.. 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

        Click :ref:`here <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 24-34

.. code-block:: default

    from os import name as os_name

    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 35-42

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 42-51

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 52-60

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 60-62

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 63-65

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

.. GENERATED FROM PYTHON SOURCE LINES 65-74

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 75-77

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

.. GENERATED FROM PYTHON SOURCE LINES 77-80

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 81-84

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

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: default

    scenario.set_differentiation_method("user")








.. GENERATED FROM PYTHON SOURCE LINES 87-92

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 92-103

.. code-block:: default


    #    The multiprocessing option has some limitations on Windows.
    #    Due to problems with sphinx, we disable it in this example.
    #    For Python versions < 3.7 and Numpy < 1.20.0, subprocesses may get hung
    #    randomly during execution. It is strongly recommended to update your
    #    environment to avoid this problem.
    #    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 104-106

We define the algorithm options. Here the criterion = center option of pyDOE
centers the points within the sampling intervals.

.. GENERATED FROM PYTHON SOURCE LINES 106-117

.. code-block:: default

    algo_options = {
        "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({"n_samples": 30, "algo": "lhs", "algo_options": algo_options})





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

 Out:

 .. code-block:: none

        INFO - 10:07:39:  
        INFO - 10:07:39: *** Start DOEScenario execution ***
        INFO - 10:07:39: DOEScenario
        INFO - 10:07:39:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
        INFO - 10:07:39:    MDO formulation: MDF
        INFO - 10:07:39: Optimization problem:
        INFO - 10:07:39:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 10:07:39:    with respect to x_1, x_2, x_3, x_shared
        INFO - 10:07:39:    subject to constraints:
        INFO - 10:07:39:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 10:07:39:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 10:07:39:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 10:07:39:    over the design space:
        INFO - 10:07:39:    +----------+-------------+-------+-------------+-------+
        INFO - 10:07:39:    | name     | lower_bound | value | upper_bound | type  |
        INFO - 10:07:39:    +----------+-------------+-------+-------------+-------+
        INFO - 10:07:39:    | x_shared |     0.01    |  0.05 |     0.09    | float |
        INFO - 10:07:39:    | x_shared |    30000    | 45000 |    60000    | float |
        INFO - 10:07:39:    | x_shared |     1.4     |  1.6  |     1.8     | float |
        INFO - 10:07:39:    | x_shared |     2.5     |  5.5  |     8.5     | float |
        INFO - 10:07:39:    | x_shared |      40     |   55  |      70     | float |
        INFO - 10:07:39:    | x_shared |     500     |  1000 |     1500    | float |
        INFO - 10:07:39:    | x_1      |     0.1     |  0.25 |     0.4     | float |
        INFO - 10:07:39:    | x_1      |     0.75    |   1   |     1.25    | float |
        INFO - 10:07:39:    | x_2      |     0.75    |   1   |     1.25    | float |
        INFO - 10:07:39:    | x_3      |     0.1     |  0.5  |      1      | float |
        INFO - 10:07:39:    +----------+-------------+-------+-------------+-------+
        INFO - 10:07:39: Solving optimization problem with algorithm lhs:
        INFO - 10:07:39: ...   0%|          | 0/30 [00:00<?, ?it]
        INFO - 10:07:39: Running DOE in parallel on n_processes = 4
        INFO - 10:07:39: ...   3%|▎         | 1/30 [00:00<00:00, 49.34 it/sec, obj=-285]
        INFO - 10:07:40: ...   7%|▋         | 2/30 [00:00<00:00, 40.97 it/sec, obj=-222]
        INFO - 10:07:40: ...  17%|█▋        | 5/30 [00:01<00:00, 28.10 it/sec, obj=-429]
        INFO - 10:07:40: ...  23%|██▎       | 7/30 [00:01<00:00, 24.00 it/sec, obj=-519]
        INFO - 10:07:40: ...  30%|███       | 9/30 [00:01<00:01, 18.68 it/sec, obj=-538]
        INFO - 10:07:41: ...  40%|████      | 12/30 [00:01<00:01, 17.19 it/sec, obj=-556]
        INFO - 10:07:41: ...  47%|████▋     | 14/30 [00:02<00:01, 14.54 it/sec, obj=-495]
        INFO - 10:07:41: ...  53%|█████▎    | 16/30 [00:02<00:01, 12.95 it/sec, obj=-621]
        INFO - 10:07:41: ...  60%|██████    | 18/30 [00:02<00:01, 11.79 it/sec, obj=-481]
        INFO - 10:07:41: ...  67%|██████▋   | 20/30 [00:02<00:00, 11.10 it/sec, obj=-602]
        INFO - 10:07:42: ...  73%|███████▎  | 22/30 [00:03<00:00,  9.93 it/sec, obj=-273]
        INFO - 10:07:42: ...  83%|████████▎ | 25/30 [00:03<00:00,  9.32 it/sec, obj=-624]
        INFO - 10:07:42: ...  90%|█████████ | 27/30 [00:03<00:00,  8.72 it/sec, obj=-383]
        INFO - 10:07:42: ...  97%|█████████▋| 29/30 [00:03<00:00,  8.17 it/sec, obj=-485]
        INFO - 10:07:43: ... 100%|██████████| 30/30 [00:03<00:00,  8.02 it/sec, obj=-405]
        INFO - 10:07:43: Optimization result:
        INFO - 10:07:43:    Optimizer info:
        INFO - 10:07:43:       Status: None
        INFO - 10:07:43:       Message: None
        INFO - 10:07:43:       Number of calls to the objective function by the optimizer: 30
        INFO - 10:07:43:    Solution:
        INFO - 10:07:43:       The solution is feasible.
        INFO - 10:07:43:       Objective: -485.49220045924955
        INFO - 10:07:43:       Standardized constraints:
        INFO - 10:07:43:          g_1 = [-0.11350951 -0.10812292 -0.1045109  -0.10204971 -0.10028641 -0.01838903
        INFO - 10:07:43:  -0.22161097]
        INFO - 10:07:43:          g_2 = -0.02400000000000002
        INFO - 10:07:43:          g_3 = [-0.33063157 -0.66936843 -0.73821755 -0.07789536]
        INFO - 10:07:43:       Design space:
        INFO - 10:07:43:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:07:43:       | name     | lower_bound |        value        | upper_bound | type  |
        INFO - 10:07:43:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:07:43:       | x_shared |     0.01    | 0.05400000000000001 |     0.09    | float |
        INFO - 10:07:43:       | x_shared |    30000    |        46500        |    60000    | float |
        INFO - 10:07:43:       | x_shared |     1.4     |  1.686666666666667  |     1.8     | float |
        INFO - 10:07:43:       | x_shared |     2.5     |         5.2         |     8.5     | float |
        INFO - 10:07:43:       | x_shared |      40     |         66.5        |      70     | float |
        INFO - 10:07:43:       | x_shared |     500     |  583.3333333333334  |     1500    | float |
        INFO - 10:07:43:       | x_1      |     0.1     |        0.185        |     0.4     | float |
        INFO - 10:07:43:       | x_1      |     0.75    |  0.9416666666666667 |     1.25    | float |
        INFO - 10:07:43:       | x_2      |     0.75    |        0.775        |     1.25    | float |
        INFO - 10:07:43:       | x_3      |     0.1     |        0.115        |      1      | float |
        INFO - 10:07:43:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:07:43: *** End DOEScenario execution (time: 0:00:03.755126) ***

    {'eval_jac': False, 'algo': 'lhs', 'algo_options': {'criterion': 'center', 'eval_jac': True, 'n_processes': 4, 'seed': 1, 'n_samples': 30}, 'n_samples': 30}



.. GENERATED FROM PYTHON SOURCE LINES 118-124

.. 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 126-128

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

.. GENERATED FROM PYTHON SOURCE LINES 128-130

.. code-block:: default

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




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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_001.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_002.png
         :alt: Evolution of the objective value
         :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: Distance to the optimum
         :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: Hessian diagonal approximation
         :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

 Out:

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f8e603a6100>



.. GENERATED FROM PYTHON SOURCE LINES 131-138

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the API function
   :meth:`~gemseo.api.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 140-142

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

.. GENERATED FROM PYTHON SOURCE LINES 142-146

.. code-block:: default

    scenario.post_process(
        "ScatterPlotMatrix", show=False, save=False, 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

 Out:

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7f8e611e2c10>



.. GENERATED FROM PYTHON SOURCE LINES 147-149

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

.. GENERATED FROM PYTHON SOURCE LINES 149-152

.. code-block:: default

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



.. 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

 Out:

 .. code-block:: none

        INFO - 10:07:46: Detected 10 correlations > 0.95





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

   **Total running time of the script:** ( 0 minutes  7.399 seconds)


.. _sphx_glr_download_examples_formulations_plot_doe_sobieski_mdf_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_doe_sobieski_mdf_example.py <plot_doe_sobieski_mdf_example.py>`



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

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


.. only:: html

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

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