Many real-life applications lead to the definition of robust optimization problems where the objective function is a black box. This may be due, for example, to the fact that the objective function is evaluated through computer simulations, and that some parameters are uncertain. When this is the case, existing algorithms for optimization are not able to provide good-quality solutions in general. We propose a heuristic algorithm for solving black box robust optimization problems based on the minimax formulation of the problem.We also apply this algorithm for the solution of a wing shape optimization where the objective function is a computationally expensive black box. Preliminary computational experiments are reported.