This study targets at determining impeller-only axial fans with optimal hub-to-tip ratio for highest achievable total-to-static efficiency. Differently from other studies, a holistic approach is chosen. Firstly, the complete class of this fans is considered. Secondly, the radial distribution of blade sweep angle, stagger angle, chord length and blade camber are varied to adapt the blades to the complex flow in the hub- and tip region. The tool being used is an optimization scheme with three key components: (i) a database created beforehand by Reynolds-Averaged Navier-Stockes (RANS-) predicted performance characteristics of 14,000 designs, (ii) an artificial neural network as a metamodel for the fan performance as a function of 26 geometrical parameters., (iii) an evolutionary algorithm for optimization, performed with the metamodel. In general, the hub-to-tip ratios for the class of axial impeller-only fans proposed by the optimization scheme are smaller than those obtained applying the classic rules. A second outcome are the shapes of adapted blades which deviate substantially from the classic and even the state-of-the-art "swept-only'' or "swept with dihydral'' design. Chord length, stagger and sweep angle are distributed from hub to tip in a complex manner. The inherent reason is that the scheme tries to minimize not only the dynamic exit loss but also frictional losses due to secondary flows in the hub and tip region which eventually results in the maximum achievable total-to-static efficiency.