In this paper, the application of visualization to aid in trade-off decisions when solving multi-objective optimization problems involving coupled subsystems under uncertainty is presented. The developed visualization method is an abstract way of representing these problems for use in a solution process where multiple resultant design points may exist. In these cases, a designer must consider potentially complex trade-off decisions in order to choose a point with which to proceed. Designers can examine the coupled subsystem design space under different uncertainty conditions through three-dimensional visual representations. Promising solution regions can be determined and explored down to a specific design point. As a result, the time to locate a trade-off solution for all subsystems has the potential to substantially decrease. This paper presents background into the type of problems being addressed as well as other visualization methods used in design. The method development is presented along with the results and discussion of a test case to illustrate the method’s viability.

1.
Simionescu
,
P. A.
, and
Beale
,
D.
, 2002, “
New Concepts in Graphics Visualization of Objective Functions
,” DETC02/DAC-34129,
Proceedings of the ASME DETC/CIE Conference
, Montreal, CA, Sept. 29–Oct. 2.
2.
Balling
,
R.
, 1999, “
Design by Shopping: A New Paradigm?
,” 21-EOM-1,
Proceedings of the Third World Congress of Structural and Multidisciplinary Optimization
, Buffalo, NY, May 17–21.
3.
Pareto
,
V.
, 1906,
Manuale di Econòmica Polìttica
, Società Editrice Libràia, Milan, Italy; translated into English by
A. S.
Schwier
, 1971, as Manual of Political Economy,
Macmillan
, New York.
4.
Eschenauer
,
H.
,
Koski
,
J.
, and
Osyczka
,
A.
, 1990,
Multicriteria Design Optimization
,
Springer-Verlag
, Berlin.
5.
Keeney
,
R. L.
, and
Raiffa
,
H.
, 1976,
Decisions With Multiple Objectives
,
Wiley
, New York.
6.
Lin
,
J. G.
, 1975, “
Three Methods for Determining Pareto-Optimal Solutions of Multiple-Objective Problems
,”
in Directions in Large-Scale Systems
,
Y. C.
Ho
and
S. K.
Mitter
, eds.,
Plenum Press
, New York, pp.
117
138
.
7.
Alexandrov
,
N. M.
, and
Lewis
,
R. M.
, 1999, “
Comparative Properties of Collaborative Optimization and Other Approaches to MDO
,”
ASMO UK/ISSMO Conference on Engineering Design Optimization
,
MCB University Press
,
Bradford, UK
, pp.
39
46
.
8.
Helig
,
M. H.
, 1992, “
El Cine del Futuro: The Cinema of the Future
,”
Presence
,
1
(
3
), pp.
279
292
.
9.
Aukstakalnis
,
S.
, and
Blatner
,
D.
, 1992,
Silicon Mirage: The Art and Science of Virtual Reality
,
Peachpit Press
, Berkeley, CA.
10.
Joining the Pieces
,” 2006,
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
127
(
12
), pp.
35
37
.
11.
Parker
,
S. G.
,
Weinstein
,
D. W.
, and
Johnson
,
C. R.
, 1997, “
The SCIRun Computational Steering Software System
,” in
Modern Software Tools for Scientific Computing
,
E.
Arge
,
A. M.
Bruaset
, and
H. P.
Langtangen
, eds.,
Birkhauser
, Boston, pp.
5
44
.
12.
Geist
,
G. A.
,
Kohl
,
J. A.
, and
Papadopoulos
,
P. M.
, 1997, “
CUMULVS: Providing Fault-Tolerance, Visualization and Steering of Parallel Applications
,”
Int. J. High Perform. Comput. Appl.
1094-3420,
11
(
3
), pp.
224
236
.
13.
Beazley
,
D. M.
, and
Lomdahl
,
P. S.
, 1996, “
Lightweight Computational Steering of Very Large Scale Molecular Dynamics Simulations
,”
Proceedings of Supercomputing ‘96
, Pittsburgh, PA, pp.
50
61
.
14.
Van Liere
,
R.
,
Mulder
,
J. D.
, and
van Wijk
,
J. J.
, 1997, “
Computational Steering
,”
FGCS, Future Gener. Comput. Syst.
0167-739X,
12
(
5
), pp.
441
450
.
15.
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
.
16.
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
.
17.
Winer
,
E. H.
, and
Bloebaum
,
C. L.
, 2001, “
Visual Design Steering for Optimization Solution Improvement
,”
Struct. Multidiscip. Optim.
1615-147X,
22
(
3
), pp.
219
229
.
18.
Nagel
,
H. R.
,
Granum
,
E.
, and
Musaeus
,
P.
, 2001, “
Methods for Visual Mining of Data in Virtual Reality
,”
Proceedings of the International Workshop on Visual Data Mining in Conjunction Second European Conference on Machine Learning and Fifth European Conference on Principles and Practice of Knowledge Discovery in Databases
, Freiburg, DE. Paper can also be accessed at: http://www.informatik.uni-freiburg.de/∼ml/ecmlpkdd/WS-Proceedings/w03/02-nagel.pdfhttp://www.informatik.uni-freiburg.de/∼ml/ecmlpkdd/WS-Proceedings/w03/02-nagel.pdf
19.
Eddy
,
J.
, and
Lewis
,
K.
, 2001, “
Effective Generation of Pareto Sets Using Genetic Programming
,” DETC02/DAC-02006,
Proceedings of the ASME Design Technical Conferences, Design Automation Conference
, Sept. 9–12, Pittsburgh, PA.
20.
Ribarsky
,
W.
,
Ayers
,
E.
,
Eble
,
J.
, and
Mukherjea
,
S.
, 1994, “
Glyphmaker: Creating Customized Visualizations of Complex Data
,”
IEEE Trans. Comput.
0018-9340,
27
(
7
), pp.
57
64
.
21.
Tweedie
,
L.
,
Spence
,
R.
,
Dawkes
,
H.
, and
Su
,
H.
, 1995, “
The Influence Explorter
,”
Proceedings of ACM CHI 95 Conference on Human Factors in Computing Systems
, May 7–11,
ACM Press
, Denver, CO, pp.
129
130
.
22.
Miner3D Visual Data Analysis Software, 2006, http://miner3d.comhttp://miner3d.com
23.
Mondrian–Interactive Statistical Data Visualization in Java, 2006, http://stats.math.uni-augsburg.de/mondrianhttp://stats.math.uni-augsburg.de/mondrian
24.
Stump
,
G. M.
,
Yukish
,
M.
,
Simpson
,
T. W.
, and
Bennett
,
L.
, 2002, “
Multidimensional Visualization and Its Application to a Design by Shopping Paradigm
,” AIAA-2002-5622,
9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Sept. 4–6, Atlanta, GA.
25.
Feiner
,
S.
, and
Beshers
,
C.
, 1990, “
Worlds Within Worlds
,”
ACM Symposium on User Interface Software and Technology
, Oct. 3–5, Snowbird, UT, pp.
76
83
.
26.
Partek Pattern Recognition Software, 2006, http://www.partek.comhttp://www.partek.com
28.
Telyingen
,
R. V.
,
Ribarsky
,
W.
, and
Mast
,
C.
, 1997, “
Virtual Data Visualizer
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
3
(
1
), pp.
65
74
.
29.
Keim
,
D.
, and
Kriegel
,
H-P.
, 1994, “
VisDB: Database Exploration using Multidimensional Visualization
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
14
(
5
), pp.
40
49
.
30.
Ward
,
M.
, 1994, “
Xmdvtool: Integrating Multiple Methods for Visualizing Multivariate Data
,”
Proceedings of IEEE Visualization ’94
, Oct. 17–21, Washington, DC, pp.
326
333
.
31.
Swayne
,
D. F.
,
Cook
,
D.
, and
Buja
,
A.
, 1998, “
XGobi: Interactive Dynamic Data Visualization in the X-Window System
,”
J. Comput. Graph. Stat.
1061-8600,
7
(
1
), pp.
113
130
.
32.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K-L.
, and
Mistree
,
F.
, 1996, “
A Procedure for Robust Design
,”
ASME J. Mech. Des.
1050-0472,
118
(
4
), pp.
478
485
.
33.
Chen
,
W.
, and
Lewis
,
K.
, 1999, “
A Robust Design Approach for Achieving Flexibility in Multidisciplinary Design
,”
AIAA J.
0001-1452,
7
(
8
), pp.
982
989
.
34.
Gu
,
X.
,
Renaud
,
J. E.
,
Batill
,
S. M.
,
Brach
,
R. M.
, and
Budhiraja
,
A. S.
, 2000, “
Worst Case Propagated Uncertainty of Multidisciplinary Systems in Robust Design Optimization
,”
Struct. Multidiscip. Optim.
1615-147X,
20
(
3
), pp.
190
213
.
35.
Halecki
,
T.
, and
Lewis
,
K.
, 2002, “
Coupled Systems Design in Probabilistic Environments
,” AIAA-2002-5586,
9th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
, Sept. 4–6, Atlanta, GA.
36.
Gould
,
H.
, and
Tobochnik
,
J.
, 1998,
An Introduction to Computer Simulation Methods, Part 2, Applications to Physical Systems
,
Addison–Wesley
, Menlo Park, CA.
37.
Golinski
,
J.
, 1970, “
Optimal Synthesis Problems by Means of Nonlinear Programming and Random Methods
,”
J. Mech.
0022-2569,
5
, pp.
287
309
.
38.
Golinski
,
J.
, 1973, “
An Adaptive Optimization System Applied to Machine Synthesis
,”
Mech. Mach. Theory
0094-114X,
8
, pp.
419
436
.
You do not currently have access to this content.