Polymer single-screw extrusion is a major industrial processing technique used to obtain plastic products. To assure high outputs, tight dimensional tolerances, and excellent product performance, extruder screws may show different design characteristics. Barrier screws, which contain a second flight in the compression zone, have become quite popular as they promote and stabilize polymer melting. Therefore, it is important to design efficient extruder screws and decide whether a conventional screw will perform the job efficiently, or a barrier screw should be considered instead. This work uses multi-objective evolutionary algorithms to design conventional and barrier screws (Maillefer screws will be studied) with optimized geometry. The processing of two polymers, low-density polyethylene and polypropylene, is analyzed. A methodology based on the use of artificial intelligence (AI) techniques, namely, data mining, decision making, and evolutionary algorithms, is presented and utilized to obtain results with practical significance, based on relevant performance measures (objectives) used in the optimization. For the various case studies selected, Maillefer screws were generally advantageous for processing LDPE, while for PP, the use of both types of screws would be feasible.