The purpose of this research was to create a predictive model for a medium-speed wire electrical discharge machine (WEDM) utilizing an artificial neural network (ANN). Medium-speed WEDM experiments were developed based on the I-optimal mixture design for machining, the Inconel 718 superalloy. During the experiment, the input parameters were the spark ontime, spark offtime, wire feed, and current, with the material removal rate (MRR) and surface roughness (Ra) selected as performance indicators. The ANN model was trained on experimental data and built using a feed-forward backpropagation neural network with a (4-8-2) structure and the Bayesian regularization (BR) learning approach. The model correctly predicted the relationship between the medium-speed WEDM’s primary process parameters and machining performance. An integrated ANN model and the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) were used to determine the ideal parameters for the MRR and Ra, resulting in a set of Pareto-optimal solutions. The confirmation experiment revealed that the mean prediction error between the experimental and ideal solutions had a maximum error percentage of 1% for the MRR and 2% for the Ra, which are within acceptable ranges. This showed that the best process–parameter combinations were better for the MRR and Ra.