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.
Issue Section:
Design Automation
Keywords:
Design automation
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/A00114726.
Herber
, D. R.
, 2015
, “Perfect Matchings of a Complete Graph
,” accessed Mar. 14, 2017, http://www.mathworks.com/matlabcentral/fileexchange/5230127.
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.org31.
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-project38.
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
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