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An information theoretic method for developing modular architectures using genetic algorithms

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Abstract

Designing modular products can result in many benefits to both manufacturers and consumers. The development of modular products requires the identification of highly interactive groups of elements and arranging (i.e., clustering) them into modules. However, no rigorous clustering technique can be found in engineering design literature. This paper uses the design structure matrix (DSM) to visualize the product architecture and to develop the basic building blocks required for the identification of product modules. The DSM architectural representation and building blocks are then used for the development of a new clustering method based on the minimum description length (MDL) principle and a simple genetic algorithm (GA). The new method is capable of partitioning the product architecture into a set of modules where interactions within modules are maximized and interactions outside modules are minimized. We demonstrate the proposed clustering method using several examples of real complex products and compare our results to clustering arrangements proposed by human experts. The proposed method is capable of mimicking the clustering preference of human experts and yields competitive clustering arrangements.

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Notes

  1. Webster’s dictionary defines the noun “module” as “a compact assembly functioning as a component of a larger unit‘’.

  2. In a graph, nodes represent product components and edges represent relationships between these components.

  3. For a comprehensive review of product modularity methods, we refer the refer the reader to Gershenson et al. (2004).

  4. A function structure is an input-output diagram of what a product does.

  5. In contrast to the standard approach of adding/substituting modules to produce product variants, this approach to product family design calls for the development of common product platforms that can be “stretched” or “scaled” in one more dimension to satisfy a variety of market requirement (Simpson et al. 2001).

  6. There are different ways of building a DSM. For a full description, please refer to the DSM website at http://www.DSMweb.org.

  7. It worth noting that “partitioning” of DSMs is different than “clustering” (Yassine and Braha 2003). Although both methods rely on re-ordering DSM elements, the objectives are different. In partitioning, the objective is to remove feedback marks from the DSM by making the DSM lower triangular (McCulley and Bloebaum 1996). In clustering, we do not care about feedbacks and DSM marks’ location above or below the matrix diagonal is immaterial.

  8. These marks may constitute the interface between the two product modules.

  9. The relationship can be representing a flow of mass, energy, information, or force/geometrical constraint between the parts.

  10. Here, the model means a description that specifies which node belongs to which cluster. This can be a graph or its DSM representation.

  11. Here we use weighting in order to match the preference of human experts. This becomes more evidential in the case study.

  12. The number of possible product architectures for a system with n elements without cluster overlaps is: \(\sum\nolimits_{i=1}^{n} C_{i}^{n}=2^{n}-1\)

  13. The program is written in C++. It takes about a day to obtain results for a (60 × 60) DSM, on an AMD AthlonTM XP 2500+ machine.

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Author notes

  1. Tian-Li Yu

    Present address: Department of Electrical Engineering, National Taiwan University, Taipei, 106, Taiwan, ROC

Authors and Affiliations

  1. Department of General Engineering, Illinois Genetic Algorithm lab, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Tian-Li Yu, Ali A. Yassine & David E. Goldberg

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  1. Tian-Li Yu
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  2. Ali A. Yassine
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  3. David E. Goldberg
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Correspondence to Tian-Li Yu.

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Yu, TL., Yassine, A.A. & Goldberg, D.E. An information theoretic method for developing modular architectures using genetic algorithms. Res Eng Design 18, 91–109 (2007). https://doi.org/10.1007/s00163-007-0030-1

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