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

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.