Formulations for multidisciplinary design problems under uncertainty.

A MDOFormulation defines an OptimizationProblem from one or several DesignSpace, an objective and constraints. The objective can be either minimized (default) or maximized.

In the context of deterministic MDO, the OptimizationProblem is handled by a driver (see DriverLib), typically an optimizer (see OptimizationLibrary), or a design of experiments (DOE, see DOELibrary).

In the frame of robust MDO, the UMDOFormulation uses a MDOFormulation with a ParameterSpace defining the uncertain variables and executes the corresponding OptimizationProblem with a particular DOE. Then, it post-processed the associated Database to estimate the statistics applied to the objective and constraints.

The most common UMDOFormulation is Sampling, consisting in estimating the statistics with (quasi) Monte Carlo techniques.