A Hybrid Optimization Framework for Spatial Packaging of Interconnected Systems

Abstract: This paper presents an optimization framework for Spatial Packaging of Interconnected Systems with Physical Interactions (SPI2) that addresses the geometric challenges of three-dimensional component placement and routing. While SPI2 generally includes physical interactions, this study isolates the spatial optimization aspect to evaluate placement and routing performance independently. The framework integrates the Maximal Disjoint Ball Decomposition (MDBD) for geometric abstraction with a hybrid optimization strategy that combines stochastic initialization and gradient-based refinement with interior point optimization. It is formulated to handle the nonlinear, non-convex, and continuous characteristics of spatially coupled design problems. The proposed framework is evaluated against a use case from prior SPI2 research and tested with a newly introduced benchmark that enables verifiable assessment of optimization performance. Results indicate that the presented method achieves more than a 10% improvement over existing SPI2 implementations and converges to spatially analytical optima across various benchmark scenarios. Benchmark experiments show solution accuracy of 0.6-2% relative to the ground truth.