Spatial Optimization of Interconnected Systems in Non-Convex Design Spaces

TL;DR

This paper introduces a novel spatial optimization framework that handles non-convex design spaces for interconnected systems, integrating physical interactions and CAD workflows for practical engineering applications.

Contribution

It extends the SPI2 framework to support arbitrary non-convex boundaries and incorporates physical and geometric calculations directly into the optimization process.

Findings

Successfully optimized interconnected components within complex geometries.

Maintains geometric feasibility within numerical tolerance.

Demonstrates potential for practical engineering design applications.

Abstract

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.