As sources of conventional energy are alarmingly being depleted, leveraging renewable energy sources, especially wind power, has been increasingly important in the electricity market to meet growing global demands for energy. However, the uncertainty in weather factors can cause large errors in wind power forecasts, raising the cost of power reservation in the power system and significantly impacting ancillary services in the electricity market. In pursuance of a higher accuracy level in wind power forecasting, this paper proposes a double-optimization approach to developing a tool for forecasting wind power generation output in the short term, using two novel models that combine an artificial neural network with the particle swarm optimization algorithm and genetic algorithm. In these models, a first particle swarm optimization algorithm is used to adjust the neural network parameters to improve accuracy. Next, the genetic algorithm or another particle swarm optimization is applied to adjust the parameters of the first particle swarm optimization algorithm to enhance the accuracy of the forecasting results. The models were tested with actual data collected from the Tuy Phong wind power plant in Binh Thuan Province, Vietnam. The testing showed improved accuracy and that this model can be widely implemented at other wind farms.