This paper presents a design optimization problem reformulation method based on singular value decomposition, dimensionality reduction, and unsupervised clustering. The method calculates linear approximations of associative patterns of symbol co-occurrences in a design problem representation to induce implicit coupling strengths between variables and constraints. Unsupervised clustering of these approximations is used to heuristically identify useful reformulations. In contrast to knowledge-rich Artificial Intelligence methods, this method derives from a knowledge-lean, unsupervised pattern recognition perspective. We explain the method on an analytically formulated decomposition problem, and apply it to various analytic and nonanalytic problem forms to demonstrate design decomposition and design “case” identification. A single method is used to demonstrate multiple design reformulation tasks. The results show that the method can be used to infer multiple well-formed reformulations starting from a single problem representation in a knowledge-lean manner.

1.
Cagan
,
J.
,
Grossman
,
I. E.
, and
Hooker
,
J.
, 1997, “
A Conceptual Framework for Combining Artificial Intelligence and Optimization in Engineering Design
,”
Res. Eng. Des.
0934-9839,
9
(
1
), pp.
20
34
.
2.
Schwabacher
,
M.
,
Ellman
,
T.
, and
Hirsh
,
H.
, 1998, “
Learning to Set Up Numerical Optimizations of Engineering Designs
,”
Artif. Intell. Eng. Des. Anal. Manuf.
0890-0604,
12
(
2
), pp.
173
192
.
3.
Ellman
,
T.
,
Keane
,
J.
,
Banerjee
,
A.
, and
Armhold
,
G.
, 1998, “
A Transformation System for Interactive Reformulation of Design Optimization Strategies
,”
Res. Eng. Des.
0934-9839,
10
(
1
), pp.
30
61
.
4.
Gelsey
,
A.
,
Schwabacher
,
M.
, and
Smith
,
D.
, 1998, “
Using Modeling Knowledge to Guide Design Space Search
,”
Artif. Intell.
0004-3702,
101
(
1-2
), pp.
35
62
.
5.
Campbell
,
M. I.
,
Cagan
,
J.
, and
Kotovsky
,
K.
, 2003, “
The A-Design Approach to Managing Automated Design Synthesis
,”
Res. Eng. Des.
0934-9839,
14
(
1
), pp.
12
24
.
6.
Medland
,
A. J.
, and
Mullineux
,
G.
, 2000, “
A Decomposition Strategy for Conceptual Design
,”
J. Eng. Design
0954-4828,
11
(
1
), pp.
3
16
.
7.
Duffy
,
A. H. B.
, and
Kerr
,
S. M.
, 1993, “
Customised Perspectives of Past Designs From Automated Group Rationalisations
,”
Artif. Intell. Eng.
0954-1810,
8
, pp.
183
200
.
8.
Dong
,
A.
, 2005, “
The Latent Semantic Approach to Studying Design Team Communication
,”
Des. Stud.
0142-694X,
26
(
5
), pp.
445
461
.
9.
Landauer
,
T. K.
, and
Dumais
,
S. T.
, 1997, “
A Solution to Plato’s Problem: The Latent Semantic Analysis Theory of Acquisition, Induction and Representation of Knowledge
,”
Psychol. Rev.
0033-295X,
104
(
2
), pp.
211
240
.
10.
Kalman
,
D.
, 1996, “
A Singularly Valuable Decomposition: The SVD of a Matrix
,”
Coll. Math. J.
0746-8342,
27
(
1
), pp.
2
23
.
11.
Strang
,
G.
, 2003,
Introduction to Linear Algebra
,
Wellesley-Cambridge
,
Wellesley
.
12.
Michelena
,
N. F.
, and
Papalambros
,
P. Y.
, 1997, “
A Hypergraph Framework for Optimal Model-Based Decomposition of Design Problems
,”
Comput. Optim. Appl.
0926-6003,
8
(
2
), pp.
173
196
.
13.
Mackay
,
D. J. C.
, 2003,
Information Theory, Inference and Learning Algorithms
,
Cambridge University Press
,
Cambridge
.
14.
Papalambros
,
P. Y.
, and
Wilde
,
D. J.
, 2000,
Principles of Optimal Design
,
Cambridge University Press
,
Cambridge
.
15.
Michelena
,
N. F.
, and
Agogino
,
A. M.
, 1988, “
Multi-Objective Hydraulic Cylinder Design
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
110
, pp.
81
87
.
16.
Chen
,
L.
, and
Li
,
S.
, 2005, “
Analysis of Decomposability and Complexity for Design Problems in the Context of Decomposition
,”
J. Mech. Des.
1050-0472,
127
(
4
), pp.
545
557
.
17.
Pimmler
,
T. U.
, and
Eppinger
,
S. D.
, 1994, “
Integration Analysis of Product Decompositions
,”
Sixth ASME-DTM Conference
, Minneapolis, MN.
18.
Simon
,
H. A.
, 1969,
The Sciences of the Artificial
,
MIT
,
Cambridge, MA
.
19.
Sosa
,
M. E.
,
Eppinger
,
S. D.
, and
Rowles
,
C. M.
, 2003, “
Identifying Modular and Integrative Systems and Their Impact on Design Team Interactions
,”
J. Mech. Des.
1050-0472,
125
, pp.
240
252
.
20.
Gu
,
X.
,
Renaud
,
J. E.
,
Ashe
,
L. M.
,
Batill
,
S. M.
,
Budhiraja
,
A. M.
, and
Krajewski
,
L. J.
, 2002, “
Descision-Based Collaborative Optimization
,”
J. Mech. Des.
1050-0472,
124
(
1
), pp.
1
13
.
21.
Liu
,
L.
,
Hawkins
,
D. M.
,
Ghosh
,
S.
, and
Young
,
S.
, 2003, “
Robust Singular Value Decomposition Analysis of Microarray Data
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
100
(
23
), pp.
13167
13172
.
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