The development of axial aircraft compressors has led to high stage loadings and therewith reductions in entire engine size and weight. This trend also promotes several disadvantages such as the risks of flow separation and higher secondary flows that are associated with increased stage loading. The application of non-axisymmetric end walls is one approach to reduce blade loading in the end wall regions and to control end wall flow with the main objectives of increasing the component efficiency and the total pressure ratio. The emphasis of this work is to analyze the steady and unsteady performance of a transonic compressor stage with non-axisymmetric end. The axisymmetric layout of Configuration I of the Darmstadt Transonic Compressor serves as the datum design. As a tool to find the optimum non-axisymmetric end wall shape, a fully-automated multi-objective optimizer connected to a steady 3D-RANS flow solver is used. The goal is to analyze how effective such a design tool can work on such a challenging task and to derive first design rules and compare the differences and features in common to the experience made by turbine researchers.