  A framework for robust optimization under uncertainty based on the use of the
generalized inverse distribution function (GIDF), also called quantile
function, is here proposed. Compared to more classical approaches that rely on
the usage of statistical moments as deterministic attributes that define the
objectives of the optimization process, the inverse cumulative distribution
function allows for the use of all the possible information available in the
probabilistic domain. Furthermore, the use of a quantile based approach leads
naturally to a multi-objective methodology which allows an a-posteriori
selection of the candidate design based on risk/opportunity criteria defined by
the designer. Finally, the error on the estimation of the objectives due to the
resolution of the GIDF will be proven to be quantifiable
