@inproceedings {pub4183,
	title = {Simultaneous Exploration of Geometric Features and Performance in Design Optimization},
	author = {Nivesh Dommaraju AND Mariusz Bujny AND Stefan Menzel AND Markus Olhofer AND Fabian Duddeck},
	year = {2020},
	month = {June},
	abstract = {Topology optimization (TO) algorithms generate novel concepts to inspire and propel the design iteration process even for highly nonlinear cases, e.g. [1-3]. LS-TaSC{\textregistered} is an industrial tool which implements TO algorithms and generates designs optimized for maximum stiffness or energy absorption, under specified constraints such as allowed mass fraction of material in the design space. Ramnath et al. [4] propose an approach for design exploration, based on LS-Opt{\textregistered} and LS-TaSC{\textregistered}, through multi-objective optimization for crash and static load cases. They introduce a method to generate a Pareto set of designs by varying a parameter representing the relative preference of the user among the different objectives. A challenge still persists as to how potentially large datasets of designs, generated using such an approach, could be reviewed efficiently by a designer. In this paper, we propose a method to identify a few design prototypes with diverse geometries and performance, which can be more easily reviewed by a designer.

The proposed method captures both geometric differences in designs, as well as differences in structural performance. More concretely, the approach identifies classes of designs that look significantly different and/or perform differently. For this purpose, we encode the information about the geometry using a voxel representation of the design. Subsequently, we use t-SNE [5] to reduce the high dimensionality of the representation and extract features that encapsulate the geometric variation in the set of designs. Without the reduction of dimensions, the variation in designs is difficult to capture ({\textquotedblleft}the curse of high dimensionality{\textquotedblright}). With the geometric and performance features identified, a step commonly known in the field of machine learning as the feature extraction, design prototypes are derived using clustering algorithms [6]. 

To evaluate the proposed approach, we consider a model which needs to be optimized for high stiffness under a static load case, and high energy absorption in a crash load case. Similar design problems are especially common in the car body design. We generate a Pareto set of feasible designs for this test case and identify design prototypes. An interesting application of this method is to find designs with similar geometric appearance but very different performance. This can help us to estimate the robustness of a design. By helping in design exploration and selection, the proposed approach shows promise in large-scale industrial applications.
},
	publisher = {ANSYS},
	booktitle = {16th International LS-DYNA Conference 2020}
}