Design exploration methods seek to identify sets of candidate designs or regions of the design space that yield desirable performance. Commonly, the dimensionality of the design space exceeds the limited dimensions supported by standard graphical techniques, making it difficult for human designers to visualize or understand the underlying structure of the design space. With standard visualization tools, it is sometimes challenging to visualize a multi-dimensional Pareto frontier, but it is even more difficult to visualize the collections of design (input) variable values that yield those Pareto solutions. It is difficult for a designer to determine not only how many distinct regions of the design (input) space may offer desirable performance but also how those design spaces are structured. In this paper, a form of spectral clustering known as ε-neighborhood clustering is proposed for identifying satisfactory regions in the design spaces of multilevel problems. By exploiting properties of graph theory, the number of satisfactory design regions can be determined accurately and efficiently, and the design space can be partitioned. The method is demonstrated to be effective at identifying clusters in a 10 dimensional space. It is also applied to a multilevel materials design problem to demonstrate its efficacy on a realistic design application. Future work intends to visualize each individually identified design region to produce an intuitive mapping of the design space.

This content is only available via PDF.
You do not currently have access to this content.