Title: Permutation-Invariant Bayesian Optimization for Offshore Wind Farm Layouts Using Optimal Transport

Abstract:

Bayesian Optimization (BO) is a widely adopted and highly successful method for addressing optimization challenges involving expensive, black-box, and non-convex objective functions. However, standard BO algorithms fail to leverage inherent symmetries present in certain problem structures. A prime example is found in optimal location problems, where decision variables represent a finite set of points within a continuous space, and the sequence of these points does not influence the objective function’s value. We designate this scenario as "optimization over layouts" to differentiate it from "optimization over point-clouds," where point ordering is significant.

To illustrate this concept, we examine a practical, industry-relevant application: optimizing the configuration of an offshore wind farm. In this context, because all wind turbines are identical, swapping any two turbines yields no change in annual energy production. Leveraging Optimal Transport theory, we introduce Permutation-Invariant Bayesian Optimization (PIBO). Our results demonstrate that PIBO generates superior wind farm layouts compared to traditional BO methods, while simultaneously reducing computational time by approximately 50%.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC