Upon manufacturing plastics parts by extrusion or injection, polymers are plasticised in single screw units. The mechanisms involved in this process are complex and material, geometry and operation dependent. Usually, the setting of the extruder operating conditions or the establishment of the adequate screw geometry is based on trial-and-error. A more efficient method consists in determining the operating conditions or screw geometry that produces the desired performance, i.e. to solve the inverse problem. In this work a multi-objective optimization methodology based on genetic algorithms is proposed and used to perform an automatic optimization of the single screw polymer extrusion process. For that purpose a modelling package capable of considering the relevant thermo-mechanical phenomena occurring inside the extruder was developed and linked to the referred optimization methodology. The computational and experimental results obtained in real optimization problems validated the methodology proposed. This text can be used either by the researchers interested in the extrusion process or by the researchers only in using multi-objective optimization.