Airborne wind energy (AWE) systems benefit from a high lift airfoil to increase the power output, to that end, multi-element airfoils are investigated for AWE applications. This thesis aims to optimize a multi-element airfoil for a rigid AWE kite that operates in a pumping cycle. Since the kite has distinct operational phases, i.e., reel-out and reel-in phase, the airfoil design must take into account the different design objectives for each phase. The airfoil is first optimized for reel-out or production phase and it is then adapted for the reel-in or return phase requirements by modifying its flap setting. The optimization is performed through a multi-objective genetic algorithm coupled to MSES as the aerodynamic solver. Once the multi-element airfoil has been optimized, its aerodynamic performance is verified through CFD RANS simulations, computed with OpenFOAM. The resulting airfoil offers a satisfactory performance for production and return phase; and the CFD verification shows a fairly good agreement in terms of lift coefficient although the drag has been significantly overpredicted by MSES.