This paper presents a 3-D optimization of a moderately loaded transonic compressor rotor by means of a multiobjective optimization system. The latter makes use of a differential evolutionary algorithm in combination with an Artificial Neural Network and a 3D Navier-Stokes solver. Operating it on a cluster of 30 processors enabled the evaluation of the off-design performance and the exploration of a large design space composed of the camber line and spanwise distribution of sweep and chord length. Objectives were an increase of efficiency at unchanged stall margin by controlling the shock waves and off-design performance curve. First designs of single blade rows allowed a better understanding of the impact of the different design parameters. Forward sweep with unchanged camber improved the peak efficiency by only 0.3% with the same stall margin. Backward sweep with an optimized S shaped camber line improved the efficiency by 0.6% at unchanged stall margin. It is explained how the camber line control can introduce the same effect as forward sweep and compensate the expected negative effects of backward sweep. The best results (0.7% increase in efficiency and unchanged stall margin) have been obtained by a stage optimization that allows also a spanwise redistribution of the rotor flow and an increase of loading by extra flow turning. The latter compensates the loading shift induced by the backward sweep in order to reduce the inlet Mach number at the downstream stator hub.