The power output of a wind turbine depends on wind speed, and on the physical and operating characteristics of the turbine. Then, the variability associated to wind power generation is relevant, and it is due to the wind uncertain and intermittent character. This intrinsic variability has a significant effect on power system operations such as regulation, load following, balancing, unit commitment and scheduling. Therefore, for the safe, reliable and economic operation of power systems, the accurate prediction of wind power and of the associated uncertainty is critical. In this study, we consider historical values of wind power for predicting future values of wind power itself, taking into account both the variability in the input and the uncertainty in the model structure. Uncertainty in the input (hourly wind power) is represented as an interval range which captures the within-hour variability. A Neural Network (NN) is trained on interval-valued input to provide output prediction intervals (PIs). A multi-objective genetic algorithm (namely, non-dominated sorting genetic algorithm-II (NSGA-II)) is used to train the NN. The multi-objective framework allows finding PIs which are optimal both in terms of accuracy (coverage probability) and efficacy (width).