# Hierarchical Bayesian optimization of an aircraft-based multi-agent system-of-systems

arXiv: https://arxiv.org/abs/2609.22130 · HTML: https://mlsanity.com/paper/2609.22130/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 62 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [A mixed-categorical correlation kernel for Gaussian process](https://mlsanity.com/paper/2211.08262/) (2022)
- [Upper Trust Bound Feasibility Criterion for Mixed Constrained Bayesian Optimization with Application to Aircraft Design](https://mlsanity.com/paper/2005.05067/) (2020)
- [An efficient application of Bayesian optimization to an industrial MDO framework for aircraft design](https://mlsanity.com/paper/2006.08434/) (2020)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- [System Architecture Optimization Strategies: Dealing with Expensive Hierarchical Problems](https://mlsanity.com/paper/2502.00838/) (2025)
- [Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design](https://mlsanity.com/paper/2504.08682/) (2025)
- [Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Exploration](https://mlsanity.com/paper/2510.16742/) (2025)
- [A distance for mixed-variable and hierarchical domains with meta variables](https://mlsanity.com/paper/2405.13073/) (2024)
- [Regularized infill criteria for multi-objective Bayesian optimization with application to aircraft design](https://mlsanity.com/paper/2504.08671/) (2025)
- [Multi-objective Bayesian Optimization With Mixed-categorical Design Variables for Expensive-to-evaluate Aeronautical Applications](https://mlsanity.com/paper/2504.09930/) (2025)
- [System-of-systems Modeling and Optimization: An Integrated Framework for Intermodal Mobility](https://mlsanity.com/paper/2507.08715/) (2025)
- [Interpretable and Explainable Surrogate Modeling for Simulations: A State-of-the-Art Survey and Perspectives on Explainable AI for Decision-Making](https://mlsanity.com/paper/2604.14240/) (2026)

## Abstract (arXiv)

Developing innovative system architectures increasingly relies on advanced modeling and optimization techniques to frame the architecting process and define the corresponding computational problems. For complex System-of-Systems (SoS), high-fidelity multiphysics and multidisciplinary simulations are essential for capturing detailed behaviors. However, their computational expense and the risk of evaluation failures make direct optimization challenging. To overcome these limitations, surrogate-based approaches, like Bayesian optimization, have emerged as effective tools for managing expensive, black-box simulation tasks. This work introduces a hierarchical Bayesian optimization framework that leverages Gaussian process meta-modeling to handle discrete architectural choices, conditional dependencies, and heterogeneous design variables inherent to SoS problems. Results show that the hierarchical formulation improves search efficiency and robustness compared to conventional surrogate-based methods, enabling the exploration of large and structurally diverse design spaces with limited simulation budgets. We apply the approach to an aircraft-based multi-agent system for wildfire suppression, a use case developed within the EU-funded COLOSSUS project that illustrates how SoS principles can coordinate heterogeneous aerial platforms with complementary roles, supporting both sustainable mobility and emergency response missions. Our framework provides a scalable methodology for SoS architecting and model exploration, offering transferable insights for applications in aviation, sustainable mobility, and resilience-oriented system design. By combining hierarchical representations with surrogate-based optimization, this work is among the first practical demonstrations of hierarchical Bayesian optimization applied to real-world SoS problems, advancing both methodology and practice.