WB5 - Derivative-free and blackbox optimization 3

We study Combinatorial Bayesian Optimization (CBO) in settings where a low-cost approximate function correlated with the true objective is available. We propose a multi-fidelity kernel framework that fuses both sources within a Gaussian process surrogate, improving the surrogate fit and guiding acquisition function optimization over the combinatorial space.

This paper proposes an anti-collision framework for autonomous drone swarms navigating in dynamic and uncertain aerial environments. The approach aims to ensure safe operation by preventing collisions between swarm members while preserving swarm formation and maintaining communication distance constraints essential for coordinated behavior. In addition, the framework addresses collision avoidance with static obstacles and external dynamic flying objects whose future motion is not known in advance. An LSTM-based trajectory prediction model is employed to capture temporal motion behavior and anticipate future positions for real-time risk evaluation. These predictions are integrated into a decision-making strategy that jointly considers safety, formation stability, and connectivity preservation. Experimental evaluation indicates that the proposed framework significantly improves navigation robustness and coordination while reducing collision risk in complex multi-agent scenarios.

When tests are costly, choosing what to measure becomes the optimization problem. In a case study on startup sequences for a 50 MW Kaplan turbine, we use the derivative-free MADS algorithm to plan which sequences to measure during an on-site measurement campaign and to calibrate a transient turbine simulation model.

In simulation-based engineering, design choices are often obtained following the optimization of complex blackbox models. These models frequently involve mixed-variable domains with quantitative and categorical variables. Unlike quantitative variables, categorical variables lack an inherent structure, which makes them difficult to handle, especially in the presence of constraints. This work proposes a systematic approach to structure and model categorical variables in constrained mixed-variable blackbox optimization. Surrogate models of the objective and constraint functions are used to induce problem-specific categorical distances. From these distances, surrogate-based neighborhoods are constructed using notions of dominance from bi-objective optimization, jointly accounting for information from both the objective and the constraint functions. This study addresses the lack of automatic and constraint-aware categorical neighborhood construction in mixed-variable blackbox optimization. As a proof of concept, these neighborhoods are employed within CatMADS, an extension of the MADS algorithm for categorical variables. The surrogate models are Gaussian processes, and the resulting method is called CatMADSGP. The method is benchmarked on the Cat-Suite collection of 60 mixed-variable optimization problems and compared against state-of-the-art solvers. Data profiles indicate that CatMADSGP achieve superior performance for both unconstrained and constrained problems.