This report approaches the question of multi-objective optimization for optimum shape design in aerodynamics. The employed optimizer is a semi-stochas- tic method, more precisely a Genetic Algorithm (GA). GAs are very robust optimization algorithms particularly well suited for problems in which (1) the initialization is not intuitive, (2) the parameters to be optimized are not all of the same type (boolean, integer, real, functionnal), (3) the cost functional may present several local minima, (4) several criteria should be accounted for simultaneously (multiphysics, efficiency, cost, quality, ...). In a multi-objective optimization problem, there is no unique optimal solution but a whole set of potential solutions since in general no solution is optimal w.r.t. all criteria simultaneously ; instead, one identifies a set of non-dominated solutions, referred to as the Pareto optimal front. After making these concepts precise, genetic algorithms are implemented and first tested on academic examples ; then a numerical experimentation is conducted to solve a multi-objective shape optimization problem for the design of an airfoil in Eulerian flow.