An electrically driven pump-fed cycle for a hybrid rocket engine is proposed and compared to a simpler gas-pressurized feed system. A liquid-oxygen/paraffin-based fuel hybrid rocket engine which powers the third stage of a Vega-like launcher is considered. Third-stage ignition conditions are assigned, and engine design and payload mass are defined by a proper set of parameters. Uncertainties in the classical regression rate correlation coefficients are taken into account and robust design optimization is carried out with an approach based on an epsilon-constrained evolutionary algorithm. A mission-specific objective function, which takes into account both the payload mass and the ability of the rocket to reach the required final orbit despite uncertainties, is determined by an indirect trajectory optimization approach. The target orbit is a 700 km altitude polar orbit. Results show that electrically driven pump-fed cycle is a viable option for the replacement of the conventional gas-pressurized feed system. Robustness in the design is granted and a remarkable payload gain is achieved, using both present and advanced technologies for electrical systems.