This paper deals with the development and comparison of prediction models established using response surface methodology (RSM) and artificial neural network (ANN) for a wire electrical discharge machining (WEDM) process. The WEDM experiments were designed using central composite design (CCD) for machining of Inconel 718 superalloy. During experimentation, the pulse-on-time (TON), pulse-off-time (TOFF), servo-voltage (SV), peak current (IP), and wire tension (WT) were chosen as control factors, whereas, the kerf width (Kf), surface roughness (Ra), and materials removal rate (MRR) were selected as performance attributes. The analysis of variance tests was performed to identify the control factors that significantly affect the performance attributes. The double hidden layer ANN model was developed using a back-propagation ANN algorithm, trained by the experimental results. The prediction accuracy of the established ANN model was found to be superior to the RSM model. Finally, the Non-Dominated Sorting Genetic Algorithm-II (NSGA- II) was implemented to determine the optimum WEDM conditions from multiple objectives.