Graph structures are fundamental in many aspects of design. This paper discusses a way to improve access to design spaces of graph structures, by converting graph structures into numerical values and vice versa. Mathematical properties of such conversions are described, and those that are desirable are identified. A candidate conversion algorithm, Indexed Stacked Blocks, is proposed. Its use and benefits are illustrated through an example graph-structure design problem. The example demonstrates that such conversions allow design spaces of graph structures to be visualized, sampled, and evaluated. In principle, they also allow other powerful numerical techniques to be applied to the design of graph-structure-based systems.
A Scheme for Numerical Representation of Graph Structures in Engineering Design
Contributed by the Design Theory and Methodology Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 21, 2012; final manuscript received October 13, 2013; published online November 26, 2013. Assoc. Editor: Irem Y. Tumer.
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Wyatt, D. F., Wynn, D. C., and Clarkson, P. J. (November 26, 2013). "A Scheme for Numerical Representation of Graph Structures in Engineering Design." ASME. J. Mech. Des. January 2014; 136(1): 011010. https://doi.org/10.1115/1.4025961
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