🤖 AI Summary
This work addresses the challenging problem of spatial packaging layout and routing in three-dimensional interconnected systems with physical interactions by proposing a hybrid optimization framework. The approach employs geometric abstraction based on Maximum Disjoint Ball Decomposition (MDBD) and integrates stochastic initialization, gradient-based refinement, and an interior-point method to effectively tackle the nonlinear, non-convex, and continuous spatially coupled design problem. A newly introduced benchmark enables verifiable performance evaluation, demonstrating that the proposed method outperforms existing techniques by over 10% across multiple scenarios. The solutions achieve a relative error of only 0.6–2% compared to ground-truth values, significantly enhancing both convergence stability and solution optimality.
📝 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.