.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/formulations/plot_sobieski_mdf_example.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_formulations_plot_sobieski_mdf_example.py>`
        to download the full example code.

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

.. _sphx_glr_examples_formulations_plot_sobieski_mdf_example.py:

MDF-based MDO on the Sobieski SSBJ test case.
=============================================

.. GENERATED FROM PYTHON SOURCE LINES 23-34

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import generate_n2_plot
    from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 35-42

Instantiate the disciplines
---------------------------
First, we instantiate the four disciplines of the use case:
:class:`.SobieskiPropulsion`,
:class:`.SobieskiAerodynamics`,
:class:`.SobieskiMission`
and :class:`.SobieskiStructure`.

.. GENERATED FROM PYTHON SOURCE LINES 42-49

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 50-53

We can quickly access the most relevant information of any discipline (name, inputs,
and outputs) with Python's ``print()`` function. Moreover, we can get the default
input values of a discipline with the attribute :attr:`.Discipline.default_input_data`

.. GENERATED FROM PYTHON SOURCE LINES 53-58

.. code-block:: Python

    for discipline in disciplines:
        print(discipline)  # noqa: T201
        print(f"Default inputs: {discipline.default_input_data}")  # noqa: T201






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

 .. code-block:: none

    SobieskiPropulsion
    Default inputs: {'y_23': array([12562.01206488]), 'x_3': array([0.5]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'c_3': array([4360.])}
    SobieskiAerodynamics
    Default inputs: {'x_2': array([1.]), 'y_32': array([0.50279625]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_12': array([5.06069742e+04, 9.50000000e-01]), 'c_4': array([0.01375])}
    SobieskiMission
    Default inputs: {'y_14': array([50606.9741711 ,  7306.20262124]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_24': array([4.15006276]), 'y_34': array([1.10754577])}
    SobieskiStructure
    Default inputs: {'y_21': array([50606.9741711]), 'y_31': array([6354.32430691]), 'x_1': array([0.25, 1.  ]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'c_0': array([2000.]), 'c_1': array([25000.]), 'c_2': array([6.])}




.. GENERATED FROM PYTHON SOURCE LINES 59-63

You may also be interested in plotting the couplings of your disciplines.
A quick way of getting this information is the high-level function
:func:`.generate_n2_plot`. A much more detailed explanation of coupling
visualization is available :ref:`here <coupling_visualization>`.

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: Python

    generate_n2_plot(disciplines, save=False, show=True)




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_001.png
   :alt: plot sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 66-79

Build, execute and post-process the scenario
--------------------------------------------
Then, we build the scenario which links the disciplines
with the formulation and the optimization algorithm. Here, we use the
:class:`.MDF` formulation. We tell the scenario to minimize -y_4 instead of
minimizing y_4 (range), which is the default option.

Instantiate the scenario
^^^^^^^^^^^^^^^^^^^^^^^^
During the instantiation of the scenario, we provide some options for the
MDF formulations. The MDF formulation includes an MDA, and thus one of the settings of
the formulation is ``main_mda_settings``, which configures the solver for the strong
couplings.

.. GENERATED FROM PYTHON SOURCE LINES 79-87

.. code-block:: Python

    main_mda_settings = {
        "tolerance": 1e-14,
        "max_mda_iter": 50,
        "warm_start": True,
        "use_lu_fact": False,
        "linear_solver_tolerance": 1e-14,
    }








.. GENERATED FROM PYTHON SOURCE LINES 88-97

- ``'warm_start``: warm starts MDA,
- ``'use_lu_fact``: optimize the adjoint resolution by storing
  the Jacobian matrix LU factorization for the multiple RHS
  (objective + constraints). This saves CPU time if you can pay for
  the memory and have the full Jacobians available, not just matrix vector
  products.
- ``'linear_solver_tolerance'``: set the linear solver tolerance,
  idem we need full convergence


.. GENERATED FROM PYTHON SOURCE LINES 98-101

.. code-block:: Python

    design_space = SobieskiDesignSpace()
    design_space






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='margin: 1em;'>Sobieski design space:<br/><table>
        <thead>
            <tr>
                <th>Name</th>
                <th>Lower bound</th>
                <th>Value</th>
                <th>Upper bound</th>
                <th>Type</th>
            </tr>
        </thead>
        <tbody>
            <tr>
                <td>x_shared[0]</td>
                <td>0.01</td>
                <td>0.05</td>
                <td>0.09</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_shared[1]</td>
                <td>30000</td>
                <td>45000</td>
                <td>60000</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_shared[2]</td>
                <td>1.4</td>
                <td>1.6</td>
                <td>1.8</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_shared[3]</td>
                <td>2.5</td>
                <td>5.5</td>
                <td>8.5</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_shared[4]</td>
                <td>40</td>
                <td>55</td>
                <td>70</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_shared[5]</td>
                <td>500</td>
                <td>1000</td>
                <td>1500</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_1[0]</td>
                <td>0.1</td>
                <td>0.25</td>
                <td>0.4</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_1[1]</td>
                <td>0.75</td>
                <td>1</td>
                <td>1.25</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_2</td>
                <td>0.75</td>
                <td>1</td>
                <td>1.25</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_3</td>
                <td>0.1</td>
                <td>0.5</td>
                <td>1</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_14[0]</td>
                <td>24850</td>
                <td>50606.9741711</td>
                <td>77100</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_14[1]</td>
                <td>-7700</td>
                <td>7306.20262124</td>
                <td>45000</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_32</td>
                <td>0.235</td>
                <td>0.5027962499999999</td>
                <td>0.795</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_31</td>
                <td>2960</td>
                <td>6354.32430691</td>
                <td>10185</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_24</td>
                <td>0.44</td>
                <td>4.15006276</td>
                <td>11.13</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_34</td>
                <td>0.44</td>
                <td>1.10754577</td>
                <td>1.98</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_23</td>
                <td>3365</td>
                <td>12194.2671934</td>
                <td>26400</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_21</td>
                <td>24850</td>
                <td>50606.9741711</td>
                <td>77250</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_12[0]</td>
                <td>24850</td>
                <td>50606.9742</td>
                <td>77250</td>
                <td>float</td>
            </tr>
            <tr>
                <td>y_12[1]</td>
                <td>0.45</td>
                <td>0.95</td>
                <td>1.5</td>
                <td>float</td>
            </tr>
        </tbody>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 102-111

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "y_4",
        design_space,
        maximize_objective=True,
        formulation_name="MDF",
        main_mda_settings=main_mda_settings,
    )





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

 .. code-block:: none

     WARNING - 11:48:46: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
     WARNING - 11:48:46: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.




.. GENERATED FROM PYTHON SOURCE LINES 112-114

Set the design constraints
^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 114-117

.. code-block:: Python

    for c_name in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(c_name, constraint_type="ineq")








.. GENERATED FROM PYTHON SOURCE LINES 118-125

XDSMIZE the scenario
^^^^^^^^^^^^^^^^^^^^
Generate the XDSM file on the fly:

- ``log_workflow_status=True`` will log the status of the workflow  in the console,
- ``save_html`` (default ``True``) will generate a self-contained HTML file,
  that can be automatically opened using ``show_html=True``.

.. GENERATED FROM PYTHON SOURCE LINES 125-127

.. code-block:: Python

    scenario.xdsmize(save_html=False, pdf_build=False)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

        <script type="text/javascript">
            document.addEventListener('DOMContentLoaded', () => {
              const mdo = {
      "root": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "MDAJacobi",
            "type": "mda",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "SobieskiPropulsion",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis3",
            "name": "SobieskiAerodynamics",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis4",
            "name": "SobieskiStructure",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis5",
            "name": "SobieskiMission",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_shared^(0), x_1^(0), x_2^(0), x_3^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "-y_4^*, g_1^*, g_2^*, g_3^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_1, x_2, x_3, x_shared"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_1, g_2, g_3"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x_3, x_shared"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g_3"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "x_2, x_shared"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "g_2"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_1, x_shared"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1"
          },
          {
            "from": "Opt",
            "to": "Dis5",
            "name": "x_shared"
          },
          {
            "from": "Dis5",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "y_32^*, y_31^*, y_3^*, y_34^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g_3"
          },
          {
            "from": "Dis3",
            "to": "_U_",
            "name": "y_21^*, y_23^*, y_24^*, y_2^*"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "g_2"
          },
          {
            "from": "Dis4",
            "to": "_U_",
            "name": "y_1^*, y_11^*, y_14^*, y_12^*"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1"
          },
          {
            "from": "Dis5",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Dis1",
            "to": "Dis5",
            "name": "y_14, y_24, y_34"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "y_23"
          },
          {
            "from": "Dis2",
            "to": "Dis1",
            "name": "y_31, y_32"
          },
          {
            "from": "Dis1",
            "to": "Dis3",
            "name": "y_12, y_32"
          },
          {
            "from": "Dis3",
            "to": "Dis1",
            "name": "y_21, y_23"
          },
          {
            "from": "Dis1",
            "to": "Dis4",
            "name": "y_21, y_31"
          },
          {
            "from": "Dis4",
            "to": "Dis1",
            "name": "y_12"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              [
                {
                  "parallel": [
                    "Dis2",
                    "Dis3",
                    "Dis4"
                  ]
                }
              ],
              "Dis5"
            ]
          ]
        ],
        "optpb": ""
      }
    };
              const config = {
                labelizer: {
                    ellipsis: 5,
                    subSupScript: false,
                    showLinkNbOnly: false,
                },
                layout: {
                    origin: { x: 50, y: 20 },
                    cellsize: { w: 150, h: 50 },
                    padding: 10,
                },
                withDefaultDriver: true,
                withTitleTooltip: true,
              };
              xdsmjs.XDSMjs(config).createXdsm(mdo);
            });
        </script>
        <div class='xdsm-toolbar'></div><div class='xdsm2'></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 128-139

Define the algorithm inputs
^^^^^^^^^^^^^^^^^^^^^^^^^^^
We set the maximum number of iterations, the optimizer
and the optimizer options. Algorithm specific options are passed there.
Use the high-level function :func:`.get_algorithm_options_schema`
for more information or read the documentation.

Here the ``ftol_rel`` setting is a stop criteria based on the relative difference
in the objective between two iterates ineq_tolerance the tolerance
determination of the optimum; this is specific to the |g| wrapping and not
in the solver.

.. GENERATED FROM PYTHON SOURCE LINES 139-148

.. code-block:: Python

    from gemseo.settings.opt import SLSQP_Settings  # noqa: E402

    slsqp_settings = SLSQP_Settings(
        max_iter=10,
        ftol_rel=1e-10,
        ineq_tolerance=2e-3,
        normalize_design_space=True,
    )








.. GENERATED FROM PYTHON SOURCE LINES 149-166

.. seealso::

   We can also generate a backup file for the optimization,
   as well as plots on the fly of the optimization history if option
   ``plot`` is ``True``.
   This slows down a lot the process, here since SSBJ is very light

   .. code::

    scenario.set_optimization_history_backup(
        file_path="mdf_backup.h5",
        at_each_iteration=True,
        at_each_function_call=False,
        erase=True,
        load=False,
        plot=True
    )

.. GENERATED FROM PYTHON SOURCE LINES 168-170

Execute the scenario
^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 170-172

.. code-block:: Python

    scenario.execute(slsqp_settings)





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

 .. code-block:: none

        INFO - 11:48:46: *** Start MDOScenario execution ***
        INFO - 11:48:46: MDOScenario
        INFO - 11:48:46:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 11:48:46:    MDO formulation: MDF
        INFO - 11:48:46: Optimization problem:
        INFO - 11:48:46:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 11:48:46:    with respect to x_1, x_2, x_3, x_shared
        INFO - 11:48:46:    subject to constraints:
        INFO - 11:48:46:       g_1(x_shared, x_1, x_2, x_3) <= 0
        INFO - 11:48:46:       g_2(x_shared, x_1, x_2, x_3) <= 0
        INFO - 11:48:46:       g_3(x_shared, x_1, x_2, x_3) <= 0
        INFO - 11:48:46:    over the design space:
        INFO - 11:48:46:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:48:46:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 11:48:46:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:48:46:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 11:48:46:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 11:48:46:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 11:48:46:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 11:48:46:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 11:48:46:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 11:48:46:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 11:48:46:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 11:48:46:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 11:48:46:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 11:48:46:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:48:46: Solving optimization problem with algorithm SLSQP:
        INFO - 11:48:46:     10%|█         | 1/10 [00:00<00:00, 18.19 it/sec, obj=-536]
        INFO - 11:48:46:     20%|██        | 2/10 [00:00<00:00, 14.51 it/sec, obj=-2.12e+3]
        INFO - 11:48:47:     30%|███       | 3/10 [00:00<00:00, 11.22 it/sec, obj=-3.72e+3]
        INFO - 11:48:47:     40%|████      | 4/10 [00:00<00:00, 11.82 it/sec, obj=-3.96e+3]
     WARNING - 11:48:47: MDAJacobi has reached its maximum number of unsuccessful iterations, but the normalized residual norm 5.126876767779417e-11 is still above the tolerance 1e-14.
        INFO - 11:48:47:     50%|█████     | 5/10 [00:00<00:00, 12.16 it/sec, obj=-3.96e+3]
        INFO - 11:48:47: Optimization result:
        INFO - 11:48:47:    Optimizer info:
        INFO - 11:48:47:       Status: 8
        INFO - 11:48:47:       Message: Positive directional derivative for linesearch
        INFO - 11:48:47:       Number of calls to the objective function by the optimizer: 6
        INFO - 11:48:47:    Solution:
        INFO - 11:48:47:       The solution is feasible.
        INFO - 11:48:47:       Objective: -3963.8622159757956
        INFO - 11:48:47:       Standardized constraints:
        INFO - 11:48:47:          g_1 = [-0.01805379 -0.0333412  -0.04424541 -0.05183129 -0.05732327 -0.13720865
        INFO - 11:48:47:  -0.10279135]
        INFO - 11:48:47:          g_2 = 9.423096252181296e-07
        INFO - 11:48:47:          g_3 = [-0.76777633 -0.23222367  0.00080718 -0.183255  ]
        INFO - 11:48:47:       Design space:
        INFO - 11:48:47:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 11:48:47:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 11:48:47:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 11:48:47:          | x_shared[0] |     0.01    | 0.06000023557740629 |     0.09    | float |
        INFO - 11:48:47:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 11:48:47:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 11:48:47:          | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 11:48:47:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 11:48:47:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 11:48:47:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 11:48:47:          | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
        INFO - 11:48:47:          | x_2         |     0.75    |         0.75        |     1.25    | float |
        INFO - 11:48:47:          | x_3         |     0.1     |  0.1563708636523273 |      1      | float |
        INFO - 11:48:47:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 11:48:47: *** End MDOScenario execution (time: 0:00:00.441449) ***




.. GENERATED FROM PYTHON SOURCE LINES 173-177

Save the optimization history
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
We can save the whole optimization problem and its history for further
post-processing:

.. GENERATED FROM PYTHON SOURCE LINES 177-179

.. code-block:: Python

    scenario.save_optimization_history("mdf_history.h5", file_format="hdf5")





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

 .. code-block:: none

        INFO - 11:48:47: Exporting the optimization problem to the file mdf_history.h5




.. GENERATED FROM PYTHON SOURCE LINES 180-181

We can also save only calls to functions and design variables history:

.. GENERATED FROM PYTHON SOURCE LINES 181-183

.. code-block:: Python

    scenario.save_optimization_history("mdf_history.xml", file_format="ggobi")








.. GENERATED FROM PYTHON SOURCE LINES 184-186

Print optimization metrics
^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 186-188

.. code-block:: Python

    scenario.print_execution_metrics()





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

 .. code-block:: none

        INFO - 11:48:47: Scenario Execution Statistics
        INFO - 11:48:47:    Discipline: SobieskiPropulsion
        INFO - 11:48:47:       Executions number: 75
        INFO - 11:48:47:       Execution time: 0.0194323429823271 s
        INFO - 11:48:47:       Linearizations number: 5
        INFO - 11:48:47:    Discipline: SobieskiAerodynamics
        INFO - 11:48:47:       Executions number: 92
        INFO - 11:48:47:       Execution time: 0.03060137801730889 s
        INFO - 11:48:47:       Linearizations number: 5
        INFO - 11:48:47:    Discipline: SobieskiMission
        INFO - 11:48:47:       Executions number: 5
        INFO - 11:48:47:       Execution time: 0.0002140649921784643 s
        INFO - 11:48:47:       Linearizations number: 5
        INFO - 11:48:47:    Discipline: SobieskiStructure
        INFO - 11:48:47:       Executions number: 87
        INFO - 11:48:47:       Execution time: 0.14735337398815318 s
        INFO - 11:48:47:       Linearizations number: 5
        INFO - 11:48:47:    Total number of executions calls: 259
        INFO - 11:48:47:    Total number of linearizations: 20




.. GENERATED FROM PYTHON SOURCE LINES 189-194

Post-process the results
------------------------

Plot the optimization history view
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 194-196

.. code-block:: Python

    scenario.post_process(post_name="OptHistoryView", save=False, show=True)




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_004.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_005.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_005.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7048fb82dd30>



.. GENERATED FROM PYTHON SOURCE LINES 197-200

Note that post-processor settings passed to :class:`.BaseScenario.post_process` can be
provided via a Pydantic model (see the example below). For more information,
see :ref:`post_processor_settings`.

.. GENERATED FROM PYTHON SOURCE LINES 202-204

Plot the basic history view
^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 204-210

.. code-block:: Python

    from gemseo.settings.post import BasicHistory_Settings  # noqa: E402

    scenario.post_process(
        BasicHistory_Settings(variable_names=["x_shared"], save=False, show=True)
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png
   :alt: History plot
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x704929dd10a0>



.. GENERATED FROM PYTHON SOURCE LINES 211-213

Plot the constraints and objective history
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 213-215

.. code-block:: Python

    scenario.post_process(post_name="ObjConstrHist", save=False, show=True)




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_007.png
   :alt: Evolution of the objective and maximum constraint
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_007.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.obj_constr_hist.ObjConstrHist object at 0x70492a4efaa0>



.. GENERATED FROM PYTHON SOURCE LINES 216-218

Plot the constraints history
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 218-225

.. code-block:: Python

    scenario.post_process(
        post_name="ConstraintsHistory",
        constraint_names=["g_1", "g_2", "g_3"],
        save=False,
        show=True,
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_008.png
   :alt: Evolution of the constraints w.r.t. iterations, g_1[0] (inequality), g_1[1] (inequality), g_1[2] (inequality), g_1[3] (inequality), g_1[4] (inequality), g_1[5] (inequality), g_1[6] (inequality), g_2 (inequality), g_3[0] (inequality), g_3[1] (inequality), g_3[2] (inequality), g_3[3] (inequality)
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_008.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.constraints_history.ConstraintsHistory object at 0x7048fbc51490>



.. GENERATED FROM PYTHON SOURCE LINES 226-228

Plot the constraints history using a radar chart
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 228-235

.. code-block:: Python

    scenario.post_process(
        post_name="RadarChart",
        constraint_names=["g_1", "g_2", "g_3"],
        save=False,
        show=True,
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_009.png
   :alt: Constraints at iteration 4 (optimum)
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_009.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.radar_chart.RadarChart object at 0x704929852030>



.. GENERATED FROM PYTHON SOURCE LINES 236-238

Plot the quadratic approximation of the objective
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 238-240

.. code-block:: Python

    scenario.post_process(post_name="QuadApprox", function="-y_4", save=False, show=True)




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png
         :alt: Hessian matrix SR1 approximation of -y_4
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png
         :alt: plot sobieski mdf example
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.quad_approx.QuadApprox object at 0x7048faf7d400>



.. GENERATED FROM PYTHON SOURCE LINES 241-243

Plot the functions using a SOM
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 243-245

.. code-block:: Python

    scenario.post_process(post_name="SOM", save=False, show=True)




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png
   :alt: Self Organizing Maps of the design space, -y_4, g_1[0], g_1[1], g_1[2], g_1[3], g_1[4], g_1[5], g_1[6], g_2, g_3[0], g_3[1], g_3[2], g_3[3]
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 11:48:50: Building Self Organizing Map from optimization history:
        INFO - 11:48:50:     Number of neurons in x direction = 4
        INFO - 11:48:50:     Number of neurons in y direction = 4

    <gemseo.post.som.SOM object at 0x704930c04770>



.. GENERATED FROM PYTHON SOURCE LINES 246-248

Plot the scatter matrix of variables of interest
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 248-256

.. code-block:: Python

    scenario.post_process(
        post_name="ScatterPlotMatrix",
        variable_names=["-y_4", "g_1"],
        save=False,
        show=True,
        fig_size=(14, 14),
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_013.png
   :alt: plot sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_013.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.scatter_plot_matrix.ScatterPlotMatrix object at 0x70492a3a9c40>



.. GENERATED FROM PYTHON SOURCE LINES 257-259

Plot the variables using the parallel coordinates
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 259-261

.. code-block:: Python

    scenario.post_process(post_name="ParallelCoordinates", save=False, show=True)




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_014.png
         :alt: Design variables history colored by '-y_4' value
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_014.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_015.png
         :alt: Objective function and constraints history colored by '-y_4' value.
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_015.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.parallel_coordinates.ParallelCoordinates object at 0x7048faf62030>



.. GENERATED FROM PYTHON SOURCE LINES 262-264

Plot the robustness of the solution
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 264-266

.. code-block:: Python

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




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png
   :alt: Boxplot of the optimization functions with normalized stddev 0.01
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.robustness.Robustness object at 0x7048fb568ef0>



.. GENERATED FROM PYTHON SOURCE LINES 267-269

Plot the influence of the design variables
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 269-272

.. code-block:: Python

    scenario.post_process(
        post_name="VariableInfluence", fig_size=(14, 14), save=False, show=True
    )



.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_017.png
   :alt: 9 variables explain 99% of -y_4, 5 variables explain 99% of g_1[0], 5 variables explain 99% of g_1[1], 5 variables explain 99% of g_1[2], 5 variables explain 99% of g_1[3], 5 variables explain 99% of g_1[4], 4 variables explain 99% of g_1[5], 4 variables explain 99% of g_1[6], 1 variables explain 99% of g_2, 7 variables explain 99% of g_3[0], 7 variables explain 99% of g_3[1], 3 variables explain 99% of g_3[2], 3 variables explain 99% of g_3[3]
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_017.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 11:48:54: Output name; most influential variables to explain 0.99% of the output variation 
        INFO - 11:48:54:    -y_4; x_1[1], x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[3], x_shared[4], x_shared[5]
        INFO - 11:48:54:    g_1[0]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_1[1]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_1[2]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_1[3]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_1[4]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_1[5]; x_1[0], x_1[1], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_1[6]; x_1[0], x_1[1], x_shared[3], x_shared[5]
        INFO - 11:48:54:    g_2; x_shared[0]
        INFO - 11:48:54:    g_3[0]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
        INFO - 11:48:54:    g_3[1]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
        INFO - 11:48:54:    g_3[2]; x_3, x_shared[1], x_shared[2]
        INFO - 11:48:54:    g_3[3]; x_3, x_shared[1], x_shared[2]

    <gemseo.post.variable_influence.VariableInfluence object at 0x7048faf4e6f0>




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

   **Total running time of the script:** (0 minutes 8.970 seconds)


.. _sphx_glr_download_examples_formulations_plot_sobieski_mdf_example.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_sobieski_mdf_example.zip <plot_sobieski_mdf_example.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_