Reliable wind turbine power prediction is imperative to the planning, scheduling and control of wind energy farms for stable power production. In recent years Machine Learning (ML) methods have been successfully applied in a wide range of domains, including renewable energy. However, due to the challenging nature of power prediction in wind farms, current models are far short of the accuracy required by industry. In this paper, we deploy a composite ML approach--namely a hybrid neuro-evolutionary algorithm--for accurate forecasting of the power output in wind-turbine farms. We use historical data in the supervisory control and data acquisition (SCADA) systems as input to estimate the power output from an onshore wind farm in Sweden. At the beginning stage, the k-means clustering method and an Autoencoder are employed, respectively, to detect and filter noise in the SCADA measurements. Next, with the prior knowledge that the underlying wind patterns are highly non-linear and diverse, we combine a self-adaptive differential evolution (SaDE) algorithm as a hyper-parameter optimizer, and a recurrent neural network (RNN) called Long Short-term memory (LSTM) to model the power curve of a wind turbine in a farm. Two short time forecasting horizons, including ten-minutes ahead and one-hour ahead, are considered in our experiments. We show that our approach outperforms its counterparts.