In this article, a class of architecture design problems is explored with perfect matchings (PMs). A perfect matching in a graph is a set of edges such that every vertex is present in exactly one edge. The perfect matching approach has many desirable properties such as complete design space coverage. Improving on the pure perfect matching approach, a tree search algorithm is developed that more efficiently covers the same design space. The effect of specific network structure constraints (NSCs) and colored graph isomorphisms on the desired design space is demonstrated. This is accomplished by determining all unique feasible graphs for a select number of architecture problems, explicitly demonstrating the specific challenges of architecture design. With this methodology, it is possible to enumerate all possible architectures for moderate scale-systems, providing both a viable solution technique for certain problems and a rich data set for the development of more capable generative methods and other design studies.

References

References
1.
Crawley
,
E.
,
de Weck
,
O.
,
Eppinger
,
S.
,
Magee
,
C.
,
Moses
,
J.
,
Seering
,
W.
,
Schindall
,
J.
,
Wallace
,
D.
, and
Whitney
,
D.
,
2004
, “
The Influence of Architecture in Engineering Systems
,” Engineering Systems Monograph, Massachusetts Institute of Technology, Cambridge, MA.
2.
Mittal
,
S.
, and
Frayman
,
F.
,
1989
, “
Towards a Generic Model of Configuration Tasks
,”
11th International Joint Conference on Artificial Intelligence
(
IJCAI
), Detroit, MI, Aug. 20–25, Morgan Kaufmann Publishers Inc., San Francisco, CA, Vol. 2, pp.
1395
1401
.
3.
Wyatt
,
D. F.
,
Wynn
,
D. C.
, and
Clarkson
,
P. J.
,
2014
, “
A Scheme for Numerical Representation of Graph Structures in Engineering Design
,”
ASME J. Mech. Des.
,
136
(
1
), p.
011010
.
4.
Cagan
,
J.
,
Campbell
,
M. I.
,
Finger
,
S.
, and
Tomiyama
,
T.
,
2005
, “
A Framework for Computational Design Synthesis: Model and Applications
,”
ASME J. Comput. Inf. Sci. Eng.
,
5
(
3
), pp.
171
181
.
5.
Chakrabarti
,
A.
,
Shea
,
K.
,
Stone
,
R.
,
Cagan
,
J.
,
Campbell
,
M.
,
Hernandez
,
N. V.
, and
Wood
,
K. L.
,
2011
, “
Computer-Based Design Synthesis Research: An Overview
,”
ASME J. Comput. Inf. Sci. Eng.
,
11
(
2
), p.
021003
.
6.
Chan
,
J.
,
Fu
,
K.
,
Schunn
,
C.
,
Cagan
,
J.
,
Wood
,
K.
, and
Kotovsky
,
K.
,
2011
, “
On the Benefits and Pitfalls of Analogies for Innovative Design: Ideation Performance Based on Analogical Distance, Commonness, and Modality of Examples
,”
ASME J. Mech. Des.
,
133
(
8
), p.
081004
.
7.
Linsey
,
J. S.
,
Tseng
,
I.
,
Fu
,
K.
,
Cagan
,
J.
,
Wood
,
K. L.
, and
Schunn
,
C.
,
2010
, “
A Study of Design Fixation, Its Mitigation and Perception in Engineering Design Faculty
,”
ASME J. Mech. Des.
,
132
(
4
), p.
041003
.
8.
Deshmukh
,
A. P.
,
Herber
,
D. R.
, and
Allison
,
J. T.
,
2015
, “
Bridging the Gap Between Open-Loop and Closed-Loop Control in Co-Design: A Framework for Complete Optimal Plant and Control Architecture Design
,”
American Control Conference
(
ACC
), Chicago, IL, Jul. 1–3, IEEE, New York, pp.
4916
4922
.
9.
Hooshmand
,
A.
,
Campbell
,
M. I.
, and
Shea
,
K.
,
2012
, “
Steps in Transforming Shapes Generated With Generative Design Into Simulation Models
,”
ASME
Paper No. DETC2012-71056.
10.
Khetan
,
A.
,
Lohan
,
D. J.
, and
Allison
,
J. T.
,
2015
, “
Managing Variable-Dimension Structural Optimization Problems Using Generative Algorithms
,”
Struct. Multidiscip. Optim.
,
52
(
4
), pp.
695
715
.
11.
Münzer
,
C.
,
Helms
,
B.
, and
Shea
,
K.
,
2013
, “
Automatically Transforming Object-Oriented Graph-Based Representations Into Boolean Satisfiability Problems for Computational Design Synthesis
,”
ASME J. Mech. Des.
,
135
(
10
), p.
101001
.
12.
Guo
,
T.
,
2014
, “
Design of Genetic Regulatory Networks
,”
M.S. thesis
, University of Illinois at Urbana-Champaign, Urbana, IL.
13.
Schmidt
,
L. C.
, and
Cagan
,
J.
,
1997
, “
GGREADA: A Graph Grammar-Based Machine Design Algorithm
,”
Res. Eng. Des.
,
9
(
4
), pp.
195
213
.
14.
Schmidt
,
L. C.
,
Shetty
,
H.
, and
Chase
,
S. C.
,
2000
, “
A Graph Grammar Approach for Structure Synthesis of Mechanisms
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
371
376
.
15.
Hornby
,
G. S.
,
Lipson
,
H.
, and
Pollack
,
J. B.
,
2003
, “
Generative Representations for the Automated Design of Modular Physical Robots
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
703
719
.
16.
Bryant
,
C. R.
,
McAdams
,
D. A.
,
Stone
,
R. B.
,
Kurtoglu
,
T.
, and
Campbell
,
M. I.
,
2005
, “
A Computational Technique for Concept Generation
,”
ASME
Paper No. DETC2005-85323.
17.
Starling
,
A. C.
, and
Shea
,
K.
,
2005
, “
A Parallel Grammar for Simulation-Driven Mechanical Design Synthesis
,”
ASME
Paper No. DETC2005-85414.
18.
Wyatt
,
D. F.
,
Wynn
,
D. C.
,
Jarrett
,
J. P.
, and
Clarkson
,
P. J.
,
2012
, “
Supporting Product Architecture Design Using Computational Design Synthesis With Network Structure Constraints
,”
Res. Eng. Des.
,
23
(
1
), pp.
17
52
.
19.
Snavely
,
G. L.
, and
Papalambros
,
P. Y.
,
1993
, “
Abstraction as a Configuration Design Methodology
,”
Advances in Design Automation
, Event 14th Biennial Conference on Mechanical Vibration and Noise, Albuquerque, NM, Sept. 19–22, ASME, New York, pp.
297
305
.
20.
Godsil
,
C.
, and
Royle
,
G.
,
2001
,
Algebraic Graph Theory
,
Springer
, New York.
21.
Diestel
,
R.
,
2000
,
Graph Theory
,
2nd ed.
,
Springer
, New York.
22.
Rispoli
,
F. J.
,
2007
, “
Applications of Subgraph Enumeration
,”
Applications of Discrete Mathematics
,
McGraw-Hill
, New York, pp.
241
262
.
23.
Wu
,
Z.
,
Campbell
,
M. I.
, and
Fernández
,
B. R.
,
2008
, “
Bond Graph Based Automated Modeling for Computer-Aided Design of Dynamic Systems
,”
ASME J. Mech. Des.
,
130
(
4
), p.
041102
.
24.
Bayrak
,
A. E.
,
Ren
,
Y.
, and
Papalambros
,
P. Y.
,
2016
, “
Topology Generation for Hybrid Electric Vehicle Architecture Design
,”
ASME J. Mech. Des.
,
138
(
8
), p.
081401
.
25.
Sloane
,
N. J. A.
, 1964, “
Sequence A001147
,” The On-Line Encyclopedia of Integer Sequences, accessed Mar. 14, 2017, https://oeis.org/A001147
26.
Herber
,
D. R.
,
2015
, “
Perfect Matchings of a Complete Graph
,” accessed Mar. 14, 2017, http://www.mathworks.com/matlabcentral/fileexchange/52301
27.
Lawler
,
E.
,
1976
,
Combinatorial Optimization: Networks and Matroids
,
Holt, Rinehart and Winston
, New York.
28.
McKay
,
B. D.
, and
Piperno
,
A.
,
2014
, “
Practical Graph Isomorphism—II
,”
J. Symbolic Comput.
,
60
, pp.
94
112
.
29.
Babai
,
L.
,
2015
, “
Graph Isomorphism in Quasipolynomial Time
,” e-print
arXiv:1512.03547
30.
Csardi, G., and Nepusz, T., 2006, “
The igraph Software Package for Complex Network Research
,” InterJournal, Complex Systems, http://igraph.org
31.
Cordella
,
L. P.
,
Foggia
,
P.
,
Sansone
,
C.
, and
Vento
,
M.
,
2001
, “
An Improved Algorithm for Matching Large Graphs
,”
IAPR TC-15
Workshop on Graph-Based Representations in Pattern Recognition
, pp.
149
159
.
32.
Königseder
,
C.
, and
Shea
,
K.
,
2016
, “
Comparing Strategies for Topologic and Parametric Rule Application in Automated Computational Design Synthesis
,”
ASME J. Mech. Des.
,
138
(
1
), p.
011102
.
33.
Read
,
R. C.
,
1978
, “
Every One a Winner or How to Avoid Isomorphism Search When Cataloguing Combinatorial Configurations
,”
Ann. Discrete Math.
,
2
, pp.
107
120
.
34.
Faulon
,
J.-L.
,
Churchwell
,
C. J.
, and
Visco
,
D. P.
, Jr.
,
2003
, “
The Signature Molecular Descriptor—2: Enumerating Molecules From Their Extended Valence Sequences
,”
J. Chem. Inf. Model.
,
43
(
3
), pp.
721
734
.
35.
Carhart
,
R. E.
,
Smith
,
D. H.
,
Brown
,
H.
, and
Djerassi
,
C.
,
1975
, “
Applications of Artificial Intelligence for Chemical Inference—XVII: Approach to Computer-Assisted Elucidation of Molecular Structure
,”
J. Am. Chem. Soc.
,
97
(
20
), pp.
5755
5762
.
36.
Colbourn
,
C. J.
, and
Read
,
R. C.
,
1979
, “
Orderly Algorithms for Generating Restricted Classes of Graphs
,”
J. Graph Theory
,
3
(
2
), pp.
187
195
.
37.
Herber
,
D. R.
,
2016
, “
PM Architectures Project
,” accessed Mar. 14, 2017, https://github.com/danielrherber/pm-architectures-project
38.
Allison
,
J. T.
,
Guo
,
T.
, and
Han
,
Z.
,
2014
, “
Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization
,”
ASME J. Mech. Des.
,
136
(
8
), p.
081003
.
39.
Flajolet
,
P.
,
Gardy
,
D.
, and
Thimonier
,
L.
,
1992
, “
Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search
,”
Discrete Appl. Math.
,
39
(
3
), pp.
207
229
.
40.
Ruddigkeit
,
L.
,
van Deursen
,
R.
,
Blum
,
L. C.
, and
Reymond
,
J.-L.
,
2012
, “
Enumeration of 166 Billion Organic Small Molecules in the Chemical Universe Database GDB-17
,”
J. Chem. Inf. Model.
,
52
(
11
), pp.
2864
2875
.
41.
Foster
,
R. M.
,
1932
, “
Geometrical Circuits of Electrical Networks
,”
Electr. Eng.
,
51
(
1
), p. 43.
42.
Ma
,
W.
,
Trusina
,
A.
,
El-Samad
,
H.
,
Lim
,
W. A.
, and
Tang
,
C.
,
2009
, “
Defining Network Topologies That Can Achieve Biochemical Adaptation
,”
Cell
,
138
(
4
), pp.
760
773
.
43.
Pennestrì
,
E.
, and
Valentini
,
P. P.
,
2015
, “
Kinematics and Enumeration of Combined Harmonic Drive Gearing
,”
ASME J. Mech. Des.
,
137
(
12
), p.
122303
.
44.
del
Castillo
,
J. M.
,
2002
, “
Enumeration of 1-DOF Planetary Gear Train Graphs Based on Functional Constraints
,”
ASME J. Mech. Des.
,
124
(
4
), p.
723
.
45.
Berlingerio
,
M.
,
Bonchi
,
F.
,
Bringmann
,
B.
, and
Gionis
,
A.
,
2009
, “
Mining Graph Evolution Rules
,”
Machine Learning and Knowledge Discovery in Databases
, Vol.
5781
,
Springer
, Berlin, pp.
115
130
.
You do not currently have access to this content.