We carried out the design optimization for the zero-thickness corrugated airfoil. The multi-objective evolutionary algorithms(MOEA)-based design framework was developed. The multi-layer Cartesian mesh-based computational fluid dynamics which employed the immersed boundary method was used as an aerodynamic evaluation for the zero-thickness airfoil and the dynamic geometrical deformation. The design problems had two objective functions; one was the minimization of the drag coefficient , the other was the maximization of the lift coefficient. CFD was carried out under Reynolds number $10^4$ and angle of attack $2.0^\circ$. MOEA has carried out 50 generations with 30 individuals per generation, and the trade-off between the two objectives could be found out. It was also found that the design which achieved the minimum drag coefficient kept several recirculating regions by the geometrical corrugations to reduce the friction drag.