.. 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 26-35

.. code-block:: default

    from __future__ import division, unicode_literals

    from matplotlib import pyplot as plt

    from gemseo.api import configure_logger, create_discipline, create_scenario
    from gemseo.problems.sobieski.core import SobieskiProblem

    configure_logger()





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

 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:`~gemseo.problems.sobieski.wrappers.SobieskiPropulsion`,
:class:`~gemseo.problems.sobieski.wrappers.SobieskiAerodynamics`,
:class:`~gemseo.problems.sobieski.wrappers.SobieskiMission`
and :class:`~gemseo.problems.sobieski.wrappers.SobieskiStructure`.

.. GENERATED FROM PYTHON SOURCE LINES 43-52

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 53-61

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 61-63

.. code-block:: default

    design_space = SobieskiProblem().read_design_space()








.. GENERATED FROM PYTHON SOURCE LINES 64-66

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

.. GENERATED FROM PYTHON SOURCE LINES 66-75

.. 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 76-78

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

.. GENERATED FROM PYTHON SOURCE LINES 78-81

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 82-85

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

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: default

    scenario.set_differentiation_method("user")








.. GENERATED FROM PYTHON SOURCE LINES 88-93

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 95-104

.. warning::
   The multiprocessing option has some limitations on Windows.
   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

.. code-block:: default

    n_processes = 4








.. GENERATED FROM PYTHON SOURCE LINES 107-109

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

.. GENERATED FROM PYTHON SOURCE LINES 109-119

.. code-block:: default

    algo_options = {
        "criterion": "center",
        # Evaluate gradient of the MDA
        # with coupled adjoint
        "eval_jac": True,
        # Run in parallel on 4 processors
        "n_processes": n_processes,
    }
    run_inputs = {"n_samples": 30, "algo": "lhs", "algo_options": algo_options}








.. GENERATED FROM PYTHON SOURCE LINES 120-123

.. warning::
   When running a parallel DOE on Windows, the execution must be
   protected to avoid recursive calls:

.. GENERATED FROM PYTHON SOURCE LINES 123-126

.. code-block:: default

    if __name__ == "__main__":
        scenario.execute(run_inputs)





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

 Out:

 .. code-block:: none

        INFO - 12:58:58:  
        INFO - 12:58:58: *** Start DOE Scenario execution ***
        INFO - 12:58:58: DOEScenario
        INFO - 12:58:58:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
        INFO - 12:58:58:    MDOFormulation: MDF
        INFO - 12:58:58:    Algorithm: lhs
        INFO - 12:58:58: Optimization problem:
        INFO - 12:58:58:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
        INFO - 12:58:58:    With respect to: x_shared, x_1, x_2, x_3
        INFO - 12:58:58:    Subject to constraints:
        INFO - 12:58:58:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 12:58:58:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 12:58:58:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 12:58:58: DOE sampling:   0%|          | 0/30 [00:00<?, ?it]
        INFO - 12:58:58: Running DOE in parallel on n_processes = 4
        INFO - 12:58:59: DOE sampling:   3%|▎         | 1/30 [00:00<00:00, 81.10 it/sec, obj=285]
        INFO - 12:58:59: DOE sampling:  10%|█         | 3/30 [00:00<00:00, 59.62 it/sec, obj=567]
        INFO - 12:58:59: DOE sampling:  13%|█▎        | 4/30 [00:00<00:00, 46.60 it/sec, obj=344]
        INFO - 12:58:59: DOE sampling:  17%|█▋        | 5/30 [00:00<00:00, 39.02 it/sec, obj=429]
        INFO - 12:58:59: DOE sampling:  23%|██▎       | 7/30 [00:00<00:00, 33.74 it/sec, obj=235]
        INFO - 12:58:59: DOE sampling:  30%|███       | 9/30 [00:01<00:00, 25.44 it/sec, obj=306]
        INFO - 12:59:00: DOE sampling:  43%|████▎     | 13/30 [00:01<00:00, 20.72 it/sec, obj=495]
        INFO - 12:59:00: DOE sampling:  50%|█████     | 15/30 [00:01<00:00, 18.87 it/sec, obj=621]
        INFO - 12:59:00: DOE sampling:  57%|█████▋    | 17/30 [00:01<00:00, 17.56 it/sec, obj=1.07e+3]
        INFO - 12:59:00: DOE sampling:  63%|██████▎   | 19/30 [00:02<00:00, 14.96 it/sec, obj=414]
        INFO - 12:59:00: DOE sampling:  70%|███████   | 21/30 [00:02<00:00, 14.13 it/sec, obj=247]
        INFO - 12:59:00: DOE sampling:  77%|███████▋  | 23/30 [00:02<00:00, 13.40 it/sec, obj=273]
        INFO - 12:59:01: DOE sampling:  83%|████████▎ | 25/30 [00:02<00:00, 12.09 it/sec, obj=606]
        INFO - 12:59:01: DOE sampling:  93%|█████████▎| 28/30 [00:02<00:00, 11.17 it/sec, obj=351]
        INFO - 12:59:01: DOE sampling: 100%|██████████| 30/30 [00:02<00:00, 10.76 it/sec, obj=405]
        INFO - 12:59:01: Optimization result:
        INFO - 12:59:01: Objective value = 485.4922996873357
        INFO - 12:59:01: The result is feasible.
        INFO - 12:59:01: Status: None
        INFO - 12:59:01: Optimizer message: None
        INFO - 12:59:01: Number of calls to the objective function by the optimizer: 30
        INFO - 12:59:01: Constraints values:
        INFO - 12:59:01:    g_1 = [-0.11350951 -0.10812292 -0.1045109  -0.10204971 -0.10028641 -0.01838903
        INFO - 12:59:01:  -0.22161097]
        INFO - 12:59:01:    g_2 = -0.02400000000000002
        INFO - 12:59:01:    g_3 = [-0.33063134 -0.66936866 -0.73821755 -0.07789536]
        INFO - 12:59:01: Design space:
        INFO - 12:59:01: +----------+-------------+---------------------+-------------+-------+
        INFO - 12:59:01: | name     | lower_bound |        value        | upper_bound | type  |
        INFO - 12:59:01: +----------+-------------+---------------------+-------------+-------+
        INFO - 12:59:01: | x_shared |     0.01    | 0.05400000000000001 |     0.09    | float |
        INFO - 12:59:01: | x_shared |    30000    |        46500        |    60000    | float |
        INFO - 12:59:01: | x_shared |     1.4     |  1.686666666666667  |     1.8     | float |
        INFO - 12:59:01: | x_shared |     2.5     |         5.2         |     8.5     | float |
        INFO - 12:59:01: | x_shared |      40     |         66.5        |      70     | float |
        INFO - 12:59:01: | x_shared |     500     |  583.3333333333334  |     1500    | float |
        INFO - 12:59:01: | x_1      |     0.1     |        0.185        |     0.4     | float |
        INFO - 12:59:01: | x_1      |     0.75    |  0.9416666666666667 |     1.25    | float |
        INFO - 12:59:01: | x_2      |     0.75    |        0.775        |     1.25    | float |
        INFO - 12:59:01: | x_3      |     0.1     |        0.115        |      1      | float |
        INFO - 12:59:01: +----------+-------------+---------------------+-------------+-------+
        INFO - 12:59:01: *** DOE Scenario run terminated ***




.. GENERATED FROM PYTHON SOURCE LINES 127-133

.. 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 135-137

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

.. GENERATED FROM PYTHON SOURCE LINES 137-139

.. code-block:: default

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




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


    *

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

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_002.png
          :alt: Evolution of the objective value
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_003.png
          :alt: Distance to the optimum
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_004.png
          :alt: Hessian diagonal approximation
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_005.png
          :alt: Evolution of the inequality constraints
          :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7fb74d006160>



.. GENERATED FROM PYTHON SOURCE LINES 140-147

.. 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 149-151

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

.. GENERATED FROM PYTHON SOURCE LINES 151-155

.. code-block:: default

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




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


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

 Out:

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7fb746621be0>



.. GENERATED FROM PYTHON SOURCE LINES 156-158

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

.. GENERATED FROM PYTHON SOURCE LINES 158-161

.. code-block:: default

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



.. image:: /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
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

        INFO - 12:59:04: Detected 10 correlations > 0.95





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

   **Total running time of the script:** ( 0 minutes  6.573 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>`_