T. Hofman

S. Westerhof, T. Hofman

This paper presents a spatial optimization methodology that extends the Spatial Packaging of Interconnected Systems with Physical Interaction (SPI2) framework to support arbitrary, non-convex design boundaries. We introduce a smooth, differentiable inside-outside evaluation for components represented using the Maximal Disjoint Ball Decomposition (MDBD) method. The framework also incorporates center-of-gravity and moment-of-inertia calculations directly into the optimization, and provides an end-to-end computer-aided design (CAD) workflow for importing components and reconstructing the optimized assembly. The method is demonstrated on a fictional aircraft auxiliary unit. Results show that the optimizer can place multiple interconnected components within a custom geometry while simultaneously handling routing and physics-based objectives. The approach maintains geometric feasibility within numerical tolerance and illustrates the potential of MDBD-based SPI2 methods for practical engineering design applications.

S. Westerhof, T. Hofman

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.