A novel two-stage design framework for 2D spatial packing of interconnected components

Packing and routing problems separately are each challenging NP-hard problems. Therefore, solving the coupled packing and routing problem simultaneously will require disruptive methods to better address pressing related challenges, such as system volume reduction, interconnect length reduction, ensuring non-intersection, and physics (heat, fluid pressure or electromagnetic) considerations. Here we present a novel two-stage sequential design framework to perform simultaneous physicsbased packing and routing optimization. Stage 1 is comprised of generating interference-free initial layouts that are fed to stage 2 as starting points to perform continuous physics-based optimization. Three distinct strategies for stage 1 have been introduced recently, 1) the force-directed layout method (FDLM), 2) an extension of the shortest path algorithms (SPAs) and 3) a unique geometric topology (UGT) generation algorithm. In stage 2, a gradient-based topology optimization method is used to simultaneously optimize both component locations and routing paths of component interconnects. In addition to geometric considerations, this method supports optimization based on system behavior by including physics-based objectives and constraints (e.g., modeled using 1D lumped parameter and 2D finite element physics models). The three layout generation methods developed for stage 1 are compared here with respect to system performance metrics obtained from stage 2. In summary, the design automation framework presented here integrates several elements together as a step toward a more comprehensive solution of 3D packing and routing problems with both geometric and physics considerations.