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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.

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Figures

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Fig. 1

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

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Fig. 2

Complete graphs on n vertices between 1 and 5

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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

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Fig. 4

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

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Fig. 6

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

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Fig. 7

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

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Fig. 8

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

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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

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Fig. 13

Suspension architecture enumeration case study

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Fig. 14

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

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Fig. 15

Two architectures for the suspension case study

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