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

Jul 16, 2026

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This paper presents a decomposition-enhanced framework for spatial packaging of interconnected systems with physical interactions (SPI2) in three-dimensional component placement. To support an automotive use case, SPI2 is extended to generate initial designs with alignment, improve numerical robustness in gradient-based optimization, and reduce computational burden. It also treats placement locations as design variables to enable penalty-based coordination and system-level feasibility. Validation uses a multi-objective NSGA-II approach on a powertrain and battery chassis integration task, showing improved efficiency over exhaustive discretized search.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages16

Reading Time40 min

Abstract

Introduction

A Decomposition-Based Framework for Joint Optimization and Spatial Packaging of Interconnected Systems with Physical Interactions J. Bückmann, J. van Kampen, T. Hofman arXiv :2607 .06087v 1 [ cs .CE] 7 Jul 2026 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 penaltybased 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, asa 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. Index Terms—Spatial Packaging of Interconnected Systems with Physical Interactions (SPI2), generative design, optimization, problem decomposition, Multi-objective optimization. I. Introduction Optimization is the cornerstone of technological ad vancement, driving eﬀiciency, sustainability, and innovation across engineering disciplines. With optimization applications ranging from robot design [1] to packaging problems such as spatial packaging of interconnected systems with physical interactions (SPI2) [2] [3] or vehicle optimization [4] . Given the rise in computational power, optimization problems can be extended to not only optimize a certain part of a system but also optimize on system-level [5] . In terms of automotive optimization such system and subsystem level optimization strategies are being investigated utilizing problem decomposition strategies [6] . When optimizing at system level, an additional J. Bückmann, J. van Kampen, and T. Hofman (e-mail: [t.hofman@tue.nl](t.hofman@tue.nl)) are with the Eindhoven University of Technology (TU/e), Dept. of Mechanical Engineering, Control Systems Technology section, Engineering Systems Design group, P.O.Box 513, 5600 MB Eindhoven, The Netherlands. Fig. 1: Overview of framework, where MDBD component approximations are used to generate a drivetrain layout and use Analytical Target Cascading as a problem decomposition to optimize placement. layer of complexity is added, namely the difference in optimization objectives between different subsystems. This means a multi-objective optimization approach must be adopted [7] . The extension into multi-objective optimization through problem decomposition strategies, however, leads to extensive design spaces with growing interdependencies to result in a feasible design, and thus coordination methods must be considered to coordinate for feasibility as well as eﬀicient coordination of complex design spaces [8] . This complexity applies especially to modern technology design that often targets tighter and more compact design layouts [9] . Related Literature: Research efforts address spatial layout and packaging optim

FAQs

What is SPI2 and what problem does the framework target?

SPI2 is a method for optimizing spatial packaging of interconnected systems with physical interactions, specifically for 3D component placement problems.

How does the proposed methodology improve SPI2 for automotive applications?

It enhances convergence rate and solution quality by improving numerical robustness in gradient-based optimization and reducing computational load, while also adding alignment capabilities for component-to-component port alignment.

How is the approach validated and what is the main result?

It is validated using a multi-objective NSGA-II framework on a combined powertrain optimization and battery chassis integration problem, demonstrating SPI2’s effectiveness both for initial design generation and as a system-level coordination mechanism with lower computational cost than discretized exhaustive search.

Jul 16, 2026

Upload by Oliver