0040-1706,
31
, pp.
41
47
.
23.
Booker
,
A. J.
, 1998, “
Design and Analysis of Computer Experiments
,”
Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
St. Louis, MO
, Sept. 2–4, Vol.
1
, pp.
118
128
.
24.
Santner
,
T. J.
,
Williams
,
B. J.
, and
Notz
,
W. I.
, 2003,
The Design and Analysis of Computer Experiments
,
Springer-Verlag
,
New York
.
25.
Jin
,
R.
,
Chen
,
W.
, and
Sudjianto
,
A.
, 2002, “
On Sequential Sampling for Global Metamodeling in Engineering Design
,”
Proceedings of ASME 2002 Design Engineering Technical Conference
,
Montreal, Canada
, Sept. 29–Oct. 2, Paper No. DETC2002/DAC-34092.
26.
Stone
,
M.
, 1974, “
Cross-Validatory Choice and Assessment of Statistical Predictions
,”
J. R. Stat. Soc. Ser. B (Methodol.)
0035-9246,
36
(
2
), pp.
111
147
.
27.
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
.
28.
Palmer
,
K. D.
, 1998, “
Data Collection Plans and Meta Models for Chemical Process Flowsheet Simulators
,” Ph.D. thesis, George Tech, Atlanta, GA.
29.
Simpson
,
T. W.
,
Allen
,
J. K.
, and
Mistree
,
F.
, 1998, “
Spatial Correlation Metamodels for Global Approximation in Structural Design Optimization
,”
Proceedings of ASME 1998 Design Engineering Technical Conferences
,
Atlanta, GA
, Sept. 13–16, Paper No. DETC98/DAC-5613.
30.
Koehler
,
J. R.
, and
Owen
,
A. B.
, 1996, “
Computer Experiments
,”
Handbook of Statistics
,
S.
Ghosh
and
C. R.
Rao
, eds.,
Elsevier Science
,
New York
, Vol.
13
, pp.
261
308
.
31.
Giunta
,
A. A.
,
Wojtkiewicz
,
S. F.
, and
Eldred
,
M. S.
, 2003, “
Overview of Modern Design of Experiments Methods for Computational Simulations
,”
Proceedings of 41st AIAA Aerospace Sciences Meeting and Exhibit
,
Reno, NV
, Jan. 6–9, Paper No. AIAA 2003-0649.
32.
Bursztyn
,
D.
, and
Steinberg
,
D. M.
, 2006, “
Comparison of Designs for Computer Experiments
,”
J. Stat. Plan. Infer.
0378-3758,
136
(
3
), pp.
1103
1119
.
33.
Simpson
,
T. W.
,
Dennis
,
L.
, and
Chen
,
W.
, 2002, “
Sampling Strategies for Computer Experiments: Design and Analysis
,”
Int. J. Reliab. Appl.
1598-0073,
2
(
3
), pp.
209
240
.
34.
Yfantis
,
E. A.
,
Flatman
,
G. T.
, and
Behar
,
J. V.
, 1987, “
Efficiency of Kriging Estimation for Square, Triangular and Hexagonal Grids
,”
Math. Geol.
0882-8121,
19
, pp.
183
205
.
35.
LaValle
,
S. R.
,
Branicky
,
M. S.
, and
Lindernann
,
S. R.
, 2004, “
On the Relationship Between Classical Grid Search and Probabilistic Roadmaps
,”
Int. J. Robot. Res.
0278-3649,
23
(
7–8
), pp.
673
692
.
36.
Cole
,
R. G.
,
Healy
,
T. R.
,
Wood
,
M. L.
, and
Foster
,
D. M.
, 2001, “
Statistical Analysis of Spatial Pattern: A Comparison of Grid and Hierarchical Sampling Approaches
,”
Environ. Monit. Assess.
0167-6369,
69
(
1
), pp.
85
99
.
37.
Fang
,
K. T.
,
Lin
,
D. K. J.
,
Winker
,
P.
, and
Zhang
,
Y.
, 2000, “
Uniform Design: Theory and Application
,”
Technometrics
0040-1706,
42
(
3
), pp.
237
248
.
38.
Matousek
,
J.
, 1999,
Geometric Discrepancy: An Illustrated Guide
,
Springer-Verlag
,
Heidelberg
.
39.
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
.
40.
Shewry
,
M. C.
, and
Wynn
,
H. P.
, 1987, “
Maximum Entropy Sampling
,”
Appl. Stat.
0285-0370,
14
(
2
), pp.
165
170
.
41.
Owen
,
A. B.
, 1992, “
Orthogonal Arrays for Computer Experiments, Integration and Visualization
,”
Stat. Sin.
1017-0405,
2
, pp.
439
452
.
42.
Hedayat
,
A. S.
,
Sloane
,
N. J. A.
, and
Stufken
,
J.
, 1999,
Orthogonal Arrays: Theory and Applications
,
Springer-Verlag
,
New York
.
43.
Roy
,
R. K.
, 2001,
Design of Experiments Using the Taguchi Approach: 16 Steps to Product and Process Improvement
,
Wiley
,
New York
.
44.
Mawardi
,
A.
, and
Pitchumani
,
R.
, 2005, “
SAMS: Stochastic Analysis with Minimal Sampling—A Fast Algorithm for Analysis and Design Under Uncertainty
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
558
571
.
45.
Audze
,
P.
, and
Eglais
,
V.
, 1977, “
New Approach for Planning Out of Experiments
,”
Problems of Dynamics and Strengths
,
35
, pp.
104
107
.
46.
Owen
,
A. B.
, and
Tavella
,
D. A.
, 1996, “
Scrambled Nets for Value at Risk Calculations
,”
Stanford University
, Technical Report, Stanford, CA.
47.
Owen
,
A. B.
, 2005, “
Local Antithetic Sampling With Scrambled Nets
,”
Stanford University
, Technical Report, Stanford, CA.
48.
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
.
49.
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
.
50.
Halton
,
J. H.
, 1960, “
On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals
,”
Numer. Math.
0029-599X,
2
, pp.
84
90
.
51.
Statnikov
,
R. B.
, and
Matusov
,
J. B.
, 2002,
Multicriteria Analysis in Engineering: Using the PSI Method With MOVI 1.0
,
Kluwer Academic
,
Dordrecht
.
52.
Husslage
,
B.
,
Rennen
,
G.
,
van Dam
,
R.
, and
den Hertog
,
D.
, 2006,
Space-Filling Latin Hypercube Designs for Computer Experiments
,
Tilburg University
,
The Netherlands
.
53.
McKey
,
M. D.
,
Beckman
,
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
.
54.
Morris
,
M. D.
, and
Mitchell
,
T. J.
, 1995, “
Exploratory Designs for Computer Experiments
,”
J. Stat. Plan. Infer.
0378-3758,
43
, pp.
381
402
.
55.
van Dam
,
E.
,
Husslage
,
B.
,
den Hertog
,
D.
, and
Melissen
,
H.
, 2005,
Maximin Latin Hypercube Designs in Two Dimensions
,
Tilburg University
,
The Netherlands
.
56.
Ye
,
K. Q.
,
Li
,
W.
, and
Sudjianto
,
A.
, 2000, “
Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs
,”
J. Stat. Plan. Infer.
0378-3758,
90
, pp.
145
159
.
57.
Tang
,
B.
, 1993, “
Orthogonal Array-Based Latin Hypercubes
,”
J. Am. Stat. Assoc.
0162-1459,
88
(
424
), pp.
1392
1397
.
58.
Crary
,
S. B.
,
Cousseau
,
P.
,
Armstrong
,
D.
,
Woodcock
,
D. M.
,
Mok
,
E. H.
,
Dubochet
,
O.
,
Lerch
,
P.
, and
Renaud
,
P.
, 2000, “
Optimal Design of Computer Experiments for Metamodel Generation Using I-OPT™
,”
Comput. Model. Eng. Sci.
1526-1492,
1
(
1
), pp.
127
139
.
59.
Crary
,
S. B.
, 2002, “
Design of Computer Experiments for Metamodel Generation
,”
Analog Integr. Circuits Signal Process.
0925-1030,
32
(
1
), pp.
7
16
.
60.
Park
,
J. S.
, 1994, “
Optimal Latin-Hypercube Designs for Computer Experiments
,”
J. Stat. Plan. Infer.
0378-3758,
39
(
1
), pp.
95
111
.
61.
Bates
,
S. J.
,
Sienz
,
J.
, and
Langley
,
D. S.
, 2003, “
Formulation of the Audze-Eglais Uniform Latin Hypercube Design of Experiments
,”
Adv. Eng. Software
0965-9978,
34
(
8
), pp.
493
506
.
62.
Bates
,
S. J.
,
Sienz
,
J.
, and
Toropov
,
V. V.
, 2004, “
Formulation of the Optimal Latin Hypercube Design of Experiments Using a Permutation Genetic Algorithm
,”
Proceedings of the 45th AIAA/ASME/ASCE/AHS /ASC Structures, Structural Dynamics and Materials Conference
,
Palm Springs, CA
Apr. 19–22, Paper No. AIAA-2004-2011.
63.
Robert
,
C. P.
, and
Casella
,
G.
, 2005,
Monte Carlo Statistical Methods
,
2nd ed.
,
Springer
,
New York
.
64.
Hammersley
,
J. M.
, 1960, “
Monte Carlo Methods for Solving Multivariable Problems
,”
Ann. N.Y. Acad. Sci.
0077-8923,
86
, pp.
844
874
.
65.
Niederreiter
,
H.
, 1992,
Random Number Generation and Quasi-Monte-Carlo Methods
,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
.
66.
Fang
,
K.-T.
,
Hickernell
,
F. J.
, and
Niederreiter
,
H.
, 2002,
Monte Carlo and Quasi-Monte Carlo Methods 2000
,
Springer-Verlag
,
Berlin
.
67.
Romero
,
V. J.
, and
Bankston
,
S. D.
, 1998, “
Finite-Element/ Progressive-Lattice-Sampling Response Surface Methodology and Application to Benchmark Probability Quantification Problems
,”
Sandia National Laboratories
, Technical Report No. SAND98-0567, Albuquerque, NM.
68.
Wang
,
X.
, and
Hickernell
,
F. J.
, 2002, “
A Historical Overview of Lattice Point Sets
,”
Monte Carlo and Quasi-Monte Carlo Methods 2000
,
F. J.
Fang
,
Hickernell
, and
H.
Niederreiter
, eds.,
Springer-Verlag
,
Berlin
, pp.
158
167
.
69.
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
.
70.
Owen
,
A. B.
, and
Zhou
,
Y.
, 1999, “
Safe and Effective Importance Sampling
,”
Stanford University
, Technical Report, Stanford, CA.
71.
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 of ASME 2003 Design Engineering Technical Conferences
,
Chicago, IL
, Sept. 2–6, Paper No. DETC2003/DAC-48708.9
72.
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
.
73.
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
.
74.
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
.
75.
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.
,
114
(
66
), pp.
291
300
.
76.
Welch
,
W. J.
, 1983, “
A Mean Squared Error Criterion for the Design of Experiments
,”
Biometrika
0006-3444,
70
(
1
), pp.
205
213
.
77.
Currin
,
C.
,
Mitchell
,
T.
,
Morris
,
M.
, 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
.
78.
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
, pp.
189
206
.
79.
Watson
,
A. G.
, and
Barnes
,
R. J.
, 1995, “
Infill Sampling Criteria to Locate Extremes
,”
Math. Geol.
0882-8121,
27
(
5
), pp.
589
608
.
80.
Sasena
,
M. J.
,
Papalambros
,
P.
, and
Goovaerts
,
P.
, 2002, “
Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization
,”
Eng. Optimiz.
0305-215X,
34
(
3
), pp.
263
278
.
81.
Schonlau
,
M.
, 1997, “
Computer Experiments and Global Optimization
,” Ph.D. thesis, University of Waterloo, Waterloo, Canada.
82.
Sóbester
,
A.
,
Leary
,
S. J.
, and
Keane
,
A. J.
, 2005, “
On the Design of Optimization Strategies Based on Global Response Surface Approximation Models
,”
J. Global Optim.
0925-5001,
33
(
1
), pp.
31
59
.
83.
Song
,
W.
, and
Keane
,
A. J.
, 2005, “
A New Hybrid Updating Scheme for an Evolutionary Search Strategy Using Genetic Algorithms and Kriging
,”
Proceedings of the 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
,
Austin, TX
, Apr. 18–21, Paper No. AIAA-2005-1901.
84.
Wang
,
G. G.
, 2003, “
Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points
,”
ASME J. Mech. Des.
1050-0472,
125
, pp.
210
220
.
85.
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
.
86.
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
.
87.
Martin
,
J. D.
, and
Simpson
,
T. W.
, 2003, “
A Study on the Use of Kriging Models to Approximate Deterministic Computer Models
,”
Proceedings of ASME 2003 Design Engineering Technical Conferences
,
Chicago, IL
, Sept. 2–6, Paper No. DETC2003/DAC-48762.
88.
Martin
,
J. D.
, and
Simpson
,
T. W.
, 2004, “
On the use of Kriging Models to Approximate Deterministic Computer Models
,”
ASME 2004 Design Engineering Technical Conferences
,
Salt Lake City, UT
, Sept. 28–Oct. 2, Paper No. DETC2004-57300.
89.
Reeves
,
C. R.
, and
Rowe
,
J. E.
, 2003,
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
,
Kluwer Academic
,
Norwell, MA
.
90.
ChipperFeld
,
A.
,
Fleming
,
P.
,
Pohlheim
,
H.
, and
Fonseca
,
C.
, 1994, Genetic Algorithm Toolbox User’s Guide Version 1.2,
University of Sheffield
, Sheffield, UK.
91.
Han
,
J.
, and
Kamber
,
M.
, 2006,
Data Mining: Concepts and Techniques
,
2nd ed.
,
Morgan Kaufmann
,
San Francisco, CA
.
92.
Spencer
,
H.
, 2003,
First Principles of a New System of Philosophy
,
Kessinger
,
Whitefish, MT
.
93.
Darwin
,
C.
, 1982,
On the Origin of Species by Means of Natural Selection: On the Preservation of Favoured Races in the Struggle for Life
,
J. W.
Burrow
, Ed.,
Penguin
,
London
.
94.
Sasena
,
M. J.
, 2002, “
Flexibility and Efficiency Enhancements for Constrained Global Design Optimization With Kriging Approximations
,” Ph.D. thessis, University of Michigan, Ann Arbor, MI.
95.
Juvinall
,
R. C.
, and
Marshek
,
K. M.
, 2000,
Fundamentals of Machine Component Design
,
3rd ed.
,
Wiley
,
New York
.
96.
Juvinall
,
R. C.
, and
Marshek
,
K. M.
, 2000,
Fundamentals of Machine Component Design
,
3rd ed.
,
Wiley
,
New York
.
97.
Moaveni
,
S.
, 2007,
Finite Element Analysis Theory and Application with ANSYS
,
3rd ed.
,
Prentice-Hall
,
Upper Saddle River, NJ
.
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