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

基于最优传输的置换不变海上风电场布局贝叶斯优化

Abstract: 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.

摘要： 贝叶斯优化（BO）被广泛且成功地应用于解决那些目标函数评估成本高昂、属于黑盒且非凸的优化问题。然而，传统的贝叶斯优化算法无法利用目标问题中可能存在的对称性。

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.

一个直观的例子是最优位置问题，其决策变量是指连续空间内的一组有限点，且点的顺序不会影响目标函数的值。我们将这种设置称为“布局优化”，以区别于“点云优化”，在点云优化中，点的顺序是有意义的。

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.

作为布局优化的一个实例，我们考虑了一个具有现实工业意义的应用，即海上风电场的布局优化：在风力发电机完全相同的情况下，交换其中任意一对发电机的位置都不会对年发电量产生任何影响。

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.

基于最优传输理论，我们提出了一种置换不变贝叶斯优化方法（PIBO）。实验证明，与传统贝叶斯优化方法相比，该方法不仅能提供更优的风电场布局，还能将计算时间缩短约一半。