Note

Click here to download the full example code

# Robustness¶

In this example, we illustrate the use of the `Robustness`

plot
on the Sobieski’s SSBJ problem.

```
from __future__ import absolute_import, division, print_function, unicode_literals
from future import standard_library
```

## Import¶

The first step is to import some functions from the API and a method to get the design space.

```
from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
configure_logger()
standard_library.install_aliases()
```

## Create disciplines¶

Then, we instantiate the disciplines of the Sobieski’s SSBJ problem: Propulsion, Aerodynamics, Structure and Mission

```
disciplines = create_discipline(
[
"SobieskiPropulsion",
"SobieskiAerodynamics",
"SobieskiStructure",
"SobieskiMission",
]
)
```

## Create design space¶

We also read the design space from the `SobieskiProblem`

.

```
design_space = SobieskiProblem().read_design_space()
```

## Create and execute scenario¶

The next step is to build a MDO scenario in order to maximize the range, encoded ‘y_4’, with respect to the design parameters, while satisfying the inequality constraints ‘g_1’, ‘g_2’ and ‘g_3’. We can use the MDF formulation, the SLSQP optimization algorithm and a maximum number of iterations equal to 100.

```
scenario = create_scenario(
disciplines,
formulation="MDF",
objective_name="y_4",
maximize_objective=True,
design_space=design_space,
)
scenario.set_differentiation_method("user")
for constraint in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
```

Out:

```
{'algo': 'SLSQP', 'max_iter': 10}
```

## Post-process scenario¶

Lastly, we post-process the scenario by means of the `Robustness`

plot which performs a quadratic approximation from an optimization history,
and plot the results as cuts of the approximation computes the quadratic
approximations of all the output functions, propagate analytically a normal
distribution centered on the optimal design variable with a standard
deviation which is a percentage of the mean passed in option (default: 1%)
and plot the corresponding output boxplot. plots any of the constraint or
objective functions w.r.t. optimization iterations or sampling snapshots.

```
scenario.post_process("Robustness", save=False, show=True)
```

Out:

```
<gemseo.post.robustness.Robustness object at 0x7fc298680850>
```

**Total running time of the script:** ( 0 minutes 0.610 seconds)