For decomposition and integration of systems, one needs extensive knowledge of system structure. A design structure matrix (DSM) model provides a simple, compact, and visual representation of dependencies between system elements. By permuting the rows and columns of a DSM using a clustering algorithm, the underlying structure of a system can be revealed. In this paper, we present a new DSM clustering algorithm based upon Markov clustering, that is able to cope with the presence of “bus” elements, returns multilevel clusters, is capable of clustering weighted, directed, and undirected DSMs, and allows the user to control the cluster results by tuning only three input parameters. Comparison with two algorithms from the literature shows that the proposed algorithm provides clusterings of similar quality at the expense of less central processing unit (CPU) time.

References

References
1.
Alizon
,
F.
,
Khadke
,
K.
,
Thevenot
,
H. J.
,
Gershenson
,
J. K.
,
Marion
,
T. J.
,
Shooter
,
S. B.
, and
Simpson
,
T. W.
,
2007
, “
Frameworks for Product Family Design and Development
,”
Concurrent Eng.
,
15
(
2
), pp.
187
199
.
2.
Maurer
,
M. S.
,
2007
, “
Structural Awareness in Complex Product Design
,”
Ph.D. thesis
, Universität München, München, Germany.
3.
Blanchard
,
B. S.
, and
Fabrycky
,
W. J.
,
1990
,
Systems Engineering and Analysis
,
Prentice Hall
,
Englewood Cliffs, NJ
.
4.
Eppinger
,
S. D.
,
Joglekar
,
N. R.
,
Olechowski
,
A.
, and
Teo
,
T.
,
2014
, “
Improving the Systems Engineering Process With Multilevel Analysis of Interactions
,”
Artif. Intell. Eng. Des. Anal. Manuf.
,
28
(
04
), pp.
323
337
.
5.
Steward
,
D.
,
1981
, “
The Design Structure System: A Method for Managing the Design of Complex Systems
,”
IEEE Trans. Eng. Manage.
,
EM-28
(
3
), pp.
71
74
.
6.
Eppinger
,
S. D.
, and
Browning
,
T. R.
,
2012
,
Design Structure Matrix Methods and Applications
,
MIT Press
,
Cambridge, MA
.
7.
Sarkar
,
S.
,
Dong
,
A.
,
Henderson
,
J. A.
, and
Robinson
,
P. A.
,
2014
, “
Spectral Characterization of Hierarchical Modularity in Product Architectures
,”
ASME J. Mech. Des.
,
136
(
1
), p.
011006
.
8.
Brady
,
T. K.
,
2002
, “
Utilization of Dependency Structure Matrix Analysis to Assess Complex Project Designs
,”
ASME
Paper No. DETC2002/DTM-34021.
9.
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.
,
125
(
2
), pp.
240
252
.
10.
Browning
,
T.
, and
Eppinger
,
S.
,
2002
, “
Modeling Impacts of Process Architecture on Cost and Schedule Risk in Product Development
,”
IEEE Trans. Eng. Manage.
,
49
(
4
), pp.
428
442
.
11.
Rogers
,
J. L.
,
1996
, “
DEMAID/GA An Enhanced Design Managers Aid for Intelligent Decomposition (Genetic Algorithms)
,”
AIAA
Paper No. 96–4157.
12.
Pimmler
,
T. U.
, and
Eppinger
,
S. D.
,
1994
, “
Integration Analysis of Product Decompositions
,” Massachusetts Institute of Technology, Cambridge, MA, Report No.
3690-94
.
13.
Gorbea
,
C.
,
Spielmannleitner
,
T.
,
Lindemann
,
U.
, and
Fricke
,
E.
,
2008
, “
Analysis of Hybrid Vehicle Architectures Using Multiple Domain Matrices
,” Tenth International Design Structure Matrix Conference (
DSM
), Stockholm, Sweden, Nov. 11–12, pp. 375–387.
14.
Braun
,
S. C.
,
Diehl
,
H.
,
Petermann
,
M.
,
Hellenbrand
,
D.
, and
Lindemann
,
U.
,
2007
, “
Approach for the Function Driven Process Design for the Development of Mechatronic Systems
,” Ninth International Design Structure Matrix Conference (
DSM
), Munich, Germany, Oct. 16–18, pp.
161
173
.
15.
de Borst
,
E. C. M.
,
Etman
,
L. F. P.
,
Gielen
,
A. W. J.
,
Hofkamp
,
A. T.
, and
Rooda
,
J. E.
,
2013
, “
Decomposition-Based Analysis of the Multi-Physical Coupling Structure in LED System-in-Package Design
,”
Tenth World Congress on Structural and Multidisciplinary Optimization
(
WCSMO
), Orlando, FL, May 19–24, pp. 1–10.
16.
de Borst
,
E. C. M.
,
Etman
,
L. F. P.
,
Gielen
,
A. W. J.
,
Hofkamp
,
A. T.
, and
Rooda
,
J. E.
,
2016
, “
Decomposition Analysis of the Multidisciplinary Coupling in LED System-in-Package Design Using a DSM and a Specification Language
,”
Struct. Multidiscip. Optim.
,
53
(
6
), pp.
1395
1411
.
17.
Browning
,
T. R.
,
2015
, “
Design Structure Matrix Extensions and Innovations: A Survey and New Opportunities
,”
IEEE Trans. Eng. Manage.
,
63
(
1
), pp.
27
52
.
18.
Browning
,
T. R.
,
2001
, “
Applying the Design Structure Matrix to System Decomposition and Integration Problems: A Review and New Directions
,”
IEEE Trans. Eng. Manage.
,
48
(
3
), pp.
292
306
.
19.
Yu
,
T.-L.
,
Yassine
,
A. A.
, and
Goldberg
,
D. E.
,
2007
, “
An Information Theoretic Method for Developing Modular Architectures Using Genetic Algorithms
,”
Res. Eng. Des.
,
18
(
2
), pp.
91
109
.
20.
Steward
,
D. V.
,
1965
, “
Partitioning and Tearing Systems of Equations
,”
J. Soc. Ind. Appl. Math., Ser. B: Numer. Anal.
,
2
(
2
), pp.
345
365
.
21.
Fortunato
,
S.
,
2010
, “
Community Detection in Graphs
,”
Phys. Rep.
,
486
(
3–5
), pp.
75
174
.
22.
Schaeffer
,
S. E.
,
2007
, “
Graph Clustering
,”
Comput. Sci. Rev.
,
1
(
1
), pp.
27
64
.
23.
MacQueen
,
J.
,
1967
, “
Some Methods for Classification and Analysis of Multivariate Observations
,”
Fifth Berkeley Symposium on Mathematical Statistics and Probability
, Oakland, CA, June 21–July 18 and Dec. 27–Jan. 7, pp.
281
297
.
24.
Hartigan
,
J. A.
, and
Wong
,
M. A.
,
1979
, “
Algorithm AS 136: A K-Means Clustering Algorithm
,”
Appl. Stat.
,
28
(
1
), pp.
100
108
.
25.
Kanungo
,
T.
,
Mount
,
D. M.
,
Netanyahu
,
N. S.
,
Piatko
,
C. D.
,
Silverman
,
R.
, and
Wu
,
A. Y.
,
2002
, “
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
24
(
7
), pp.
881
892
.
26.
Dhillon
,
I. S.
,
Guan
,
Y.
, and
Kulis
,
B.
,
2007
, “
Weighted Graph Cuts Without Eigenvectors a Multilevel Approach
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
29
(
11
), pp.
1944
1957
.
27.
Lloyd
,
S. P.
,
1982
, “
Least Squares Quantization in PCM
,”
IEEE Trans. Inf. Theory
,
28
(
2
), pp.
129
137
.
28.
Donath
,
W. E.
, and
Hoffman
,
A. J.
,
1973
, “
Lower Bounds for the Partitioning of Graphs
,”
IBM J. Res. Dev.
,
17
(
5
), pp.
420
425
.
29.
Chung
,
F. R. K.
,
1997
,
Spectral Graph Theory
,
University of Pennsylvania
,
Philadelphia, PA
.
30.
Agaev
,
R.
, and
Chebotarev
,
P.
,
2005
, “
On the Spectra of Nonsymmetric Laplacian Matrices
,”
Linear Algebra Appl.
,
399
, pp.
157
168
.
31.
Capocci
,
A.
,
Servedio
,
V. D.
,
Caldarelli
,
G.
, and
Colaiori
,
F.
,
2005
, “
Detecting Communities in Large Networks
,”
Phys. A
,
352
(
2
), pp.
669
676
.
32.
Pentney
,
W.
, and
Meila
,
M.
,
2005
, “
Spectral Clustering of Biological Sequence Data
,”
AIAA National Conference on Artificial Intelligence
, Pittsburgh, PA, July 9–13, pp.
845
850
.
33.
Kernighan
,
B. W.
, and
Lin
,
S.
,
1970
, “
An Efficient Heuristic Procedure for Partitioning Graphs
,”
Bell Syst. Tech. J.
,
49
(
2
), pp.
291
307
.
34.
Karypis
,
G.
, and
Kumar
,
V.
,
2006
, “
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
,”
SIAM J. Sci. Comput.
,
20
(
1
), pp.
359
392
.
35.
Lu
,
Z.
, and
Martins
,
J. R. R. A.
,
2012
, “
Graph Partitioning-Based Coordination Methods for Large-Scale Multidisciplinary Design Optimization Problems
,”
ISSMO Multidisciplinary Analysis Optimization Conference
, Indianapolis, IN, Sept. 17–19, pp.
1
13
.
36.
Yager
,
R.
,
2000
, “
Intelligent Control of the Hierarchical Agglomerative Clustering Process
,”
IEEE Trans. Syst. Man Cybern. Part B
,
30
(
6
), pp.
835
845
.
37.
AlGeddawy
,
T.
, and
ElMaraghy
,
H.
,
2013
, “
Optimum Granularity Level of Modular Product Design Architecture
,”
CIRP Ann.—Manuf. Technol.
,
62
(
1
), pp.
151
154
.
38.
Thebeau
,
R. E.
,
2001
, “
Knowledge Management of System Interfaces and Interactions From Product Development Processes
,”
Master's thesis
, Massachusetts Institute of Technology, Cambridge, MA.
39.
Borjesson
,
F.
, and
Hölttä-Otto
,
K.
,
2012
, “
Improved Clustering Algorithm for Design Structure Matrix
,”
ASME
Paper No. DETC2012-70076.
40.
Borjesson
,
F.
, and
Hölttä-Otto
,
K.
,
2014
, “
A Module Generation Algorithm for Product Architecture Based on Component Interactions and Strategic Drivers
,”
Res. Eng. Des.
,
25
(
1
), pp.
31
51
.
41.
Helmer
,
R.
,
Yassine
,
A.
, and
Meier
,
C.
,
2010
, “
Systematic Module and Interface Definition Using Component Design Structure Matrix
,”
J. Eng. Des.
,
21
(
6
), pp.
647
675
.
42.
Leskovec
,
J.
,
Lang
,
K. J.
,
Dasgupta
,
A.
, and
Mahoney
,
M. W.
,
2009
, “
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters
,”
Int. Math.
,
6
(
1
), pp.
29
123
.
43.
Chen
,
L.-C.
, and
Lin
,
L.
,
2002
, “
Optimization of Product Configuration Design Using Functional Requirements and Constraints
,”
Res. Eng. Des.
,
13
(
3
), pp.
167
182
.
44.
Allison
,
J. T.
,
Kokkolaras
,
M.
, and
Papalambros
,
P. Y.
,
2009
, “
Optimal Partitioning and Coordination Decisions in Decomposition-Based Design Optimization
,”
ASME J. Mech. Des.
,
131
(
8
), p.
081008
.
45.
Booth
,
J. G.
,
Casella
,
G.
, and
Hobert
,
J. P.
,
2008
, “
Clustering Using Objective Functions and Stochastic Search
,”
J. R. Stat. Soc. Ser. B (Stat. Methodol.)
,
70
(
1
), pp.
119
139
.
46.
Van Dongen
,
S.
,
2008
, “
Graph Clustering Via a Discrete Uncoupling Process
,”
SIAM J. Matrix Anal. Appl.
,
30
(
1
), pp.
121
141
.
47.
Dongen
,
S. M. V.
,
2001
, “
Graph Clustering by Flow Simulation
,”
Ph.D. thesis
, Utrecht University, Utrecht, The Netherlands.
48.
Karlin
,
S.
,
2014
,
A First Course in Stochastic Processes
,
Academic Press
,
London
.
49.
Sharman
,
D. M.
, and
Yassine
,
A. A.
,
2004
, “
Characterizing Complex Product Architectures
,”
Syst. Eng.
,
7
(
1
), pp.
35
60
.
50.
Barabasi
,
A.-L.
, and
Albert
,
R.
,
1999
, “
Emergence of Scaling in Random Networks
,”
Science
,
286
(
5439
), pp.
509
512
.
51.
Braha
,
D.
, and
Bar-Yam
,
Y.
,
2006
, “
From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks
,”
Complexity
,
12
(
2
), pp.
59
63
.
52.
Sosa
,
M.
,
Mihm
,
J.
, and
Browning
,
T.
,
2011
, “
Degree Distribution and Quality in Complex Engineered Systems
,”
ASME J. Mech. Des.
,
133
(
10
), p.
101008
.
53.
Gutierrez
,
C. I.
,
1998
, “
Integration Analysis of Product Architecture to Support Effective Team Co-Location
,”
Master's thesis
, Massachusetts Institute of Technology, Cambridge MA.
54.
De Borst
,
E. C. M.
,
2013
, “
Multi-Level Decomposition-Based Analysis of LED System-in-Package Design
,”
Master's thesis
, Eindhoven University of Technology, Eindhoven, The Netherlands.
You do not currently have access to this content.