  Successful development of wind farms relies on the optimal siting of wind
turbines to maximize the power capacity under stochastic wind conditions and
wake losses caused by neighboring turbines. This paper presents a novel method
to quickly generate approximate optimal layouts to support infrastructure
design decisions. We model the quadratic integer formulation of the discretized
layout design problem with an undirected graph that succinctly captures the
spatial dependencies of the design parameters caused by wake interactions. On
the undirected graph, we apply probabilistic inference using sequential
tree-reweighted message passing to approximate turbine siting. We assess the
effectiveness of our method by benchmarking against a state-of-the-art branch
and cut algorithm under varying wind regime complexities and wind farm
discretization resolutions. For low resolutions, probabilistic inference can
produce optimal or nearly optimal turbine layouts that are within 3% of the
power capacity of the optimal layouts achieved by state-of-the-art
formulations, at a fraction of the computational cost. As the discretization
resolution (and thus the problem size) increases, probabilistic inference
produces optimal layouts with up to 9% more power capacity than the best
state-of-the-art solutions at a much lower computational cost.
