0
Research Papers: Design Automation

Enumeration of Architectures With Perfect Matchings

[+] Author and Article Information
Daniel R. Herber

Industrial and Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: herber1@illinois.edu

Tinghao Guo

Industrial and Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: guo32@illinois.edu

James T. Allison

Industrial and Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jtalliso@illinois.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 12, 2016; final manuscript received February 17, 2017; published online April 4, 2017. Assoc. Editor: Carolyn Seepersad.

J. Mech. Des 139(5), 051403 (Apr 04, 2017) (13 pages) Paper No: MD-16-1635; doi: 10.1115/1.4036132 History: Received September 12, 2016; Revised February 17, 2017

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

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.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
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. [CrossRef]
Guo, T. , 2014, “ Design of Genetic Regulatory Networks,” M.S. thesis, University of Illinois at Urbana-Champaign, Urbana, IL.
Schmidt, L. C. , and Cagan, J. , 1997, “ GGREADA: A Graph Grammar-Based Machine Design Algorithm,” Res. Eng. Des., 9(4), pp. 195–213. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Starling, A. C. , and Shea, K. , 2005, “ A Parallel Grammar for Simulation-Driven Mechanical Design Synthesis,” ASME Paper No. DETC2005-85414.
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. [CrossRef]
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.
Godsil, C. , and Royle, G. , 2001, Algebraic Graph Theory, Springer, New York.
Diestel, R. , 2000, Graph Theory, 2nd ed., Springer, New York.
Rispoli, F. J. , 2007, “ Applications of Subgraph Enumeration,” Applications of Discrete Mathematics, McGraw-Hill, New York, pp. 241–262.
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. [CrossRef]
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. [CrossRef]
Sloane, N. J. A. , 1964, “ Sequence A001147,” The On-Line Encyclopedia of Integer Sequences, accessed Mar. 14, 2017, https://oeis.org/A001147
Herber, D. R. , 2015, “ Perfect Matchings of a Complete Graph,” accessed Mar. 14, 2017, http://www.mathworks.com/matlabcentral/fileexchange/52301
Lawler, E. , 1976, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York.
McKay, B. D. , and Piperno, A. , 2014, “ Practical Graph Isomorphism—II,” J. Symbolic Comput., 60, pp. 94–112. [CrossRef]
Babai, L. , 2015, “ Graph Isomorphism in Quasipolynomial Time,” e-print arXiv:1512.03547
Csardi, G., and Nepusz, T., 2006, “ The igraph Software Package for Complex Network Research,” InterJournal, Complex Systems, http://igraph.org
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.
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. [CrossRef]
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.
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.
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. [CrossRef]
Colbourn, C. J. , and Read, R. C. , 1979, “ Orderly Algorithms for Generating Restricted Classes of Graphs,” J. Graph Theory, 3(2), pp. 187–195. [CrossRef]
Herber, D. R. , 2016, “ PM Architectures Project,” accessed Mar. 14, 2017, https://github.com/danielrherber/pm-architectures-project
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
Foster, R. M. , 1932, “ Geometrical Circuits of Electrical Networks,” Electr. Eng., 51(1), p. 43.
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. [CrossRef] [PubMed]
Pennestrì, E. , and Valentini, P. P. , 2015, “ Kinematics and Enumeration of Combined Harmonic Drive Gearing,” ASME J. Mech. Des., 137(12), p. 122303. [CrossRef]
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. [CrossRef]
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.

Figures

Grahic Jump Location
Fig. 2

Complete graphs on n vertices between 1 and 5

Grahic Jump Location
Fig. 1

Architectures represented as graphs: (a) suspension, (b) hybrid powertrain, and (c) mechanism

Grahic Jump Location
Fig. 3

Perfect matchings for K2, K4, and K6: (a) 1!! perfect matchings for K2, (b) 3!! perfect matchings for K4, and (c) 5!! perfect matchings for K6

Grahic Jump Location
Fig. 6

Tree structure for case study 1 using the basic tree search algorithm in Algorithm 4

Grahic Jump Location
Fig. 7

GP graphs for two examples: (a) case study 1 and (b) case study 2

Grahic Jump Location
Fig. 8

Select interconnectivity graphs for case study 1: (a) K10, (b) PM 1, and (c) PM 462

Grahic Jump Location
Fig. 4

Comparison of number of graphs with PM approach and adjacency matrix approach

Grahic Jump Location
Fig. 13

Suspension architecture enumeration case study

Grahic Jump Location
Fig. 9

Select connected ports and connected component graphs for case study 1: (a) GCP for PM 1, (b) GCC for PM 1, and (c) GCC for PM 462

Grahic Jump Location
Fig. 14

Suspension case study matrices for S7 and the tree search algorithm: (a) reduced potential adjacency matrix AR and (b) potential adjacency matrix

Grahic Jump Location
Fig. 15

Two architectures for the suspension case study

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In