An efficient formulation for the robust shape optimization of aerodynamic objects is introduced in this paper. The formulation has three essential features. First, an Euler solver based on a second-order Godunov scheme is used for the flow calculations. Second, a genetic algorithm with binary number encoding is implemented for the optimization procedure. The third ingredient of the procedure is the use of previous flow that is closest in terms of geometric parameters to the new shape as an initial condition for the new function evaluation. This makes the solution towards the final value progressively faster and reduces the computer time for the convergence of the algorithm. The algorithm is used to optimize two different problems, a simple bump problem, and a two-dimensional transonic airfoil problem using an Euler solver solver equation. The results indicate that GA/flow algorithm is robust and can optimize a wide range of problems with a minimum implementation effort.