A Decomposition-Based Framework for Joint Optimization and Spatial Packaging of Interconnected Systems with Physical Interactions

2026-07-07

AI Summary

This study addresses the challenge of simultaneously achieving component alignment, system coordination, solution reliability, and computational efficiency in physically interacting interconnected systems within three-dimensional space. To this end, the authors propose a decomposition-based collaborative optimization framework that, for the first time, embeds port-alignment constraints into the SPI² architecture. Treating component positions as design variables, the method employs a penalty function to enforce system-level feasibility and enables automatic generation of initial designs. By integrating gradient-based optimization for enhanced numerical stability and coupling it with NSGA-II for efficient multi-objective search, the approach achieves high-quality coordinated solutions. Demonstrated on automotive powertrain and battery-chassis integration cases, the framework significantly outperforms discrete exhaustive search, delivering superior system-level coordination while substantially reducing computational cost.

Abstract

This paper presents an approach and application of optimization of spatial packaging of interconnected systems with physical interactions (SPI2) in three-dimensional component placement problems. To enable its application for an automotive use case, SPI2 must support both initial design generation, including component alignment, and robust system-level coordination, requiring improved solution reliability and tractable computational cost. To address these requirements, the proposed methodology improves convergence rate and solution quality by enhancing numerical robustness in gradient-based optimization while reducing computational load. Existing SPI2 approaches are extended through the addition of alignment capabilities, enabling the representation of port-to-port alignments between components. Furthermore, the applicability of SPI2 is expanded by treating component placement locations as design variables, allowing for penalty-based coordination to ensure design feasibility and enabling integration within system-level optimization. The approach is validated using a multi-objective optimization framework based on Nondominated Sorting Genetic Algorithm II (NSGA-II), applied to a combined powertrain optimization and battery chassis integration problem. This demonstrates the effectiveness of the SPI2 in a system-level design context. The results show a twofold application of SPI2 in an automotive use case: first, as a tool for initial design generation, and second, as part of a system-level design coordinator that outperforms a discretized exhaustive search while requiring lower computational cost.

Problem

• spatial packaging
• interconnected systems
• physical interactions
• component placement
• system-level optimization

Innovation

• spatial packaging
• physical interactions
• gradient-based optimization
• design coordination
• multi-objective optimization