Fused deposition modeling (FDM) is a widely-used extrusion-based additive manufacturing process, primarily for 3D printing. It facilitates the cost-effective production of customized products. The polymer is melted and then extruded through a nozzle, with which the product is built up layer by layer. The quality of parts produced with FDM depends on multiple factors, including the extrusion nozzle (e.g., type and geometry) and the process parameters. In this work, we will focus on the impact of the nozzle, which ensures precise material deposition but often limits the maximum achievable printing speed due to pressure losses. The polymer melt’s high viscosity and shear-thinning behavior result in significant pressure drops within the nozzle. These can restrict printing speed and lead to feeder slip, reducing dimensional accuracy. Depending on the nozzle geometry and the viscoelastic material properties, vertex formations of the polymer flow can occur inside the nozzle, influencing the pressure drop and leading to material degradation. Reducing the pressure drop can enable higher printing speeds, improved line precision, and better overall quality. To address this, we are optimizing the nozzle shape. We have developed a computational framework integrating fluid dynamics simulations with optimization algorithms to enhance nozzle performance. Polymer melt flow is simulated using a Giesekus model to capture the viscoelastic effects. For shape optimization, we use a spline-based parameterization that enables low-dimensional geometry modification via control-point adjustments and compare it with a simpler, angle-based parametrization. Gradient-free optimization algorithms are used to effectively explore design variations. We present results comparing optimal nozzle designs under different manufacturing constraints and material parameters. The optimized designs demonstrate reduced pressure drop, enabling higher printing speeds and improved dimensional accuracy. This highlights the potential of shape optimization to advance FDM processes.