The majority of problems in aircraft production and operation require decisions made in the presence of uncertainty. For this reason aerodynamic designs obtained with traditional deterministic optimization techniques seeking only optimality in a specific set of conditions may have very poor off-design performances or may even be unreliable. In this work we present a novel approach for robust optimization of aerodynamic shapes based on the combination of single and multi-objective Evolutionary Algorithms and a Continuation Multi Level Monte Carlo methodology to estimate robust designs, without relying on derivatives and meta-models. Detailed numerical studies are presented for a transonic airfoil design affected by geometrical and operational uncertainties.