Fused Deposition Modeling is increasingly employed for the fabrication of functional polymer components, although their mechanical response and dimensional accuracy remain strongly dependent on processing parameters and local geometric features. This study proposes an integrated predictive and optimization framework for FDM-printed parts incorporating functional bosses and heat-set metallic inserts. The approach addresses a relevant gap in the current literature, as most existing studies focus on standard specimens or global manufacturing parameters, whereas limited attention has been given to local functional geometries controlling the performance of joints and assembled structures. Experimental data were obtained from controlled tensile pull-out tests conducted on Z-ULTRAT specimens manufactured under constant processing conditions. The investigated design variables were the outer boss diameter, inner cavity diameter, and taper angle, selected using a face-centered central composite design. The resulting dataset was statistically processed and used to train feed-forward artificial neural network models for predicting the principal mechanical responses. The developed models exhibited satisfactory predictive performance and good agreement with the experimental observations. Based on these models, a genetic algorithm was applied to identify parameter combinations that improve pull-out response and dimensional accuracy. The results demonstrate the significant effect of boss geometry on the mechanical behavior of the polymer-metal interface and support the proposed ANN-GA framework as an effective data-driven methodology for the design and optimization of hybrid FDM components for functional engineering applications.