Research Papers: Design Automation

Multilevel Flow-Based Markov Clustering for Design Structure Matrices

[+] Author and Article Information
T. Wilschut

Department of Mechanical Engineering,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: t.wilschut@tue.nl

L. F. P. Etman

Department of Mechanical Engineering,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: l.f.p.etman@tue.nl

J. E. Rooda

Department of Mechanical Engineering,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: j.e.rooda@tue.nl

I. J. B. F. Adan

Department of Industrial Engineering,
Eindhoven University of Technology,
Eindhoven 5600 MB, The Netherlands
e-mail: i.adan@tue.nl

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 21, 2016; final manuscript received July 26, 2017; published online October 3, 2017. Assoc. Editor: Christina Bloebaum.

J. Mech. Des 139(12), 121402 (Oct 03, 2017) (10 pages) Paper No: MD-16-1852; doi: 10.1115/1.4037626 History: Received December 21, 2016; Revised July 26, 2017

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.

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Grahic Jump Location
Fig. 1

(a) Unclustered example DSM and (b) clustered example DSM, revealing a bus cluster and two modular clusters

Grahic Jump Location
Fig. 3

Graph coarsening: the clusters found in graph G are aggregated into super nodes in graph G′. The clusters found in G′ are aggregated into super nodes in graph G″.

Grahic Jump Location
Fig. 2

A simple graph containing two clusters

Grahic Jump Location
Fig. 4

Multiple clusterings of the ford climate control system DSM [12] obtained with the proposed algorithm using different parameter settings. (a) Settings: α = 2.0, β = 2.0, μ = 1.5, and γ = 1.8, (b) ettings: α = 2.0, β = 2.5, μ = 2.5, and γ = 1.8, (c) settings: α = 2.0, β = 2.0, μ = 1.5, and γ = 1.5, (d) settings: α = 2.0, β = 2.0, μ = 1.5, and γ = 1.2, and (e) settings: α = 2.0, β = 1.5, μ = 1.5, and γ = 1.2.

Grahic Jump Location
Fig. 5

Multiple clusterings of the Pratt and Whitney jet engine DSM [9] obtained using different algorithms: (a) original handmade clustering [9], (b) spectral clustering, settings: kbus = 2, knon_bus = 5, (c) stochastic hill climbing, settings: pow_cc = 2, pow_bid = 1, pow_dep = 4, (d) Markov clustering, settings: α = 2, β = 2, μ = 2



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