<p>Fused Filament Fabrication (FFF), a popular additive manufacturing (AM) technology, has transformed rapid prototyping and low-volume production. However, the inherent layer-wise deposition process often results in surface imperfections, such as roughness, waviness, and layer lines, which significantly limit the application of FFF parts in industries demanding high esthetic and functional standards. To address this challenge and expand the potential of FFF technology, a comprehensive understanding of the factors influencing surface quality is essential. This study examines the influence of four process parameters, including layer height, extrusion temperature, printing speed, and extrusion width, on the surface quality of polycarbonate samples produced through FFF. Predictive models were developed using both Response Surface Methodology (RSM) and Artificial Neural Networks (ANN) to estimate the surface roughness and waviness of polycarbonate parts. The results were evaluated by comparing predicted vs. actual plots and comparing key performance metrics, including mean squared error, mean absolute error, root mean squared error, and the coefficient of determination. In addition, the desirability function was utilized for the multi-objective optimization. The findings demonstrated that both Response Surface models and ANN effectively predict the surface roughness and waviness of FDM parts with high accuracy and reliability. However, Neural Network models outperformed response surface models in accuracy and performance. These models achieved lower error values and higher coefficients of determination, indicating better accuracy and a closer fit to the experimental data. Multi-objective optimization through the desirability function was used to find the best parameter settings to minimize the surface roughness and waviness in polycarbonate parts fabricated through FFF.</p>