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.

翻译：本文提出了一种面向具有物理交互的互联系统空间布局(SPI2)的优化框架，用于解决三维组件布置与布线的几何挑战。尽管SPI2通常涵盖物理交互，本研究将空间优化方面分离处理，以独立评估布局与布线性能。该框架将最大不相交球体分解(MDBD)用于几何抽象，并与混合优化策略相结合——该策略融合了随机初始化、基于梯度的精化方法及内点优化。框架设计旨在处理空间耦合设计问题中非线性、非凸及连续等特性。通过SPI2先前研究中的实例对所提框架进行评估，并采用新引入的可验证优化性能基准进行测试。结果表明，该方法相比现有SPI2实现提升了超过10%，且能在多种基准场景下收敛至空间解析最优解。基准实验显示，相对于真实值的求解精度达0.6%-2%。