.. 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 24-35

.. 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 36-43

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 43-50

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 51-54

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:`.MDODiscipline.default_inputs`

.. GENERATED FROM PYTHON SOURCE LINES 54-58

.. code-block:: Python

    for discipline in disciplines:
        print(discipline)
        print(f"Default inputs: {discipline.default_inputs}")





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

 .. code-block:: none

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




.. 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 66-77

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:

.. GENERATED FROM PYTHON SOURCE LINES 77-85

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 86-95

- ``'warm_start``: warm starts MDA,
- ``'warm_start``: optimize the adjoints 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 96-99

.. code-block:: Python

    design_space = SobieskiDesignSpace()
    design_space






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>Sobieski design space:<br/><table>
        <tr>
            <th style='text-align: left;'>Name</th>
            <th style='text-align: left;'>Lower bound</th>
            <th style='text-align: left;'>Value</th>
            <th style='text-align: left;'>Upper bound</th>
            <th style='text-align: left;'>Type</th>
        </tr>
        <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>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 100-109

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "MDF",
        "y_4",
        design_space,
        maximize_objective=True,
        **formulation_options,
    )








.. GENERATED FROM PYTHON SOURCE LINES 110-112

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

.. GENERATED FROM PYTHON SOURCE LINES 112-115

.. 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 116-123

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 123-125

.. code-block:: Python

    scenario.xdsmize(save_html=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"
          },
          {
            "id": "Dis1",
            "name": "MDAJacobi",
            "type": "mda"
          },
          {
            "id": "Dis2",
            "name": "SobieskiPropulsion",
            "type": "analysis"
          },
          {
            "id": "Dis3",
            "name": "SobieskiAerodynamics",
            "type": "analysis"
          },
          {
            "id": "Dis4",
            "name": "SobieskiStructure",
            "type": "analysis"
          },
          {
            "id": "Dis5",
            "name": "SobieskiMission",
            "type": "analysis"
          }
        ],
        "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": "Optimization problem:\n   minimize -y_4(x_shared, x_1, x_2, x_3)\n   with respect to x_1, x_2, x_3, x_shared\n   subject to constraints:\n      g_1(x_shared, x_1, x_2, x_3) <= 0.0\n      g_2(x_shared, x_1, x_2, x_3) <= 0.0\n      g_3(x_shared, x_1, x_2, x_3) <= 0.0"
      }
    };
              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 126-137

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 ftol_rel option 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 137-144

.. code-block:: Python

    algo_options = {
        "ftol_rel": 1e-10,
        "ineq_tolerance": 2e-3,
        "normalize_design_space": True,
    }
    scn_inputs = {"max_iter": 15, "algo": "SLSQP", "algo_options": algo_options}








.. GENERATED FROM PYTHON SOURCE LINES 145-159

.. seealso::

   We can also generate a backup file for the optimization,
   as well as plots on the fly of the optimization history if option
   ``generate_opt_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",
                                             each_new_iter=True,
                                             each_store=False, erase=True,
                                             pre_load=False,
                                             generate_opt_plot=True)

.. GENERATED FROM PYTHON SOURCE LINES 161-163

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

.. GENERATED FROM PYTHON SOURCE LINES 163-165

.. code-block:: Python

    scenario.execute(scn_inputs)





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

 .. code-block:: none

        INFO - 08:57:19:  
        INFO - 08:57:19: *** Start MDOScenario execution ***
        INFO - 08:57:19: MDOScenario
        INFO - 08:57:19:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 08:57:19:    MDO formulation: MDF
        INFO - 08:57:19: Optimization problem:
        INFO - 08:57:19:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 08:57:19:    with respect to x_1, x_2, x_3, x_shared
        INFO - 08:57:19:    subject to constraints:
        INFO - 08:57:19:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 08:57:19:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 08:57:19:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 08:57:19:    over the design space:
        INFO - 08:57:19:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:19:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 08:57:19:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:19:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 08:57:19:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 08:57:19:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 08:57:19:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 08:57:19:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 08:57:19:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 08:57:19:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 08:57:19:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 08:57:19:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 08:57:19:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 08:57:19:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:57:19: Solving optimization problem with algorithm SLSQP:
        INFO - 08:57:19:      7%|▋         | 1/15 [00:00<00:01,  9.29 it/sec, obj=-536]
        INFO - 08:57:19:     13%|█▎        | 2/15 [00:00<00:01,  6.85 it/sec, obj=-2.12e+3]
        INFO - 08:57:19:     20%|██        | 3/15 [00:00<00:02,  5.58 it/sec, obj=-3.72e+3]
        INFO - 08:57:19:     27%|██▋       | 4/15 [00:00<00:01,  5.62 it/sec, obj=-3.97e+3]
        INFO - 08:57:20: Optimization result:
        INFO - 08:57:20:    Optimizer info:
        INFO - 08:57:20:       Status: 8
        INFO - 08:57:20:       Message: Positive directional derivative for linesearch
        INFO - 08:57:20:       Number of calls to the objective function by the optimizer: 5
        INFO - 08:57:20:    Solution:
        INFO - 08:57:20:       The solution is feasible.
        INFO - 08:57:20:       Objective: -3716.555963095829
        INFO - 08:57:20:       Standardized constraints:
        INFO - 08:57:20:          g_1 = [-0.01608807 -0.03194613 -0.04316738 -0.05095364 -0.05658344 -0.1380806
        INFO - 08:57:20:  -0.1019194 ]
        INFO - 08:57:20:          g_2 = -0.0005956359157315294
        INFO - 08:57:20:          g_3 = [-0.67076432 -0.32923568 -0.10429595 -0.183255  ]
        INFO - 08:57:20:       Design space:
        INFO - 08:57:20:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:57:20:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 08:57:20:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:57:20:          | x_shared[0] |     0.01    | 0.05985109102106711 |     0.09    | float |
        INFO - 08:57:20:          | x_shared[1] |    30000    |   59785.5639131558  |    60000    | float |
        INFO - 08:57:20:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 08:57:20:          | x_shared[3] |     2.5     |  2.540129655171779  |     8.5     | float |
        INFO - 08:57:20:          | x_shared[4] |      40     |  69.80684214977607  |      70     | float |
        INFO - 08:57:20:          | x_shared[5] |     500     |  1493.746505655324  |     1500    | float |
        INFO - 08:57:20:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 08:57:20:          | x_1[1]      |     0.75    |  0.7530970468499044 |     1.25    | float |
        INFO - 08:57:20:          | x_2         |     0.75    |  0.7530625218813826 |     1.25    | float |
        INFO - 08:57:20:          | x_3         |     0.1     |  0.1411034879427379 |      1      | float |
        INFO - 08:57:20:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:57:20: *** End MDOScenario execution (time: 0:00:00.823589) ***

    {'max_iter': 15, 'algo_options': {'ftol_rel': 1e-10, 'ineq_tolerance': 0.002, 'normalize_design_space': True}, 'algo': 'SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 166-170

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

.. GENERATED FROM PYTHON SOURCE LINES 170-172

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 08:57:20: Exporting the optimization problem to the file mdf_history.h5 at node 




.. GENERATED FROM PYTHON SOURCE LINES 173-174

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

.. GENERATED FROM PYTHON SOURCE LINES 174-176

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 177-179

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

.. GENERATED FROM PYTHON SOURCE LINES 179-181

.. code-block:: Python

    scenario.print_execution_metrics()





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

 .. code-block:: none

        INFO - 08:57:20: Scenario Execution Statistics
        INFO - 08:57:20:    Discipline: SobieskiPropulsion
        INFO - 08:57:20:       Executions number: 67
        INFO - 08:57:20:       Execution time: 0.024764827994658845 s
        INFO - 08:57:20:       Linearizations number: 4
        INFO - 08:57:20:    Discipline: SobieskiAerodynamics
        INFO - 08:57:20:       Executions number: 76
        INFO - 08:57:20:       Execution time: 0.035504796000168426 s
        INFO - 08:57:20:       Linearizations number: 4
        INFO - 08:57:20:    Discipline: SobieskiMission
        INFO - 08:57:20:       Executions number: 4
        INFO - 08:57:20:       Execution time: 0.0002837100037140772 s
        INFO - 08:57:20:       Linearizations number: 4
        INFO - 08:57:20:    Discipline: SobieskiStructure
        INFO - 08:57:20:       Executions number: 75
        INFO - 08:57:20:       Execution time: 0.18365335499038338 s
        INFO - 08:57:20:       Linearizations number: 4
        INFO - 08:57:20:    Total number of executions calls: 222
        INFO - 08:57:20:    Total number of linearizations: 16




.. GENERATED FROM PYTHON SOURCE LINES 182-187

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

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

.. GENERATED FROM PYTHON SOURCE LINES 187-189

.. code-block:: Python

    scenario.post_process("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: 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: Hessian diagonal approximation
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f1dad5a1a90>



.. GENERATED FROM PYTHON SOURCE LINES 190-192

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

.. GENERATED FROM PYTHON SOURCE LINES 192-196

.. code-block:: Python

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




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_007.png
   :alt: History plot
   :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.basic_history.BasicHistory object at 0x7f1daad9ffd0>



.. GENERATED FROM PYTHON SOURCE LINES 197-199

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

.. GENERATED FROM PYTHON SOURCE LINES 199-201

.. code-block:: Python

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




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_008.png
   :alt: Evolution of the objective and maximum constraint
   :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.obj_constr_hist.ObjConstrHist object at 0x7f1daacfda60>



.. GENERATED FROM PYTHON SOURCE LINES 202-204

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

.. GENERATED FROM PYTHON SOURCE LINES 204-211

.. code-block:: Python

    scenario.post_process(
        "ConstraintsHistory",
        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: 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_009.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.constraints_history.ConstraintsHistory object at 0x7f1daa8a2d60>



.. GENERATED FROM PYTHON SOURCE LINES 212-214

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

.. GENERATED FROM PYTHON SOURCE LINES 214-221

.. code-block:: Python

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




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png
   :alt: Constraints at iteration 3 (optimum)
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.radar_chart.RadarChart object at 0x7f1daa7b9d30>



.. GENERATED FROM PYTHON SOURCE LINES 222-224

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

.. GENERATED FROM PYTHON SOURCE LINES 224-226

.. code-block:: Python

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




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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png
         :alt: Hessian matrix SR1 approximation of -y_4
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png
         :alt: plot sobieski mdf example
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.quad_approx.QuadApprox object at 0x7f1daa2b9550>



.. GENERATED FROM PYTHON SOURCE LINES 227-229

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

.. GENERATED FROM PYTHON SOURCE LINES 229-231

.. code-block:: Python

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




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_013.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_013.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 08:57:23: Building Self Organizing Map from optimization history:
        INFO - 08:57:23:     Number of neurons in x direction = 4
        INFO - 08:57:23:     Number of neurons in y direction = 4

    <gemseo.post.som.SOM object at 0x7f1daa26fc40>



.. GENERATED FROM PYTHON SOURCE LINES 232-234

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

.. GENERATED FROM PYTHON SOURCE LINES 234-242

.. code-block:: Python

    scenario.post_process(
        "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_014.png
   :alt: plot sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_014.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7f1da9654a90>



.. GENERATED FROM PYTHON SOURCE LINES 243-245

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

.. GENERATED FROM PYTHON SOURCE LINES 245-247

.. code-block:: Python

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




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


    *

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

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png
         :alt: Objective function and constraints history colored by '-y_4' value.
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.para_coord.ParallelCoordinates object at 0x7f1da9654eb0>



.. GENERATED FROM PYTHON SOURCE LINES 248-250

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

.. GENERATED FROM PYTHON SOURCE LINES 250-252

.. code-block:: Python

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





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

 .. code-block:: none


    <gemseo.post.robustness.Robustness object at 0x7f1da8326e50>



.. GENERATED FROM PYTHON SOURCE LINES 253-255

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

.. GENERATED FROM PYTHON SOURCE LINES 255-256

.. code-block:: Python

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



.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_017.png
   :alt: Partial variation of the functions wrt design variables, 9 variables required to explain 99% of -y_4 variations, 5 variables required to explain 99% of g_1[0] variations, 5 variables required to explain 99% of g_1[1] variations, 5 variables required to explain 99% of g_1[2] variations, 5 variables required to explain 99% of g_1[3] variations, 5 variables required to explain 99% of g_1[4] variations, 4 variables required to explain 99% of g_1[5] variations, 4 variables required to explain 99% of g_1[6] variations, 1 variables required to explain 99% of g_2 variations, 7 variables required to explain 99% of g_3[0] variations, 7 variables required to explain 99% of g_3[1] variations, 3 variables required to explain 99% of g_3[2] variations, 3 variables required to explain 99% of g_3[3] variations
   :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 - 08:57:28: Output name; most influential variables to explain 0.99% of the output variation 
        INFO - 08:57:28:    -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 - 08:57:28:    g_1[0]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_1[1]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_1[2]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_1[3]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_1[4]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_1[5]; x_1[0], x_1[1], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_1[6]; x_1[0], x_1[1], x_shared[3], x_shared[5]
        INFO - 08:57:28:    g_2; x_shared[0]
        INFO - 08:57:28:    g_3[0]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
        INFO - 08:57:28:    g_3[1]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
        INFO - 08:57:28:    g_3[2]; x_3, x_shared[1], x_shared[2]
        INFO - 08:57:28:    g_3[3]; x_3, x_shared[1], x_shared[2]

    <gemseo.post.variable_influence.VariableInfluence object at 0x7f1da821df10>




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

   **Total running time of the script:** (0 minutes 10.416 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>`


.. only:: html

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

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