Robust optimization is a twofold challenge. First, the solution of the
problem should be optimal; this requires mathematical programming to
develop methods for optimization solvers. Second, the solution should
be robust, i.e., safeguarded against uncertain perturbations.


Based on the potential clouds formalism one can overcome several
problems of traditional uncertainty modeling. Clouds have already
succeeded to deal with higher dimensional uncertainties, even in case
of lack of some statistical information. Moreover, they can be easily
combined with standard constrained optimization problems towards a
robust optimization problem formulation.


However, in several real-life applications, the number of objective
function evaluations available to propagate the uncertainties is too
limited. Inspired by the Cauchy deviates method, we propose a
simulation based method for optimization over a polyhedron that is
able to meet the limits.


To perform numerical tests of the methods a test environment is being
developed. Real world test cases are given by aerospace design
optimization problems.