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

arXiv: https://arxiv.org/abs/2606.00009 · HTML: https://mlsanity.com/paper/2606.00009/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Architecture Search with Bayesian Optimisation and Optimal Transport](https://mlsanity.com/paper/1802.07191/) (2018)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters](https://mlsanity.com/paper/1406.7758/) (2014)
- [Permutation Invariant Representations with Applications to Graph Deep Learning](https://mlsanity.com/paper/2203.07546/) (2022)
- [Bayesian Optimization over Permutation Spaces](https://mlsanity.com/paper/2112.01049/) (2021)
- [EXPObench: Benchmarking Surrogate-based Optimisation Algorithms on Expensive Black-box Functions](https://mlsanity.com/paper/2106.04618/) (2021)
- [Advancing Bayesian Optimization: The Mixed-Global-Local (MGL) Kernel and Length-Scale Cool Down](https://mlsanity.com/paper/1612.03117/) (2016)
- [Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks](https://mlsanity.com/paper/2501.11350/) (2025)
- [Bayesian Optimization with Inexact Acquisition: Is Random Grid Search Sufficient?](https://mlsanity.com/paper/2506.11831/) (2025)
- [Bayesian Optimisation Against Climate Change: Applications and Benchmarks](https://mlsanity.com/paper/2306.04343/) (2023)
- [Quantification using Permutation-Invariant Networks based on Histograms](https://mlsanity.com/paper/2403.15123/) (2024)
- [The Asteroid Routing Problem: A Benchmark for Expensive Black-Box Permutation Optimization](https://mlsanity.com/paper/2203.15708/) (2022)
- [From Sorting Algorithms to Scalable Kernels: Bayesian Optimization in High-Dimensional Permutation Spaces](https://mlsanity.com/paper/2507.13263/) (2025)
- [Permutation-Invariant Physics-Informed Neural Network for Region-to-Region Sound Field Reconstruction](https://mlsanity.com/paper/2601.19491/) (2026)

## Abstract (arXiv)

Bayesian Optimization (BO) is widely and successfully adopted for solving optimization problems having an expensive-to-evaluate, black-box, and non-convex objective function. However, the vanilla BO algorithm is not able to exploit possible symmetries characterizing the target problem. An intuitive case is given by optimal location problems, whose decision variables refer to a finite set of points within a continuous space, with the order of points not affecting the value of the objective function. We refer to this setting as optimization over layouts to distinguish from optimization over point-clouds where, instead, the order of points counts. As an instance of optimization over layouts we consider a real-life industrial-relevant application, that is the optimization of the layout of an offshore wind farm: given identical wind turbines, switching any pair of them has not any effect on the annual energy production. Based on Optimal Transport theory, we propose a Permutation-Invariant BO approach, namely PIBO, proved to provide better wind farm layouts when compared to the vanilla BO approach while cutting computation time roughly in half.