In this paper, an effective process optimization approach based on artificial neural networks with a back propagation algorithm and response surface methodology including central composite design is presented for the modeling and prediction of surface roughness in the wire electrical discharge machining process. In the development of predictive models, cutting parameters of pulse duration, open circuit voltage, wire speed and dielectric flushing are considered as model variables. After experiments are carried out, the analysis of variance is implemented to identify the contribution of uncontrollable process parameters effecting surface roughness. Then, a comparative analysis of the proposed approaches is carried out to determine the most efficient one. The performance of the developed artificial neural networks and response surface methodology predictive models is tested for prediction accuracy in terms of the coefficient of determination and root mean square error metrics. The results indicate that an artificial neural networks model provides more accurate prediction than the response surface methodology model.