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


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



Create disciplines

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

disciplines = create_discipline(

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(
for constraint in ["g_1", "g_2", "g_3"]:
    scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})


{'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)
Box plot of the optimization functions with normalized stddev 0.01


< object at 0x7fc298680850>

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

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