.. 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

        Click :ref:`here <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 24-32

.. code-block:: default

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.problems.sobieski.core.problem import SobieskiProblem
    from matplotlib import pyplot as plt

    configure_logger()





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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 33-40

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

.. GENERATED FROM PYTHON SOURCE LINES 40-49

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 50-59

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 59-68

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 69-71

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

.. GENERATED FROM PYTHON SOURCE LINES 71-74

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 75-79

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

.. GENERATED FROM PYTHON SOURCE LINES 79-87

.. 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 88-90

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

.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. code-block:: default

    scenario.execute(scn_inputs)





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

 Out:

 .. code-block:: none

        INFO - 10:05:40:  
        INFO - 10:05:40: *** Start MDOScenario execution ***
        INFO - 10:05:40: MDOScenario
        INFO - 10:05:40:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
        INFO - 10:05:40:    MDO formulation: IDF
        INFO - 10:05:40: Optimization problem:
        INFO - 10:05:40:    minimize -y_4(x_shared, y_14, y_24, y_34)
        INFO - 10:05:40:    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 - 10:05:40:    subject to constraints:
        INFO - 10:05:40:       g_1(x_shared, x_1, y_31, y_21) <= 0.0
        INFO - 10:05:40:       g_2(x_shared, x_2, y_32, y_12) <= 0.0
        INFO - 10:05:40:       g_3(x_shared, x_3, y_23) <= 0.0
        INFO - 10:05:40:       y_31_y_32_y_34: 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 - 10:05:40:                                            y_32(x_shared, x_3, y_23) - y_32 == 0.0
        INFO - 10:05:40:                                            y_34(x_shared, x_3, y_23) - y_34 == 0.0
        INFO - 10:05:40:       y_21_y_23_y_24: 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 - 10:05:40:                                                  y_23(x_shared, x_2, y_32, y_12) - y_23 == 0.0
        INFO - 10:05:40:                                                  y_24(x_shared, x_2, y_32, y_12) - y_24 == 0.0
        INFO - 10:05:40:       y_12_y_14: 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 - 10:05:40:                                             y_14(x_shared, x_1, y_31, y_21) - y_14 == 0.0
        INFO - 10:05:40:    over the design space:
        INFO - 10:05:40:    +----------+-------------+--------------------+-------------+-------+
        INFO - 10:05:40:    | name     | lower_bound |       value        | upper_bound | type  |
        INFO - 10:05:40:    +----------+-------------+--------------------+-------------+-------+
        INFO - 10:05:40:    | x_shared |     0.01    |        0.05        |     0.09    | float |
        INFO - 10:05:40:    | x_shared |    30000    |       45000        |    60000    | float |
        INFO - 10:05:40:    | x_shared |     1.4     |        1.6         |     1.8     | float |
        INFO - 10:05:40:    | x_shared |     2.5     |        5.5         |     8.5     | float |
        INFO - 10:05:40:    | x_shared |      40     |         55         |      70     | float |
        INFO - 10:05:40:    | x_shared |     500     |        1000        |     1500    | float |
        INFO - 10:05:40:    | x_1      |     0.1     |        0.25        |     0.4     | float |
        INFO - 10:05:40:    | x_1      |     0.75    |         1          |     1.25    | float |
        INFO - 10:05:40:    | x_2      |     0.75    |         1          |     1.25    | float |
        INFO - 10:05:40:    | x_3      |     0.1     |        0.5         |      1      | float |
        INFO - 10:05:40:    | y_14     |    24850    |   50606.9741711    |    77100    | float |
        INFO - 10:05:40:    | y_14     |    -7700    |   7306.20262124    |    45000    | float |
        INFO - 10:05:40:    | y_32     |    0.235    | 0.5027962499999999 |    0.795    | float |
        INFO - 10:05:40:    | y_31     |     2960    |   6354.32430691    |    10185    | float |
        INFO - 10:05:40:    | y_24     |     0.44    |     4.15006276     |    11.13    | float |
        INFO - 10:05:40:    | y_34     |     0.44    |     1.10754577     |     1.98    | float |
        INFO - 10:05:40:    | y_23     |     3365    |   12194.2671934    |    26400    | float |
        INFO - 10:05:40:    | y_21     |    24850    |   50606.9741711    |    77250    | float |
        INFO - 10:05:40:    | y_12     |    24850    |     50606.9742     |    77250    | float |
        INFO - 10:05:40:    | y_12     |     0.45    |        0.95        |     1.5     | float |
        INFO - 10:05:40:    +----------+-------------+--------------------+-------------+-------+
        INFO - 10:05:40: Solving optimization problem with algorithm SLSQP:
        INFO - 10:05:40: ...   0%|          | 0/20 [00:00<?, ?it]
        INFO - 10:05:40: ...  40%|████      | 8/20 [00:00<00:00, 191.28 it/sec, obj=-3.96e+3]
        INFO - 10:05:40: ... 100%|██████████| 20/20 [00:00<00:00, 104.47 it/sec, obj=-3.96e+3]
        INFO - 10:05:40: Optimization result:
        INFO - 10:05:40:    Optimizer info:
        INFO - 10:05:40:       Status: None
        INFO - 10:05:40:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 10:05:40:       Number of calls to the objective function by the optimizer: 22
        INFO - 10:05:40:    Solution:
        INFO - 10:05:40:       The solution is feasible.
        INFO - 10:05:40:       Objective: -3966.790848506069
        INFO - 10:05:40:       Standardized constraints:
        INFO - 10:05:40:          g_1 = [-0.01812782 -0.03339445 -0.0442868  -0.0518651  -0.05735184 -0.13720865
        INFO - 10:05:40:  -0.10279135]
        INFO - 10:05:40:          g_2 = 2.535682693616259e-05
        INFO - 10:05:40:          g_3 = [-7.67489138e-01 -2.32510862e-01  9.20908972e-05 -1.83255000e-01]
        INFO - 10:05:40:          y_12_y_14 = [ 3.34629122e-05 -1.85828412e-05  3.35589780e-05 -5.48378413e-05]
        INFO - 10:05:40:          y_21_y_23_y_24 = [ 0.00000000e+00  9.05477756e-05 -2.83060860e-04]
        INFO - 10:05:40:          y_31_y_32_y_34 = [6.90641576e-08 6.03563891e-08 1.07078689e-04]
        INFO - 10:05:40:       Design space:
        INFO - 10:05:40:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:05:40:       | name     | lower_bound |        value        | upper_bound | type  |
        INFO - 10:05:40:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:05:40:       | x_shared |     0.01    | 0.06000633920673407 |     0.09    | float |
        INFO - 10:05:40:       | x_shared |    30000    |        60000        |    60000    | float |
        INFO - 10:05:40:       | x_shared |     1.4     |         1.4         |     1.8     | float |
        INFO - 10:05:40:       | x_shared |     2.5     |         2.5         |     8.5     | float |
        INFO - 10:05:40:       | x_shared |      40     |          70         |      70     | float |
        INFO - 10:05:40:       | x_shared |     500     |         1500        |     1500    | float |
        INFO - 10:05:40:       | x_1      |     0.1     |         0.4         |     0.4     | float |
        INFO - 10:05:40:       | x_1      |     0.75    |         0.75        |     1.25    | float |
        INFO - 10:05:40:       | x_2      |     0.75    |         0.75        |     1.25    | float |
        INFO - 10:05:40:       | x_3      |     0.1     |  0.156259134365097  |      1      | float |
        INFO - 10:05:40:       | y_14     |    24850    |  44746.56244377587  |    77100    | float |
        INFO - 10:05:40:       | y_14     |    -7700    |  19355.27544458607  |    45000    | float |
        INFO - 10:05:40:       | y_32     |    0.235    |  0.7325108278699097 |    0.795    | float |
        INFO - 10:05:40:       | y_31     |     2960    |  9433.274956925387  |    10185    | float |
        INFO - 10:05:40:       | y_24     |     0.44    |  8.059470045805423  |    11.13    | float |
        INFO - 10:05:40:       | y_34     |     0.44    |  0.9237614560895575 |     1.98    | float |
        INFO - 10:05:40:       | y_23     |     3365    |  5552.047264915329  |    26400    | float |
        INFO - 10:05:40:       | y_21     |    24850    |  44746.56244377587  |    77250    | float |
        INFO - 10:05:40:       | y_12     |    24850    |  44746.56244377587  |    77250    | float |
        INFO - 10:05:40:       | y_12     |     0.45    |  0.9028108618065331 |     1.5     | float |
        INFO - 10:05:40:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:05:40: *** End MDOScenario execution (time: 0:00:00.211049) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 93-97

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

.. GENERATED FROM PYTHON SOURCE LINES 97-98

.. code-block:: default

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




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

 Out:

 .. code-block:: none

        INFO - 10:05:40: Export optimization problem to file: idf_history.h5




.. GENERATED FROM PYTHON SOURCE LINES 99-100

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

.. GENERATED FROM PYTHON SOURCE LINES 100-102

.. code-block:: default

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





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

 Out:

 .. code-block:: none

        INFO - 10:05:40: Export to ggobi for functions: ['-y_4', 'Iter', 'g_1', 'g_2', 'g_3', 'y_12_y_14', 'y_21_y_23_y_24', 'y_31_y_32_y_34']
        INFO - 10:05:40: Export to ggobi file: idf_history.xml




.. GENERATED FROM PYTHON SOURCE LINES 103-105

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

.. GENERATED FROM PYTHON SOURCE LINES 105-107

.. code-block:: default

    scenario.print_execution_metrics()





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

 Out:

 .. code-block:: none

        INFO - 10:05:40: Scenario Execution Statistics
        INFO - 10:05:40:    Discipline: SobieskiPropulsion
        INFO - 10:05:40:       Executions number: 20
        INFO - 10:05:40:       Execution time: 0.006103995990997646 s
        INFO - 10:05:40:       Linearizations number: 7
        INFO - 10:05:40:    Discipline: SobieskiAerodynamics
        INFO - 10:05:40:       Executions number: 20
        INFO - 10:05:40:       Execution time: 0.009110703998885583 s
        INFO - 10:05:40:       Linearizations number: 7
        INFO - 10:05:40:    Discipline: SobieskiMission
        INFO - 10:05:40:       Executions number: 20
        INFO - 10:05:40:       Execution time: 0.000919604986847844 s
        INFO - 10:05:40:       Linearizations number: 7
        INFO - 10:05:40:    Discipline: SobieskiStructure
        INFO - 10:05:40:       Executions number: 20
        INFO - 10:05:40:       Execution time: 0.03358767099416582 s
        INFO - 10:05:40:       Linearizations number: 7
        INFO - 10:05:40:    Total number of executions calls: 80
        INFO - 10:05:40:    Total number of linearizations: 28




.. GENERATED FROM PYTHON SOURCE LINES 108-110

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

.. GENERATED FROM PYTHON SOURCE LINES 110-112

.. code-block:: default

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




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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_001.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_002.png
         :alt: Evolution of the objective value
         :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: Distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_004.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_005.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_006.png
         :alt: Evolution of the equality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_006.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7fdbe16cc760>



.. GENERATED FROM PYTHON SOURCE LINES 113-115

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

.. GENERATED FROM PYTHON SOURCE LINES 115-118

.. code-block:: default

    scenario.post_process("QuadApprox", function="-y_4", save=False, show=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_007.png
         :alt: Hessian matrix SR1 approximation of -y_4
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_008.png
         :alt: plot sobieski idf example
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_008.png
         :class: sphx-glr-multi-img






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

   **Total running time of the script:** ( 0 minutes  3.112 seconds)


.. _sphx_glr_download_examples_formulations_plot_sobieski_idf_example.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: 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>`_