Optimization studies have been performed on single screw extrusion of polymers. Experimental optimization of the selected process parameters, screw rotation speed and screw metering section length has been performed from the point of view of maximum extrusion output and minimum current intensity of the extruder motor. Because experimental optimization is extremely expensive and time consuming, the process simulation using evolutionary techniques (Genetic Algorithms) has been proposed. Extrusion simulation software GSEM has been used for that purpose, and the optimization program GASEO has been developed to optimize the process. The results of optimization will be presented in the second part of the paper.