.. 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 24-34

.. code-block:: default

    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.problem import SobieskiProblem

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 35-42

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

.. GENERATED FROM PYTHON SOURCE LINES 42-51

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 52-55

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 55-59

.. code-block:: default

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




.. GENERATED FROM PYTHON SOURCE LINES 60-64

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 64-66

.. code-block:: default

    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 67-76

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 76-86

.. code-block:: default

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





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

 .. code-block:: none

    Design space: 
    +-------------+-------------+--------------------+-------------+-------+
    | name        | lower_bound |       value        | upper_bound | type  |
    +-------------+-------------+--------------------+-------------+-------+
    | x_shared[0] |     0.01    |        0.05        |     0.09    | float |
    | x_shared[1] |    30000    |       45000        |    60000    | float |
    | x_shared[2] |     1.4     |        1.6         |     1.8     | float |
    | x_shared[3] |     2.5     |        5.5         |     8.5     | float |
    | x_shared[4] |      40     |         55         |      70     | float |
    | x_shared[5] |     500     |        1000        |     1500    | float |
    | x_1[0]      |     0.1     |        0.25        |     0.4     | float |
    | x_1[1]      |     0.75    |         1          |     1.25    | float |
    | x_2         |     0.75    |         1          |     1.25    | float |
    | x_3         |     0.1     |        0.5         |      1      | float |
    | y_14[0]     |    24850    |   50606.9741711    |    77100    | float |
    | y_14[1]     |    -7700    |   7306.20262124    |    45000    | float |
    | y_32        |    0.235    | 0.5027962499999999 |    0.795    | float |
    | y_31        |     2960    |   6354.32430691    |    10185    | float |
    | y_24        |     0.44    |     4.15006276     |    11.13    | float |
    | y_34        |     0.44    |     1.10754577     |     1.98    | float |
    | y_23        |     3365    |   12194.2671934    |    26400    | float |
    | y_21        |    24850    |   50606.9741711    |    77250    | float |
    | y_12[0]     |    24850    |     50606.9742     |    77250    | float |
    | y_12[1]     |     0.45    |        0.95        |     1.5     | float |
    +-------------+-------------+--------------------+-------------+-------+




.. GENERATED FROM PYTHON SOURCE LINES 87-89

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

.. GENERATED FROM PYTHON SOURCE LINES 89-92

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 93-100

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 100-102

.. code-block:: default

    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_shared, x_3"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_34, y_32, g_3, y_31"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x_2, y_32, x_shared, y_12"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "y_23, g_2, y_21, y_24"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "y_34, x_shared, y_14, y_24"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_shared, y_21, y_31, x_1"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1, y_14, y_12"
          },
          {
            "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 103-107

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

.. GENERATED FROM PYTHON SOURCE LINES 107-115

.. code-block:: default

    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 116-118

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

.. GENERATED FROM PYTHON SOURCE LINES 118-120

.. code-block:: default

    scenario.execute(scn_inputs)





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

 .. code-block:: none

        INFO - 16:26:26:  
        INFO - 16:26:26: *** Start MDOScenario execution ***
        INFO - 16:26:26: MDOScenario
        INFO - 16:26:26:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 16:26:26:    MDO formulation: IDF
        INFO - 16:26:26: Optimization problem:
        INFO - 16:26:26:    minimize -y_4(x_shared, y_14, y_24, y_34)
        INFO - 16:26:26:    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 - 16:26:26:    subject to constraints:
        INFO - 16:26:26:       g_1(x_shared, x_1, y_31, y_21) <= 0.0
        INFO - 16:26:26:       g_2(x_shared, x_2, y_32, y_12) <= 0.0
        INFO - 16:26:26:       g_3(x_shared, x_3, y_23) <= 0.0
        INFO - 16:26:26:       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 - 16:26:26:                                            y_32(x_shared, x_3, y_23) - y_32 == 0.0
        INFO - 16:26:26:                                            y_34(x_shared, x_3, y_23) - y_34 == 0.0
        INFO - 16:26:26:       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 - 16:26:26:                                                  y_23(x_shared, x_2, y_32, y_12) - y_23 == 0.0
        INFO - 16:26:26:                                                  y_24(x_shared, x_2, y_32, y_12) - y_24 == 0.0
        INFO - 16:26:26:       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 - 16:26:26:                                             y_14(x_shared, x_1, y_31, y_21) - y_14 == 0.0
        INFO - 16:26:26:    over the design space:
        INFO - 16:26:26:    +-------------+-------------+--------------------+-------------+-------+
        INFO - 16:26:26:    | name        | lower_bound |       value        | upper_bound | type  |
        INFO - 16:26:26:    +-------------+-------------+--------------------+-------------+-------+
        INFO - 16:26:26:    | x_shared[0] |     0.01    |        0.05        |     0.09    | float |
        INFO - 16:26:26:    | x_shared[1] |    30000    |       45000        |    60000    | float |
        INFO - 16:26:26:    | x_shared[2] |     1.4     |        1.6         |     1.8     | float |
        INFO - 16:26:26:    | x_shared[3] |     2.5     |        5.5         |     8.5     | float |
        INFO - 16:26:26:    | x_shared[4] |      40     |         55         |      70     | float |
        INFO - 16:26:26:    | x_shared[5] |     500     |        1000        |     1500    | float |
        INFO - 16:26:26:    | x_1[0]      |     0.1     |        0.25        |     0.4     | float |
        INFO - 16:26:26:    | x_1[1]      |     0.75    |         1          |     1.25    | float |
        INFO - 16:26:26:    | x_2         |     0.75    |         1          |     1.25    | float |
        INFO - 16:26:26:    | x_3         |     0.1     |        0.5         |      1      | float |
        INFO - 16:26:26:    | y_14[0]     |    24850    |   50606.9741711    |    77100    | float |
        INFO - 16:26:26:    | y_14[1]     |    -7700    |   7306.20262124    |    45000    | float |
        INFO - 16:26:26:    | y_32        |    0.235    | 0.5027962499999999 |    0.795    | float |
        INFO - 16:26:26:    | y_31        |     2960    |   6354.32430691    |    10185    | float |
        INFO - 16:26:26:    | y_24        |     0.44    |     4.15006276     |    11.13    | float |
        INFO - 16:26:26:    | y_34        |     0.44    |     1.10754577     |     1.98    | float |
        INFO - 16:26:26:    | y_23        |     3365    |   12194.2671934    |    26400    | float |
        INFO - 16:26:26:    | y_21        |    24850    |   50606.9741711    |    77250    | float |
        INFO - 16:26:26:    | y_12[0]     |    24850    |     50606.9742     |    77250    | float |
        INFO - 16:26:26:    | y_12[1]     |     0.45    |        0.95        |     1.5     | float |
        INFO - 16:26:26:    +-------------+-------------+--------------------+-------------+-------+
        INFO - 16:26:26: Solving optimization problem with algorithm SLSQP:
        INFO - 16:26:26: ...   0%|          | 0/20 [00:00<?, ?it]
        INFO - 16:26:26: ...   5%|▌         | 1/20 [00:00<00:00, 205.06 it/sec, obj=-536]
        INFO - 16:26:26: ...  10%|█         | 2/20 [00:00<00:00, 57.22 it/sec, obj=-1.49e+3]
        INFO - 16:26:26: ...  15%|█▌        | 3/20 [00:00<00:00, 64.03 it/sec, obj=-3.83e+3]
        INFO - 16:26:26: ...  20%|██        | 4/20 [00:00<00:00, 68.42 it/sec, obj=-3.87e+3]
        INFO - 16:26:26: ...  25%|██▌       | 5/20 [00:00<00:00, 71.34 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  30%|███       | 6/20 [00:00<00:00, 73.37 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  35%|███▌      | 7/20 [00:00<00:00, 74.27 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  40%|████      | 8/20 [00:00<00:00, 79.96 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  45%|████▌     | 9/20 [00:00<00:00, 85.20 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  50%|█████     | 10/20 [00:00<00:00, 89.85 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  55%|█████▌    | 11/20 [00:00<00:00, 94.12 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  60%|██████    | 12/20 [00:00<00:00, 98.00 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  65%|██████▌   | 13/20 [00:00<00:00, 101.53 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  70%|███████   | 14/20 [00:00<00:00, 104.79 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  75%|███████▌  | 15/20 [00:00<00:00, 107.73 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  80%|████████  | 16/20 [00:00<00:00, 110.52 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  85%|████████▌ | 17/20 [00:00<00:00, 113.08 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: ...  90%|█████████ | 18/20 [00:00<00:00, 110.28 it/sec, obj=-3.97e+3]
        INFO - 16:26:26: ...  95%|█████████▌| 19/20 [00:00<00:00, 112.57 it/sec, obj=-3.97e+3]
        INFO - 16:26:26: ... 100%|██████████| 20/20 [00:00<00:00, 114.44 it/sec, obj=-3.96e+3]
        INFO - 16:26:26: Optimization result:
        INFO - 16:26:26:    Optimizer info:
        INFO - 16:26:26:       Status: None
        INFO - 16:26:26:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 16:26:26:       Number of calls to the objective function by the optimizer: 22
        INFO - 16:26:26:    Solution:
        INFO - 16:26:26:       The solution is feasible.
        INFO - 16:26:26:       Objective: -3966.790848506069
        INFO - 16:26:26:       Standardized constraints:
        INFO - 16:26:26:          g_1 = [-0.01812782 -0.03339445 -0.0442868  -0.0518651  -0.05735184 -0.13720865
        INFO - 16:26:26:  -0.10279135]
        INFO - 16:26:26:          g_2 = 2.535682693616259e-05
        INFO - 16:26:26:          g_3 = [-7.67489138e-01 -2.32510862e-01  9.20908972e-05 -1.83255000e-01]
        INFO - 16:26:26:          y_12_y_14 = [ 3.34629122e-05 -1.85828412e-05  3.35589780e-05 -5.48378413e-05]
        INFO - 16:26:26:          y_21_y_23_y_24 = [ 0.00000000e+00  9.05477756e-05 -2.83060860e-04]
        INFO - 16:26:26:          y_31_y_32_y_34 = [6.90641576e-08 6.03563891e-08 1.07078689e-04]
        INFO - 16:26:26:       Design space: 
        INFO - 16:26:26:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:26:26:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 16:26:26:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:26:26:       | x_shared[0] |     0.01    | 0.06000633920673407 |     0.09    | float |
        INFO - 16:26:26:       | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 16:26:26:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 16:26:26:       | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 16:26:26:       | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 16:26:26:       | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 16:26:26:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 16:26:26:       | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
        INFO - 16:26:26:       | x_2         |     0.75    |         0.75        |     1.25    | float |
        INFO - 16:26:26:       | x_3         |     0.1     |  0.156259134365097  |      1      | float |
        INFO - 16:26:26:       | y_14[0]     |    24850    |  44746.56244377587  |    77100    | float |
        INFO - 16:26:26:       | y_14[1]     |    -7700    |  19355.27544458607  |    45000    | float |
        INFO - 16:26:26:       | y_32        |    0.235    |  0.7325108278699097 |    0.795    | float |
        INFO - 16:26:26:       | y_31        |     2960    |  9433.274956925387  |    10185    | float |
        INFO - 16:26:26:       | y_24        |     0.44    |  8.059470045805423  |    11.13    | float |
        INFO - 16:26:26:       | y_34        |     0.44    |  0.9237614560895575 |     1.98    | float |
        INFO - 16:26:26:       | y_23        |     3365    |  5552.047264915329  |    26400    | float |
        INFO - 16:26:26:       | y_21        |    24850    |  44746.56244377587  |    77250    | float |
        INFO - 16:26:26:       | y_12[0]     |    24850    |  44746.56244377587  |    77250    | float |
        INFO - 16:26:26:       | y_12[1]     |     0.45    |  0.9028108618065331 |     1.5     | float |
        INFO - 16:26:26:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:26:26: *** End MDOScenario execution (time: 0:00:00.207399) ***

    {'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 121-125

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

.. GENERATED FROM PYTHON SOURCE LINES 125-127

.. code-block:: default

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





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

 .. code-block:: none

        INFO - 16:26:26: Export optimization problem to file: idf_history.h5




.. GENERATED FROM PYTHON SOURCE LINES 128-129

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

.. GENERATED FROM PYTHON SOURCE LINES 129-131

.. code-block:: default

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





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

 .. code-block:: none

        INFO - 16:26:26: 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 - 16:26:26: Export to ggobi file: idf_history.xml




.. GENERATED FROM PYTHON SOURCE LINES 132-134

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

.. GENERATED FROM PYTHON SOURCE LINES 134-136

.. code-block:: default

    scenario.print_execution_metrics()





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

 .. code-block:: none

        INFO - 16:26:26: Scenario Execution Statistics
        INFO - 16:26:26:    Discipline: SobieskiPropulsion
        INFO - 16:26:26:       Executions number: 20
        INFO - 16:26:26:       Execution time: 0.005850181999448978 s
        INFO - 16:26:26:       Linearizations number: 7
        INFO - 16:26:26:    Discipline: SobieskiAerodynamics
        INFO - 16:26:26:       Executions number: 20
        INFO - 16:26:26:       Execution time: 0.00852488800046558 s
        INFO - 16:26:26:       Linearizations number: 7
        INFO - 16:26:26:    Discipline: SobieskiMission
        INFO - 16:26:26:       Executions number: 20
        INFO - 16:26:26:       Execution time: 0.0010573070003374596 s
        INFO - 16:26:26:       Linearizations number: 7
        INFO - 16:26:26:    Discipline: SobieskiStructure
        INFO - 16:26:26:       Executions number: 20
        INFO - 16:26:26:       Execution time: 0.02969086699795298 s
        INFO - 16:26:26:       Linearizations number: 7
        INFO - 16:26:26:    Total number of executions calls: 80
        INFO - 16:26:26:    Total number of linearizations: 28




.. GENERATED FROM PYTHON SOURCE LINES 137-139

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

.. GENERATED FROM PYTHON SOURCE LINES 139-141

.. code-block:: default

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





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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.0/lib/python3.9/site-packages/genson/schema/strategies/base.py:42: UserWarning: Schema incompatible. Keyword 'description' has conflicting values ('The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.' vs. 'The width and height of the figure in inches, e.g. `(w, h)`.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'). Using 'The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'
      warn(('Schema incompatible. Keyword {0!r} has conflicting '

    <gemseo.post.opt_history_view.OptHistoryView object at 0x7fea4262a7c0>



.. GENERATED FROM PYTHON SOURCE LINES 142-144

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

.. GENERATED FROM PYTHON SOURCE LINES 144-145

.. code-block:: default

    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 0x7fea45672f10>




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

   **Total running time of the script:** ( 0 minutes  5.049 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-python

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

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

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


.. only:: html

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

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