Abstract. It is important to optimize wind turbine positions to mitigate potential wake losses. To perform this optimization, atmospheric conditions, such as the inflow speed and direction, are assigned probability distributions according to measured data, and these conditions are propagated through engineering wake models to estimate the annual energy production (AEP). This study presents stochastic gradient descent (SGD) for wind farm optimization, which is an approach that estimates the gradient of the AEP using Monte Carlo simulation, allowing for the consideration of an arbitrarily large number of atmospheric conditions. This method does not require that the atmospheric conditions be discretized, in contrast to the typical rectangular quadrature approximation of AEP. SGD is demonstrated using wind farms with square boundaries, considering cases with 25, 64, and 100 turbines, and the results are compared to a deterministic optimization approach. It is shown that SGD finds a larger optimal AEP in substantially less time than the deterministic counterpart as the number of wind turbines is increased.

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