Surface roughness (SR) is one of the major parameters used to govern the quality of the fused deposition modeling (FDM)-printed products, and the FDM process parameters can be easily regulated in order to obtain a good surface finish. The surface quality of the product produced by the FDM is generally affected by the staircase effect that needs to be managed. Also, the production time (PT) to fabricate the product and volume percentage error (VPE) should be minimized to make the FDM process more efficient. The aim of this paper is to accomplish these three objectives with the use of the parametric optimization technique integrating the artificial neural network (ANN) and the whale optimization algorithm (WOA). The FDM parameters which have been taken into consideration are layer thickness, nozzle temperature, printing speed, and raster width. Experimentation has been conducted on printed samples to examine the impact of the input parameters on SR, VPE, and PT according to Taguchi's L27 orthogonal array. The ANN model has been built up using the experimental data, which was further used as an objective function in the WOA with an aim to minimize output responses. The robustness of the proposed method has been validated on the optimal combinations of FDM process parameters.