Organizations: IRIT, UMR 5505 CNRS, Universit´e Toulouse Capitole, Universit´e de Toulouse, Toulouse, France. · ONERA, DTIS, Universit´e de Toulouse, Toulouse, France. · F´ed´eration ENAC ISAE-SUPAERO ONERA, Universit´e de Toulouse, 31000, Toulouse, France. · German Aerospace Center (DLR), Institute of System Architectures in Aeronautics. Hein-Saß-Weg 22, 21129 Hamburg, Germany.
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.
Figures & tables
Figure 1: COLOSSUS EU project overview Shiva Prakasha et al. 2024 .
Figure 2: The COLOSSUS pull paradigm based on EVE.
Figure 3: Wildfire fighting with mixed hierarchical components.
Figure 4: Mixed hierarchical variables associated with the ConOps in the design space graph. Red lines are incompatibilities, arrows are decreed dependencies, and light blue nodes are selection choices from which exactly one output arrow is selected.
Figure 5: The Bayesian optimization framework ( Bussemaker et al. 2024 , Figure 2) .
xt:=x∈Ωfargmaxαf\mboxreg(x)
Algorithm 1 SEGOMOE for constrained multi-objective and mixed-integer problems.
Figure 6: EVE scenario - Salamis Island.
Figure 7: Mixed hierarchical variables associated with the ConOps for the optimization problem of Table 5.1 represented in the design space graph.
Figure 8: Baseline fleet solution on Salamis scenario
Figure 9: Optimization results: initial DOE of 40 points (9 feasible identified by black circles) and 116 feasible enrichment points with 2 points on the Pareto Front identified by the red diamonds. The differences in shape and color depend on the number of seaplanes in the fleet (8, 10, or 12).
Figure 10: Optimization results: initial DOE of 40 points (9 feasible) and 101 feasible enrichment points with 5 points on the Pareto Front identified by the red diamonds (zoom).
Configuration
Total Fire Cost
CO 2 Emissions
Burnt Area
Effective Mission Time
[M€]
[t]
[km 2 ]
[h]
Baseline
11.53
1.63
11.79
7.68
8 Seaplanes
6.83
2.60
6.67
12 Seaplanes
6.53
2.64
6.37
1.6
Table 1: Comparison of the baseline and optimized fleet configurations.
Figure 11: Optimal fleet solutions on Salamis scenario
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Ali Tfaily, Youssef Diouane, Nathalie Bartoli +1
1*Department of Mechanical Engineering, McGill University, Canada. · 2Advanced Product Development, Bombardier, Canada. · Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Canada. +4
Designing effective multi-agent systems (MAS) remains a challenging and resource-intensive task. We propose a Bayesian Evolutionary Optimization framework for automatically discovering task-specific MAS topologies. The approach combines evolutionary operators to generate diverse workflow graphs with Bayesian optimization to focus cost intensive evaluations on promising candidates. In contrast to LLM-based candidate selection, our approach uses a graph-aware Gaussian Process and Expected Improvement to provide an explicit selection criterion during evolutionary search. We evaluate the method on BigCodeBench for code generation and on a tabular preprocessing benchmark using TabPFN. On BigCodeBench, evolved architectures achieve the highest overall performance among the evaluated agent systems. On temporal tabular datasets, optimized MAS preprocessing improves over the default TabPFN model on several tasks, while remaining competitive on IID datasets. Overall, the results demonstrate the potential of Bayesian selection for guiding evolutionary MAS search under expensive evaluation budgets.
Dominik Jehle, Tom Zehle
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Niki Triantafyllou, Andrea Bernardi, Maria M. Papathanasiou
Sargent Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, UK