.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/formulations/plot_doe_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_doe_sobieski_mdf_example.py>`
        to download the full example code.

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

.. _sphx_glr_examples_formulations_plot_doe_sobieski_mdf_example.py:


MDF-based DOE on the Sobieski SSBJ test case
============================================

.. GENERATED FROM PYTHON SOURCE LINES 24-38

.. code-block:: Python


    from __future__ import annotations

    from os import name as os_name

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import generate_n2_plot
    from gemseo.algos.doe.pydoe.settings.pydoe_lhs import PYDOE_LHS_Settings
    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 39-46

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 46-53

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 54-57

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 57-61

.. code-block:: Python

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





.. 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 62-66

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 66-68

.. code-block:: Python

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




.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_001.png
   :alt: plot doe sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 69-77

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:`.BiLevel` formulation. We tell the scenario to minimize -y_4
instead of minimizing y_4 (range), which is the default option.

We need to define the design space.

.. GENERATED FROM PYTHON SOURCE LINES 77-80

.. 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 81-83

Instantiate the scenario
^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 83-92

.. code-block:: Python

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





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

 .. code-block:: none

     WARNING - 08:37:27: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
     WARNING - 08:37:27: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.




.. GENERATED FROM PYTHON SOURCE LINES 93-95

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

.. GENERATED FROM PYTHON SOURCE LINES 95-98

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 99-106

Visualize the XDSM
^^^^^^^^^^^^^^^^^^
Generate the XDSM 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 106-108

.. 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": "DOE",
            "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 109-112

Execute the scenario
^^^^^^^^^^^^^^^^^^^^
Use provided analytic derivatives

.. GENERATED FROM PYTHON SOURCE LINES 112-114

.. code-block:: Python

    scenario.set_differentiation_method()








.. GENERATED FROM PYTHON SOURCE LINES 115-120

Multiprocessing
^^^^^^^^^^^^^^^
It is possible to run a DOE in parallel using multiprocessing, in order to do
this, we specify the number of processes to be used for the computation of
the samples.

.. GENERATED FROM PYTHON SOURCE LINES 122-129

.. warning::
   The multiprocessing option has some limitations on Windows.
   Due to problems with sphinx, we disable it in this example.
   The features :class:`.MemoryFullCache` and :class:`.HDF5Cache` are not
   available for multiprocessing on Windows.
   As an alternative, we recommend the method
   :meth:`.DOEScenario.set_optimization_history_backup`.

.. GENERATED FROM PYTHON SOURCE LINES 131-135

We define the algorithm settings. Here the criterion "center" of pyDOE
centers the points within the sampling intervals.
Note that it is also possible to pass the settings one by one, see
:ref:`algorithm_settings`.

.. GENERATED FROM PYTHON SOURCE LINES 135-148

.. code-block:: Python


    lhs_settings = PYDOE_LHS_Settings(
        n_samples=30,
        criterion="center",
        # Evaluate gradient of the MDA
        # with coupled adjoint
        eval_jac=True,
        # Run in parallel on 1 or 4 processors
        n_processes=1 if os_name == "nt" else 4,
    )

    scenario.execute(lhs_settings)





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

 .. code-block:: none

        INFO - 08:37:27:  
        INFO - 08:37:27: *** Start DOEScenario execution ***
        INFO - 08:37:27: DOEScenario
        INFO - 08:37:27:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 08:37:27:    MDO formulation: MDF
        INFO - 08:37:27: Optimization problem:
        INFO - 08:37:27:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 08:37:27:    with respect to x_1, x_2, x_3, x_shared
        INFO - 08:37:27:    subject to constraints:
        INFO - 08:37:27:       g_1(x_shared, x_1, x_2, x_3) <= 0
        INFO - 08:37:27:       g_2(x_shared, x_1, x_2, x_3) <= 0
        INFO - 08:37:27:       g_3(x_shared, x_1, x_2, x_3) <= 0
        INFO - 08:37:27:    over the design space:
        INFO - 08:37:27:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:37:27:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 08:37:27:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:37:27:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 08:37:27:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 08:37:27:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 08:37:27:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 08:37:27:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 08:37:27:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 08:37:27:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 08:37:27:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 08:37:27:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 08:37:27:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 08:37:27:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:37:27: Solving optimization problem with algorithm PYDOE_LHS:
        INFO - 08:37:27: Running DOE in parallel on n_processes = 4
        INFO - 08:37:27:      3%|▎         | 1/30 [00:00<00:11,  2.51 it/sec, obj=-222]
        INFO - 08:37:27:      7%|▋         | 2/30 [00:00<00:05,  4.98 it/sec, obj=-285]
        INFO - 08:37:27:     10%|█         | 3/30 [00:00<00:04,  6.55 it/sec, obj=-567]
        INFO - 08:37:27:     13%|█▎        | 4/30 [00:00<00:03,  7.23 it/sec, obj=-344]
        INFO - 08:37:27:     17%|█▋        | 5/30 [00:00<00:03,  6.94 it/sec, obj=-429]
        INFO - 08:37:27:     20%|██        | 6/30 [00:00<00:02,  8.22 it/sec, obj=-235]
        INFO - 08:37:27:     23%|██▎       | 7/30 [00:00<00:02,  8.50 it/sec, obj=-481]
        INFO - 08:37:27:     27%|██▋       | 8/30 [00:00<00:02,  9.68 it/sec, obj=-519]
        INFO - 08:37:28:     30%|███       | 9/30 [00:01<00:02,  8.70 it/sec, obj=-556]
        INFO - 08:37:28:     33%|███▎      | 10/30 [00:01<00:02,  9.24 it/sec, obj=-419]
        INFO - 08:37:28:     37%|███▋      | 11/30 [00:01<00:01,  9.71 it/sec, obj=-306]
        INFO - 08:37:28:     40%|████      | 12/30 [00:01<00:01, 10.46 it/sec, obj=-538]
        INFO - 08:37:28:     43%|████▎     | 13/30 [00:01<00:01,  9.50 it/sec, obj=-495]
        INFO - 08:37:28:     47%|████▋     | 14/30 [00:01<00:01, 10.02 it/sec, obj=-621]
        INFO - 08:37:28:     50%|█████     | 15/30 [00:01<00:01, 10.70 it/sec, obj=-433]
        INFO - 08:37:28:     53%|█████▎    | 16/30 [00:01<00:01, 11.22 it/sec, obj=-574]
        INFO - 08:37:28:     57%|█████▋    | 17/30 [00:01<00:01, 10.47 it/sec, obj=-1.07e+3]
        INFO - 08:37:28:     60%|██████    | 18/30 [00:01<00:01, 10.85 it/sec, obj=-481]
        INFO - 08:37:28:     63%|██████▎   | 19/30 [00:01<00:00, 11.00 it/sec, obj=-287]
        INFO - 08:37:28:     67%|██████▋   | 20/30 [00:01<00:00, 11.57 it/sec, obj=-602]
        INFO - 08:37:28:     70%|███████   | 21/30 [00:01<00:00, 10.99 it/sec, obj=-247]
        INFO - 08:37:29:     73%|███████▎  | 22/30 [00:01<00:00, 11.12 it/sec, obj=-414]
        INFO - 08:37:29:     77%|███████▋  | 23/30 [00:01<00:00, 11.50 it/sec, obj=-1.18e+3]
        INFO - 08:37:29:     80%|████████  | 24/30 [00:02<00:00, 11.42 it/sec, obj=-273]
        INFO - 08:37:29:     83%|████████▎ | 25/30 [00:02<00:00, 11.33 it/sec, obj=-624]
        INFO - 08:37:29:     87%|████████▋ | 26/30 [00:02<00:00, 11.73 it/sec, obj=-606]
        INFO - 08:37:29:     90%|█████████ | 27/30 [00:02<00:00, 11.79 it/sec, obj=-383]
        INFO - 08:37:29:     93%|█████████▎| 28/30 [00:02<00:00, 11.53 it/sec, obj=-351]
        INFO - 08:37:29:     97%|█████████▋| 29/30 [00:02<00:00, 11.87 it/sec, obj=-405]
        INFO - 08:37:29:    100%|██████████| 30/30 [00:02<00:00, 12.17 it/sec, obj=-485]
        INFO - 08:37:29: Optimization result:
        INFO - 08:37:29:    Optimizer info:
        INFO - 08:37:29:       Status: None
        INFO - 08:37:29:       Message: None
        INFO - 08:37:29:       Number of calls to the objective function by the optimizer: 30
        INFO - 08:37:29:    Solution:
        INFO - 08:37:29:       The solution is feasible.
        INFO - 08:37:29:       Objective: -485.49213288049987
        INFO - 08:37:29:       Standardized constraints:
        INFO - 08:37:29:          g_1 = [-0.11350951 -0.10812292 -0.1045109  -0.10204971 -0.10028641 -0.01838903
        INFO - 08:37:29:  -0.22161097]
        INFO - 08:37:29:          g_2 = -0.02400000000000002
        INFO - 08:37:29:          g_3 = [-0.33063169 -0.66936831 -0.73821755 -0.07789536]
        INFO - 08:37:29:       Design space:
        INFO - 08:37:29:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:37:29:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 08:37:29:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:37:29:          | x_shared[0] |     0.01    | 0.05400000000000001 |     0.09    | float |
        INFO - 08:37:29:          | x_shared[1] |    30000    |        46500        |    60000    | float |
        INFO - 08:37:29:          | x_shared[2] |     1.4     |  1.686666666666667  |     1.8     | float |
        INFO - 08:37:29:          | x_shared[3] |     2.5     |         5.2         |     8.5     | float |
        INFO - 08:37:29:          | x_shared[4] |      40     |         66.5        |      70     | float |
        INFO - 08:37:29:          | x_shared[5] |     500     |  583.3333333333334  |     1500    | float |
        INFO - 08:37:29:          | x_1[0]      |     0.1     |        0.185        |     0.4     | float |
        INFO - 08:37:29:          | x_1[1]      |     0.75    |  0.9416666666666667 |     1.25    | float |
        INFO - 08:37:29:          | x_2         |     0.75    |        0.775        |     1.25    | float |
        INFO - 08:37:29:          | x_3         |     0.1     |        0.115        |      1      | float |
        INFO - 08:37:29:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:37:29: *** End DOEScenario execution (time: 0:00:02.517307) ***




.. GENERATED FROM PYTHON SOURCE LINES 149-155

.. warning::
   On Windows, the progress bar may show duplicated instances during the
   initialization of each subprocess. In some cases it may also print the
   conclusion of an iteration ahead of another one that was concluded first.
   This is a consequence of the pickling process and does not affect the
   computations of the scenario.

.. GENERATED FROM PYTHON SOURCE LINES 157-162

Exporting the problem data.
^^^^^^^^^^^^^^^^^^^^^^^^^^^
After the execution of the scenario, you may want to export your data to use it
elsewhere. The method :meth:`.Scenario.to_dataset` will allow you to export
your results to a :class:`.Dataset`, the basic |g| class to store data.

.. GENERATED FROM PYTHON SOURCE LINES 162-164

.. code-block:: Python

    dataset = scenario.to_dataset("a_name_for_my_dataset")








.. GENERATED FROM PYTHON SOURCE LINES 165-167

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

.. GENERATED FROM PYTHON SOURCE LINES 167-169

.. 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_doe_sobieski_mdf_example_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_004.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_005.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_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 0x7f24dee94c70>



.. GENERATED FROM PYTHON SOURCE LINES 170-177

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the high-level function
   :func:`.get_post_processing_options_schema` to print a table with
   the attributes for any post-processing algo. Or refer to our dedicated page:
   :ref:`gen_post_algos`.

.. GENERATED FROM PYTHON SOURCE LINES 179-181

Plot the scatter matrix
^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 181-188

.. code-block:: Python

    scenario.post_process(
        post_name="ScatterPlotMatrix",
        save=False,
        show=True,
        variable_names=["y_4", "x_shared"],
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_006.png
   :alt: plot doe sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_006.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.scatter_plot_matrix.ScatterPlotMatrix object at 0x7f24de42af40>



.. GENERATED FROM PYTHON SOURCE LINES 189-191

Plot correlations
^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 191-192

.. code-block:: Python

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



.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_007.png
   :alt: R=0.98987, R=0.97511, R=0.99671, R=0.96235, R=0.99119, R=0.99866, R=0.95205, R=0.98584, R=0.99618, R=0.99936
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_007.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 08:37:33: Detected 10 correlations > 0.95

    <gemseo.post.correlations.Correlations object at 0x7f24ddedbac0>




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

   **Total running time of the script:** (0 minutes 7.008 seconds)


.. _sphx_glr_download_examples_formulations_plot_doe_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_doe_sobieski_mdf_example.ipynb <plot_doe_sobieski_mdf_example.ipynb>`

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

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

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

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


.. only:: html

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

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