# gemseo.problems.scalable.data_driven.study¶

## Benchmark MDO formulations based on scalable disciplines¶

The `study`

package implements several classes
to benchmark MDO formulations based on scalable disciplines.

The `ScalabilityStudy`

class implements
the concept of scalability study:

By instantiating a

`ScalabilityStudy`

, the user defines the MDO problem in terms of design parameters, objective function and constraints.For each discipline, the user adds a dataset stored in a

`AbstractFullCache`

and select a type of`ScalableModel`

to build the`ScalableDiscipline`

associated with this discipline.The user adds different optimization strategies, defined in terms of both optimization algorithms and MDO formulation.

The user adds different scaling strategies, in terms of sizes of design parameters, coupling variables and equality and inequality constraints. The user can also define a scaling strategies according to particular parameters rather than groups of parameters.

Lastly, the user executes the

`ScalabilityStudy`

and the results are written in several files and stored into directories in a hierarchical way, where names depend on both MDO formulation, scaling strategy and replications when it is necessary. Different kinds of files are stored: optimization graphs, dependency matrix plots and of course, scalability results by means of a dedicated class:`ScalabilityResult`

.

The `PostScalabilityStudy`

class implements the way as the set of
`ScalabilityResult`

-based result files
contained in the study directory are graphically post-processed. This class
provides several methods to easily change graphical properties, notably
the plot labels. It also makes it possible to define a cost function per
MDO formulation, converting the numbers of executions and linearizations
of the different disciplines required by an MDO process in an estimation
of the computational cost associated with what would be a scaled version
of the true problem.

Warning

Comparing MDO formulations in terms of estimated true computational time
rather than CPU time of the `ScalabilityStudy`

is highly
recommended.
Indeed, time is often an obviousness criterion to distinguish between
MDO formulations having the same performance in terms of distance to the
optimum: look at our calculation budget and choose the best formulation
that satisfies this budget, or even saves us time. Thus, it is important
to carefully define these cost functions.