Spatial Packaging and Routing Optimization of Complex Interacting Engineered Systems

Abstract Designing the 3D layout of interconnected systems (SPI2), which is a ubiquitous task in engineered systems, is of crucial importance. Intuitively, it can be thought of as the simultaneous placement of (typically rigid) components and subsystems, as well as the design of the routing of (typically deformable) interconnects between these components and subsystems. However, obtaining solutions that meet the design, manufacturing, and life-cycle constraints is extremely challenging due to highly complex and nonlinear interactions between geometries, the multi-physics environment in which the systems participate, the intricate mix of rigid and deformable geometry, as well as the difficult manufacturing and life-cycle constraints. Currently, this design task heavily relies on human interaction even though the complexity of searching the design space of most practical problems rapidly exceeds human abilities. In this work, we take advantage of high-performance hierarchical geometric representations and automatic differentiation to simultaneously optimize the packing and routing of complex engineered systems, while completely relaxing the constraints on the complexity of the solid shapes that can be handled and enable intricate yet functionally meaningful objective functions. Moreover, we show that by simultaneously optimizing the packing volume as well as the routing lengths, we produce tighter packing and routing designs than by focusing on the bounding volume alone. We show that our proposed approach has a number of significant advantages and offers a highly parallelizable, more integrated solution for complex SPI2 designs, leading to faster development cycles with fewer iterations, and better system complexity management. Moreover, we show that our formulation can handle complex cost functions in the optimization, such as manufacturing and life-cycle constraints, thus paving the way for significant advancements in engineering novel complex interconnected systems.