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

Packing and routing 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 (thermal, hydraulic, or electromagnetic) considerations. Here we present a novel two-stage sequential design framework to perform simultaneous physics-based packing and routing optimization. Stage 1 generates 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 interconnect routing paths. In addition to geometric considerations, this method supports optimization based on system behavior by including physics-based objectives and constraints. The proposed framework is demonstrated using three case studies. First, the layout generation methods developed for stage 1 are compared with respect to system performance metrics obtained from stage 2. Second, a multi-objective optimization problem using the epsilon-constraint method is solved to obtain Pareto optimal solutions. Third, an extension to multi-loop systems is demonstrated. In summary, the design automation framework integrates several elements together as a step toward a more comprehensive solution of 3D packing and routing problems with both geometric and physics considerations.