## 1 Introduction  
In recent years, wind power has grown rapidly in many countries as a type of clean and renewable energy source. However, the uncertainty and intermittency of wind power have brought great challenges to large-scale electrical power systems. Accurate short-term wind power forecasting is a necessary condition to dispatch the electrical power resources in time, reduce the operating costs, and then ensure the electrical power systems operate reliably and safely [1, 2]. Many studies on wind power forecasting have been reported which can be mainly divided into two categories: one is based on statistical models, including regression models [3, 4], the Kalman filter [5, 6], and time series [7, 8]. The other is based on artificial intelligence models, such as fuzzy systems [9], neural networks (NN) [10, 11], and so on. Compared with the statistical model, artificial intelligence models are more flexible. More and more commercial prediction software used by utility companies have been developed based on artificial intelligent models [12], especially the NN model. These forecasting models are often called point prediction, mainly aiming to forecast values in the future, with less care about the prediction reliability, which is of limited value for uncertainties in the data or variability in the underlying system [13]. Recently there have been some reports about prediction intervals (PIs), which are considered as an excellent tool for the quantification of the wind power uncertainties that have never been considered in point predictions. Typical PIs are composed of a lower bound, an upper bound, and a confidence level indicating prediction reliability. PIs provide not only an interval covering the target value, but also a coverage probability indicating the prediction accuracy. In the literature, several models have been proposed for the construction of PIs and assessments of the uncertainties of prediction results. The PIs' models [14; 15], based on neural networks, require special assumptions about the data distribution and the computational complexity is massive. Then, a model called the lower upper bound estimation (LUBE) model was proposed in [16] with more reliability and simplicity. From the perspective of making decisions, the larger the coverage probability and smaller width of PIs, the more accurate the wind power forecasting is. However, in fact, in order to achieve a larger coverage probability, the width of the intervals will increase simultaneously, and vice versa. Thus, this is a typical multi-objective optimization problem. Previously, the literature solved this problem by translating the multi-objective problem into a single-objective problem with penalty parameters [13; 16; 17], such as [13]; the coverage probability is transformed to a hard constraint and then the problem becomes to the minimization of the width of the PIs. In this paper, this two-objective optimization problem is directly considered to use the multi-objective artificial bee colony algorithm with no penalty parameters for optimization. Then, a new formulation to calculate the width of the PIs is proposed. In this formulation, the prediction value of the PIs is considered as a misleading result, especially when the deviation is large, so the width can be closer to that of the primary without any negative effects of the value out of PIs. Considering that the wind power data is nonlinear, highly dimensional, and strongly coupled, the Wavelet Neural Network (WNN) is a more suitable and flexible neural network that can deal with the data of wind power efficiently, because it can instigate a superior system model for complex and seismic applications in comparison to the NN with a sigmoidal activation function [18; 19], so it is used to construct the PI model. In addition, a new multi-objective artificial bee colony (MOABC) algorithm is proposed to optimize the parameters of WNN.