In this work, the non-dominated sorting genetic algorithm-II (NSGA-II) is applied to determine the weights of a neural network trained for short-term forecasting of wind speed. More precisely, the neural network is trained to produce the lower and upper bounds of the prediction intervals of wind speed. The objectives driving the search for the optimal values of the neural network weights are the coverage of the prediction intervals (to be maximized) and the width (to be minimized). A real application is shown with reference to hourly wind speed, temperature, relative humidity and pressure data in the region of Regina, Saskatchewan, Canada. Correlation analysis shows that the wind speed has weak dependence on the above mentioned meteorological parameters; hence, only hourly historical wind speed is used as input to a neural network model trained to provide in output the one-hour-ahead prediction of wind speed. The originality of the work lies in proposing a multi-objective framework for estimating wind speed prediction intervals (PIs), optimal both in terms of accuracy (coverage probability) and efficacy (width). In the case study analyzed, a comparison with two single-objective methods has been done and the results show that the PIs produced by NSGA-II compare well with those and are satisfactory in both objectives of high coverage and small width.