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.. "examples/post_process/plot_robustness.py"
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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_post_process_plot_robustness.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_post_process_plot_robustness.py:


Robustness
==========

In this example, we illustrate the use of the :class:`.Robustness` plot
on the Sobieski's SSBJ problem.

.. GENERATED FROM PYTHON SOURCE LINES 28-36

.. code-block:: default

    from __future__ import annotations

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.problems.sobieski.core.problem import SobieskiProblem
    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 37-41

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

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: default


    configure_logger()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-60

Description
-----------

In the :class:`~gemseo.post.robustness.Robustness` post-processing,
the robustness of the optimum is represented by a box plot. Using the
quadratic approximations of all the output functions, we
propagate analytically a normal distribution with 1% standard deviation
on all the design variables, assuming no cross-correlations of inputs,
to obtain the mean and standard deviation of the resulting normal
distribution. A series of samples are randomly generated from the resulting
distribution, whose quartiles are plotted, relatively to the values of
the function at the optimum. For each function (in abscissa), the plot
shows the extreme values encountered in the samples (top and bottom
bars). Then, 95% of the values are within the blue boxes. The average is
given by the red bar.

.. GENERATED FROM PYTHON SOURCE LINES 62-66

Create disciplines
------------------
At this point, we instantiate the disciplines of Sobieski's SSBJ problem:
Propulsion, Aerodynamics, Structure and Mission

.. GENERATED FROM PYTHON SOURCE LINES 66-75

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 76-79

Create design space
-------------------
We also read the design space from the :class:`.SobieskiProblem`.

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 82-89

Create and execute scenario
---------------------------
The next step is to build an 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.

.. GENERATED FROM PYTHON SOURCE LINES 89-101

.. code-block:: default

    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})





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 14:43:48:  
        INFO - 14:43:48: *** Start MDOScenario execution ***
        INFO - 14:43:48: MDOScenario
        INFO - 14:43:48:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 14:43:48:    MDO formulation: MDF
        INFO - 14:43:48: Optimization problem:
        INFO - 14:43:48:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 14:43:48:    with respect to x_1, x_2, x_3, x_shared
        INFO - 14:43:48:    subject to constraints:
        INFO - 14:43:48:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:48:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:48:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:48:    over the design space:
        INFO - 14:43:48:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:48:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 14:43:48:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:48:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 14:43:48:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 14:43:48:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 14:43:48:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 14:43:48:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 14:43:48:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 14:43:48:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 14:43:48:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:48:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:48:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 14:43:48:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:48: Solving optimization problem with algorithm SLSQP:
        INFO - 14:43:48: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:43:48: ...  20%|██        | 2/10 [00:00<00:00, 40.47 it/sec, obj=-2.12e+3]
     WARNING - 14:43:48: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
        INFO - 14:43:48: ...  30%|███       | 3/10 [00:00<00:00, 23.45 it/sec, obj=-3.75e+3]
        INFO - 14:43:48: ...  40%|████      | 4/10 [00:00<00:00, 17.17 it/sec, obj=-4.01e+3]
     WARNING - 14:43:49: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
        INFO - 14:43:49: ...  50%|█████     | 5/10 [00:00<00:00, 13.04 it/sec, obj=-4.49e+3]
        INFO - 14:43:49: ...  60%|██████    | 6/10 [00:00<00:00, 11.04 it/sec, obj=-3.4e+3]
        INFO - 14:43:49: ...  80%|████████  | 8/10 [00:01<00:00,  9.39 it/sec, obj=-4.76e+3]
        INFO - 14:43:49: ... 100%|██████████| 10/10 [00:01<00:00,  8.18 it/sec, obj=-4.56e+3]
        INFO - 14:43:49: ... 100%|██████████| 10/10 [00:01<00:00,  8.16 it/sec, obj=-4.56e+3]
        INFO - 14:43:49: Optimization result:
        INFO - 14:43:49:    Optimizer info:
        INFO - 14:43:49:       Status: None
        INFO - 14:43:49:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 14:43:49:       Number of calls to the objective function by the optimizer: 12
        INFO - 14:43:49:    Solution:
        INFO - 14:43:49:       The solution is feasible.
        INFO - 14:43:49:       Objective: -3749.8868975554387
        INFO - 14:43:49:       Standardized constraints:
        INFO - 14:43:49:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
        INFO - 14:43:49:  -0.10219342]
        INFO - 14:43:49:          g_2 = -0.0004062839430756249
        INFO - 14:43:49:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
        INFO - 14:43:49:       Design space: 
        INFO - 14:43:49:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:49:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 14:43:49:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:49:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
        INFO - 14:43:49:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
        INFO - 14:43:49:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 14:43:49:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
        INFO - 14:43:49:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
        INFO - 14:43:49:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
        INFO - 14:43:49:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 14:43:49:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
        INFO - 14:43:49:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
        INFO - 14:43:49:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
        INFO - 14:43:49:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:49: *** End MDOScenario execution (time: 0:00:01.241684) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 102-107

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.Robustness`
which plots any of the constraint or
objective functions w.r.t. the optimization iterations or sampling snapshots.

.. GENERATED FROM PYTHON SOURCE LINES 109-117

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the API function
   :meth:`~gemseo.api.get_post_processing_options_schema` to print a table with
   the options for any post-processing algorithm.
   Or refer to our dedicated page:
   :ref:`gen_post_algos`.

.. GENERATED FROM PYTHON SOURCE LINES 117-121

.. code-block:: default


    scenario.post_process("Robustness", save=False, show=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



.. image-sg:: /examples/post_process/images/sphx_glr_plot_robustness_001.png
   :alt: Boxplot of the optimization functions with normalized stddev 0.01
   :srcset: /examples/post_process/images/sphx_glr_plot_robustness_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  1.468 seconds)


.. _sphx_glr_download_examples_post_process_plot_robustness.py:

.. only:: html

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    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_robustness.py <plot_robustness.py>`

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      :download:`Download Jupyter notebook: plot_robustness.ipynb <plot_robustness.ipynb>`


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