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

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

.. _sphx_glr_examples_formulations_plot_sobieski_idf_example.py:


IDF-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.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: {'c_3': array([4360.]), '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])}
    SobieskiAerodynamics
    Default inputs: {'y_12': array([5.06069742e+04, 9.50000000e-01]), 'x_2': array([1.]), 'y_32': array([0.50279625]), 'c_4': array([0.01375]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03])}
    SobieskiMission
    Default inputs: {'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]), 'y_14': array([50606.9741711 ,  7306.20262124])}
    SobieskiStructure
    Default inputs: {'y_31': array([6354.32430691]), 'c_0': array([2000.]), 'c_2': array([6.]), 'x_1': array([0.25, 1.  ]), 'y_21': array([50606.9741711]), 'c_1': array([25000.]), '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 API 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_idf_example_001.png
   :alt: plot sobieski idf example
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 66-75

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

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

.. GENERATED FROM PYTHON SOURCE LINES 75-78

.. 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 79-87

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "IDF",
        objective_name="y_4",
        design_space=design_space,
        maximize_objective=True,
    )








.. GENERATED FROM PYTHON SOURCE LINES 88-90

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

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 94-101

Visualize the XDSM
^^^^^^^^^^^^^^^^^^
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 101-103

.. 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": "SobieskiPropulsion",
            "type": "analysis"
          },
          {
            "id": "Dis2",
            "name": "SobieskiAerodynamics",
            "type": "analysis"
          },
          {
            "id": "Dis3",
            "name": "SobieskiMission",
            "type": "analysis"
          },
          {
            "id": "Dis4",
            "name": "SobieskiStructure",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_shared^(0), x_1^(0), x_2^(0), x_3^(0), y_14^(0), y_32^(0), y_31^(0), y_24^(0), y_34^(0), y_23^(0), y_21^(0), y_12^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "-y_4^*, y_31_y_32_y_34^*, y_21_y_23_y_24^*, y_12_y_14^*, g_1^*, g_2^*, g_3^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "y_23, x_3, x_shared"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_34, y_32, y_31, g_3"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "y_12, x_2, y_32, x_shared"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "y_24, y_21, y_23, g_2"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "y_14, y_24, y_34, x_shared"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_1, y_31, y_21, x_shared"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1, y_12, y_14"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_3^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_32, y_31, g_3, y_34"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "y_2^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "y_21, y_23, y_24, g_2"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Dis4",
            "to": "_U_",
            "name": "y_1^*, y_11^*"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "y_14, g_1, y_12"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              {
                "parallel": [
                  "Dis1",
                  "Dis2",
                  "Dis3",
                  "Dis4"
                ]
              }
            ]
          ]
        ],
        "optpb": "Optimization problem:\n   minimize -y_4(x_shared, y_14, y_24, y_34)\n   with respect to x_1, x_2, x_3, x_shared, y_12, y_14, y_21, y_23, y_24, y_31, y_32, y_34\n   subject to constraints:\n      g_1(x_shared, x_1, y_31, y_21) <= 0.0\n      g_2(x_shared, x_2, y_32, y_12) <= 0.0\n      g_3(x_shared, x_3, y_23) <= 0.0\n      y_31_y_32_y_34(x_shared, x_3, y_23): y_31(x_shared, x_3, y_23) - y_31 == 0.0\n                                           y_32(x_shared, x_3, y_23) - y_32 == 0.0\n                                           y_34(x_shared, x_3, y_23) - y_34 == 0.0\n      y_21_y_23_y_24(x_shared, x_2, y_32, y_12): y_21(x_shared, x_2, y_32, y_12) - y_21 == 0.0\n                                                 y_23(x_shared, x_2, y_32, y_12) - y_23 == 0.0\n                                                 y_24(x_shared, x_2, y_32, y_12) - y_24 == 0.0\n      y_12_y_14(x_shared, x_1, y_31, y_21): y_12(x_shared, x_1, y_31, y_21) - y_12 == 0.0\n                                            y_14(x_shared, x_1, y_31, y_21) - y_14 == 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 104-108

Define the algorithm inputs
^^^^^^^^^^^^^^^^^^^^^^^^^^^
We set the maximum number of iterations, the optimizer
and the optimizer options

.. GENERATED FROM PYTHON SOURCE LINES 108-116

.. code-block:: Python

    algo_options = {
        "ftol_rel": 1e-10,
        "ineq_tolerance": 1e-3,
        "eq_tolerance": 1e-3,
        "normalize_design_space": True,
    }
    scn_inputs = {"max_iter": 20, "algo": "SLSQP", "algo_options": algo_options}








.. GENERATED FROM PYTHON SOURCE LINES 117-119

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

.. GENERATED FROM PYTHON SOURCE LINES 119-121

.. code-block:: Python

    scenario.execute(scn_inputs)





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

 .. code-block:: none

        INFO - 10:54:33:  
        INFO - 10:54:33: *** Start MDOScenario execution ***
        INFO - 10:54:33: MDOScenario
        INFO - 10:54:33:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 10:54:33:    MDO formulation: IDF
        INFO - 10:54:33: Optimization problem:
        INFO - 10:54:33:    minimize -y_4(x_shared, y_14, y_24, y_34)
        INFO - 10:54:33:    with respect to x_1, x_2, x_3, x_shared, y_12, y_14, y_21, y_23, y_24, y_31, y_32, y_34
        INFO - 10:54:33:    subject to constraints:
        INFO - 10:54:33:       g_1(x_shared, x_1, y_31, y_21) <= 0.0
        INFO - 10:54:33:       g_2(x_shared, x_2, y_32, y_12) <= 0.0
        INFO - 10:54:33:       g_3(x_shared, x_3, y_23) <= 0.0
        INFO - 10:54:33:       y_31_y_32_y_34(x_shared, x_3, y_23): y_31(x_shared, x_3, y_23) - y_31 == 0.0
        INFO - 10:54:33:                                            y_32(x_shared, x_3, y_23) - y_32 == 0.0
        INFO - 10:54:33:                                            y_34(x_shared, x_3, y_23) - y_34 == 0.0
        INFO - 10:54:33:       y_21_y_23_y_24(x_shared, x_2, y_32, y_12): y_21(x_shared, x_2, y_32, y_12) - y_21 == 0.0
        INFO - 10:54:33:                                                  y_23(x_shared, x_2, y_32, y_12) - y_23 == 0.0
        INFO - 10:54:33:                                                  y_24(x_shared, x_2, y_32, y_12) - y_24 == 0.0
        INFO - 10:54:33:       y_12_y_14(x_shared, x_1, y_31, y_21): y_12(x_shared, x_1, y_31, y_21) - y_12 == 0.0
        INFO - 10:54:33:                                             y_14(x_shared, x_1, y_31, y_21) - y_14 == 0.0
        INFO - 10:54:33:    over the design space:
        INFO - 10:54:33:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 10:54:33:       | Name        | Lower bound |       Value        | Upper bound | Type  |
        INFO - 10:54:33:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 10:54:33:       | x_shared[0] |     0.01    |        0.05        |     0.09    | float |
        INFO - 10:54:33:       | x_shared[1] |    30000    |       45000        |    60000    | float |
        INFO - 10:54:33:       | x_shared[2] |     1.4     |        1.6         |     1.8     | float |
        INFO - 10:54:33:       | x_shared[3] |     2.5     |        5.5         |     8.5     | float |
        INFO - 10:54:33:       | x_shared[4] |      40     |         55         |      70     | float |
        INFO - 10:54:33:       | x_shared[5] |     500     |        1000        |     1500    | float |
        INFO - 10:54:33:       | x_1[0]      |     0.1     |        0.25        |     0.4     | float |
        INFO - 10:54:33:       | x_1[1]      |     0.75    |         1          |     1.25    | float |
        INFO - 10:54:33:       | x_2         |     0.75    |         1          |     1.25    | float |
        INFO - 10:54:33:       | x_3         |     0.1     |        0.5         |      1      | float |
        INFO - 10:54:33:       | y_14[0]     |    24850    |   50606.9741711    |    77100    | float |
        INFO - 10:54:33:       | y_14[1]     |    -7700    |   7306.20262124    |    45000    | float |
        INFO - 10:54:33:       | y_32        |    0.235    | 0.5027962499999999 |    0.795    | float |
        INFO - 10:54:33:       | y_31        |     2960    |   6354.32430691    |    10185    | float |
        INFO - 10:54:33:       | y_24        |     0.44    |     4.15006276     |    11.13    | float |
        INFO - 10:54:33:       | y_34        |     0.44    |     1.10754577     |     1.98    | float |
        INFO - 10:54:33:       | y_23        |     3365    |   12194.2671934    |    26400    | float |
        INFO - 10:54:33:       | y_21        |    24850    |   50606.9741711    |    77250    | float |
        INFO - 10:54:33:       | y_12[0]     |    24850    |     50606.9742     |    77250    | float |
        INFO - 10:54:33:       | y_12[1]     |     0.45    |        0.95        |     1.5     | float |
        INFO - 10:54:33:       +-------------+-------------+--------------------+-------------+-------+
        INFO - 10:54:33: Solving optimization problem with algorithm SLSQP:
        INFO - 10:54:33:      5%|▌         | 1/20 [00:00<00:00, 198.23 it/sec, obj=-536]
        INFO - 10:54:33:     10%|█         | 2/20 [00:00<00:00, 50.15 it/sec, obj=-1.49e+3]
        INFO - 10:54:33:     15%|█▌        | 3/20 [00:00<00:00, 53.94 it/sec, obj=-3.83e+3]
        INFO - 10:54:33:     20%|██        | 4/20 [00:00<00:00, 55.94 it/sec, obj=-3.96e+3]
        INFO - 10:54:33:     25%|██▌       | 5/20 [00:00<00:00, 57.32 it/sec, obj=-3.96e+3]
        INFO - 10:54:33:     30%|███       | 6/20 [00:00<00:00, 58.35 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     35%|███▌      | 7/20 [00:00<00:00, 58.70 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     40%|████      | 8/20 [00:00<00:00, 59.06 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     45%|████▌     | 9/20 [00:00<00:00, 62.84 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     50%|█████     | 10/20 [00:00<00:00, 62.67 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     55%|█████▌    | 11/20 [00:00<00:00, 65.59 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     60%|██████    | 12/20 [00:00<00:00, 68.41 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     65%|██████▌   | 13/20 [00:00<00:00, 71.01 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     70%|███████   | 14/20 [00:00<00:00, 73.42 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     75%|███████▌  | 15/20 [00:00<00:00, 75.64 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     80%|████████  | 16/20 [00:00<00:00, 77.69 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     85%|████████▌ | 17/20 [00:00<00:00, 79.61 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     90%|█████████ | 18/20 [00:00<00:00, 81.39 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:     95%|█████████▌| 19/20 [00:00<00:00, 82.97 it/sec, obj=-3.96e+3]
        INFO - 10:54:34:    100%|██████████| 20/20 [00:00<00:00, 84.52 it/sec, obj=-3.96e+3]
        INFO - 10:54:34: Optimization result:
        INFO - 10:54:34:    Optimizer info:
        INFO - 10:54:34:       Status: 8
        INFO - 10:54:34:       Message: Positive directional derivative for linesearch
        INFO - 10:54:34:       Number of calls to the objective function by the optimizer: 21
        INFO - 10:54:34:    Solution:
        INFO - 10:54:34:       The solution is feasible.
        INFO - 10:54:34:       Objective: -3963.909125280606
        INFO - 10:54:34:       Standardized constraints:
        INFO - 10:54:34:          g_1 = [-0.01807265 -0.03335477 -0.04425595 -0.0518399  -0.05733055 -0.13720865
        INFO - 10:54:34:  -0.10279135]
        INFO - 10:54:34:          g_2 = 7.162693463458325e-06
        INFO - 10:54:34:          g_3 = [-7.67188159e-01 -2.32811841e-01 -3.73860557e-05 -1.83255000e-01]
        INFO - 10:54:34:          y_12_y_14 = [ 1.12943503e-05  4.28787041e-07  1.13267743e-05 -1.50426345e-05]
        INFO - 10:54:34:          y_21_y_23_y_24 = [-2.77708306e-16  1.33085464e-05 -2.62473913e-05]
        INFO - 10:54:34:          y_31_y_32_y_34 = [-2.35661889e-06 -2.32437808e-06  1.57269783e-05]
        INFO - 10:54:34:       Design space:
        INFO - 10:54:34:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 10:54:34:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 10:54:34:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 10:54:34:          | x_shared[0] |     0.01    | 0.06000179067336589 |     0.09    | float |
        INFO - 10:54:34:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 10:54:34:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 10:54:34:          | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 10:54:34:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 10:54:34:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 10:54:34:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 10:54:34:          | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
        INFO - 10:54:34:          | x_2         |     0.75    |         0.75        |     1.25    | float |
        INFO - 10:54:34:          | x_3         |     0.1     |  0.156238904271528  |      1      | float |
        INFO - 10:54:34:          | y_14[0]     |    24850    |  44749.85202975167  |    77100    | float |
        INFO - 10:54:34:          | y_14[1]     |    -7700    |  19351.86291108692  |    45000    | float |
        INFO - 10:54:34:          | y_32        |    0.235    |  0.7328131425977524 |    0.795    | float |
        INFO - 10:54:34:          | y_31        |     2960    |  9437.362336215188  |    10185    | float |
        INFO - 10:54:34:          | y_24        |     0.44    |   8.05763183450019  |    11.13    | float |
        INFO - 10:54:34:          | y_34        |     0.44    |  0.9239115967364436 |     1.98    | float |
        INFO - 10:54:34:          | y_23        |     3365    |   5553.60943830111  |    26400    | float |
        INFO - 10:54:34:          | y_21        |    24850    |  44749.85202975168  |    77250    | float |
        INFO - 10:54:34:          | y_12[0]     |    24850    |  44749.85202975167  |    77250    | float |
        INFO - 10:54:34:          | y_12[1]     |     0.45    |  0.9027908995968825 |     1.5     | float |
        INFO - 10:54:34:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 10:54:34: *** End MDOScenario execution (time: 0:00:00.282239) ***

    {'max_iter': 20, 'algo_options': {'ftol_rel': 1e-10, 'ineq_tolerance': 0.001, 'eq_tolerance': 0.001, 'normalize_design_space': True}, 'algo': 'SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 122-126

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

.. GENERATED FROM PYTHON SOURCE LINES 126-128

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 10:54:34: Export optimization problem to file: idf_history.h5




.. GENERATED FROM PYTHON SOURCE LINES 129-130

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

.. GENERATED FROM PYTHON SOURCE LINES 130-132

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 10:54:34: Export to ggobi for functions: ['-y_4', 'g_1', 'g_2', 'g_3', 'y_12_y_14', 'y_21_y_23_y_24', 'y_31_y_32_y_34']
        INFO - 10:54:34: Export to ggobi file: idf_history.xml




.. GENERATED FROM PYTHON SOURCE LINES 133-135

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

.. GENERATED FROM PYTHON SOURCE LINES 135-137

.. code-block:: Python

    scenario.print_execution_metrics()





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

 .. code-block:: none

        INFO - 10:54:34: Scenario Execution Statistics
        INFO - 10:54:34:    Discipline: SobieskiPropulsion
        INFO - 10:54:34:       Executions number: 20
        INFO - 10:54:34:       Execution time: 0.01252255000099467 s
        INFO - 10:54:34:       Linearizations number: 9
        INFO - 10:54:34:    Discipline: SobieskiAerodynamics
        INFO - 10:54:34:       Executions number: 20
        INFO - 10:54:34:       Execution time: 0.01579668599924844 s
        INFO - 10:54:34:       Linearizations number: 9
        INFO - 10:54:34:    Discipline: SobieskiMission
        INFO - 10:54:34:       Executions number: 20
        INFO - 10:54:34:       Execution time: 0.0014030970005478594 s
        INFO - 10:54:34:       Linearizations number: 9
        INFO - 10:54:34:    Discipline: SobieskiStructure
        INFO - 10:54:34:       Executions number: 20
        INFO - 10:54:34:       Execution time: 0.07588864699982878 s
        INFO - 10:54:34:       Linearizations number: 9
        INFO - 10:54:34:    Total number of executions calls: 80
        INFO - 10:54:34:    Total number of linearizations: 36




.. GENERATED FROM PYTHON SOURCE LINES 138-140

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

.. GENERATED FROM PYTHON SOURCE LINES 140-142

.. code-block:: Python

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





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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7efd31533160>



.. GENERATED FROM PYTHON SOURCE LINES 143-145

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

.. GENERATED FROM PYTHON SOURCE LINES 145-146

.. 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_idf_example_002.png
         :alt: Hessian matrix SR1 approximation of -y_4
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_003.png
         :alt: plot sobieski idf example
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_003.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.quad_approx.QuadApprox object at 0x7efd30f77280>




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

   **Total running time of the script:** (0 minutes 5.070 seconds)


.. _sphx_glr_download_examples_formulations_plot_sobieski_idf_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_idf_example.ipynb <plot_sobieski_idf_example.ipynb>`

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

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


.. only:: html

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

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