An ejector is a technologically simple and yet wide-application fluid machine. While it has favorable characteristics for a significant number of technological processes, its main downside is probably its high operational energy demands. The present paper is an initial result of an ongoing research aimed at improving energy efficiency of the ejector via optimization of its geometry. In the paper, we focus mostly on presenting a general multi-objective optimization framework usable for an ejector shape optimization. The approach applicability is illustrated on a simplified problem comprising only a single phase flow in an ejector mixing tube and diffuser. Nevertheless, the achieved simulation and optimization results are validated against experimental data. The proposed optimization method itself is based on multi-objective evolutionary algorithms (MOEAs) combined with computational fluid dynamics (CFD) for evaluation of the vector-valued objective function.