Optimal Transport-based Permutation-Invariant Bayesian Optimization of Offshore Wind Farm Layouts

Wind farm layout optimization becomes increasingly difficult as turbine count grows, especially when high-fidelity aerodynamic models are used. Conventional Kriging-based Bayesian optimization often suffers from low sample efficiency in high-dimensional layout spaces because sparse training data provide limited domain coverage. We develop a Graph-informed Kriging framework that embeds reusable aerodynamic interaction information into the surrogate mean function. The wind farm is represented as a directed aerodynamic graph, where pairwise turbine interactions defined in a low-dimensional relative-coordinate space are assembled into a farm-scale mean. This structured mean captures the dominant variation in annual energy production (AEP), allowing the Gaussian process to model only the residual structure and uncertainty. Numerical experiments show that Graph-informed Kriging consistently improves AEP prediction accuracy over ordinary and generic-trend Kriging under sparse-data conditions, with increasing benefits as layout dimension and wake-interaction strength grow. Embedded in Bayesian optimization, it substantially improves sample efficiency and achieves competitive solutions for the IEA Wind Task 37 benchmark with about 280 AEP evaluations. In a controlled 16-turbine case, it also outperforms ordinary and multi-fidelity Kriging under the same high-fidelity evaluation budget. The framework is further extended to a 48-turbine wind farm, demonstrating applicability to large-scale CFD-based layout optimization. These results show that Graph-informed surrogate modeling can enable more efficient use of high-fidelity aerodynamic models for reliable large-scale wind farm layout design.

Bayesian optimization (BO) is typically used only for problems where the underlying function is deemed "expensive" (e.g. in time or money), with the speed of the BO algorithm being of little importance. In the real world, however, problems span a continuous range of values, going from cheap to expensive. In this paper, we present BO algorithms through the lens of a speed-performance Pareto frontier: we compare BO against faster algorithms like CMA-ES, and highlight how certain regions of the Pareto frontier are currently empty. As a solution, we propose a new set of fast BO methods that exploit the linear structure in existing BO algorithms, for both continuous and combinatorial inputs (from ~10 to 6000+ dimensions). Our methods achieve performance similar to state-of-the-art BO, while being more than $10^2\times$ to $10^3\times$ faster, opening the field of BO to an entirely new class of problems.

Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function. Preferential BO (PBO) removes this requirement by learning from pairwise human feedback, yet existing methods struggle to efficiently optimize beyond low- and medium-dimensional problems due to their global search approaches. We address this limitation by developing a family of local PBO methods that transfer key ideas from high-dimensional BO to the preferential setting. In particular, we introduce local PBO methods which adapt trust-region and derivative-informed local search to pairwise preference feedback, where the latter exploits first- and second-order derivatives of the Laplace-approximated GP posterior. Our benchmark on GP sample paths, standard optimization benchmark functions, and policy-search tasks shows that local PBO methods are especially effective in high-dimensional and complex landscapes with steep optima. Compared with global preference-based baselines, they can substantially reduce cumulative regret, making them particularly useful for real-world preference-based optimization tasks such as policy search.