The classical approach to extrusion die design relies heavily on the experience of the die designer; Especially the designer's ability to create an initial die design from a product design, the designer's constructional knowledge and performance during the running-in trials. Furthermore, the relative unpredictability of the running-in trials combined with the additional resource usage introduce uncertainties and delays in the time-to-market of a given product. To lower these delays and resource usage, extrusion die design can benefit greatly from numerical shape optimization.In this application, however, plastics melts pose a difficult obstacle, due to their rather unintuitive and nonlinear behavior. These properties complicate the numerical optimization process, which mimics running-in trials and relies on a minimal number of optimization iterations. As part of the Cluster of Excellence Integrative Production Technologies for High-Wage Countries at the RWTH Aachen University, an effort is made to shorten the manual running-in process by the means of numerical shape optimization.Using an in-house numerical shape optimization framework, a set of optimization algorithms, consisting of global, derivativefree and gradient-based optimizers, are evaluated with respect to the best die quality and a minimal number of optimization iterations. This evaluation is an important step on the way to include more computationally intensive material models into the optimization framework and identify the best possible optimization strategy for the numerical design of extrusion dies.