Visualizing and Evaluating High-Dimensional Mappings of Sets of High Performance Design

Design space exploration can reveal the underlying structure of design problems. In a set-based approach, for example, exploration can map sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the input design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. To convey the structure of such high-dimensional design regions, a two-stage approach is proposed to (1) identify and (2) visualize each distinct cluster or region of interest in the input design space. This paper focuses on the visualization stage of the approach. Rather than select a singular technique to map high-dimensional design spaces to low-dimensional, visualizable spaces, a selection procedure is investigated. Metrics are available for comparing different visualizations, but the current metrics either overestimate the quality or favor selection of certain visualizations. Therefore, this work introduces and validates a more objective metric, termed preservation, to compare the quality of alternative visualization strategies. Furthermore, a new visualization technique previously unexplored in the design automation community, t-Distributed Neighbor Embedding, is introduced and compared to other visualization strategies. Finally, the new metric and visualization technique are integrated into a two-stage visualization strategy to identify and visualize clusters of high-performance designs for a high-dimensional negative stiffness metamaterials design problem.