.. 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 26-39

.. code-block:: default

    from __future__ import division, unicode_literals

    from os import name as os_name

    from matplotlib import pyplot as plt

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

    IS_NT = os_name == "nt"

    configure_logger()





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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 40-47

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 47-56

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 57-65

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 65-67

.. code-block:: default

    design_space = SobieskiProblem().read_design_space()








.. GENERATED FROM PYTHON SOURCE LINES 68-70

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

.. GENERATED FROM PYTHON SOURCE LINES 70-78

.. 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 79-81

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

.. GENERATED FROM PYTHON SOURCE LINES 81-84

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 85-88

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

.. GENERATED FROM PYTHON SOURCE LINES 88-94

.. code-block:: default

    scenario.set_differentiation_method("user")

    n_processes = 4
    if IS_NT:  # Under windows, don't do multiprocessing
        n_processes = 1








.. GENERATED FROM PYTHON SOURCE LINES 95-97

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

.. GENERATED FROM PYTHON SOURCE LINES 97-108

.. 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}
    scenario.execute(run_inputs)





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

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 .. code-block:: none

        INFO - 09:24:48:  
        INFO - 09:24:48: *** Start DOE Scenario execution ***
        INFO - 09:24:48: DOEScenario
        INFO - 09:24:48:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
        INFO - 09:24:48:    MDOFormulation: MDF
        INFO - 09:24:48:    Algorithm: lhs
        INFO - 09:24:48: Optimization problem:
        INFO - 09:24:48:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
        INFO - 09:24:48:    With respect to: x_shared, x_1, x_2, x_3
        INFO - 09:24:48:    Subject to constraints:
        INFO - 09:24:48:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 09:24:48:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 09:24:48:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 09:24:48: DOE sampling:   0%|          | 0/30 [00:00<?, ?it]
        INFO - 09:24:48: Running DOE in parallel on n_processes = 4
        INFO - 09:24:52: DOE sampling:   0%|          | 0/30 [00:03<00:03,  8.20 it/sec]
        INFO - 09:24:52: Optimization result:
        INFO - 09:24:52: Objective value = 485.49220045924955
        INFO - 09:24:52: The result is feasible.
        INFO - 09:24:52: Status: None
        INFO - 09:24:52: Optimizer message: None
        INFO - 09:24:52: Number of calls to the objective function by the optimizer: 30
        INFO - 09:24:52: Constraints values w.r.t. 0: 
        INFO - 09:24:52:    g_1 = [-0.11350951 -0.10812292 -0.1045109  -0.10204971 -0.10028641 -0.01838903
        INFO - 09:24:52:  -0.22161097]
        INFO - 09:24:52:    g_2 = -0.02400000000000002
        INFO - 09:24:52:    g_3 = [-0.33063157 -0.66936843 -0.73821755 -0.07789536]
        INFO - 09:24:52: Design Space:
        INFO - 09:24:52: +----------+-------------+---------------------+-------------+-------+
        INFO - 09:24:52: | name     | lower_bound |        value        | upper_bound | type  |
        INFO - 09:24:52: +----------+-------------+---------------------+-------------+-------+
        INFO - 09:24:52: | x_shared |     0.01    | 0.05400000000000001 |     0.09    | float |
        INFO - 09:24:52: | x_shared |    30000    |        46500        |    60000    | float |
        INFO - 09:24:52: | x_shared |     1.4     |  1.686666666666667  |     1.8     | float |
        INFO - 09:24:52: | x_shared |     2.5     |         5.2         |     8.5     | float |
        INFO - 09:24:52: | x_shared |      40     |         66.5        |      70     | float |
        INFO - 09:24:52: | x_shared |     500     |  583.3333333333334  |     1500    | float |
        INFO - 09:24:52: | x_1      |     0.1     |        0.185        |     0.4     | float |
        INFO - 09:24:52: | x_1      |     0.75    |  0.9416666666666667 |     1.25    | float |
        INFO - 09:24:52: | x_2      |     0.75    |        0.775        |     1.25    | float |
        INFO - 09:24:52: | x_3      |     0.1     |        0.115        |      1      | float |
        INFO - 09:24:52: +----------+-------------+---------------------+-------------+-------+
        INFO - 09:24:52: *** DOE Scenario run terminated ***

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



.. GENERATED FROM PYTHON SOURCE LINES 109-111

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

.. GENERATED FROM PYTHON SOURCE LINES 111-113

.. 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 0x7f61b4c81eb0>



.. GENERATED FROM PYTHON SOURCE LINES 114-116

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

.. GENERATED FROM PYTHON SOURCE LINES 116-120

.. 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 0x7f61b4c81940>



.. GENERATED FROM PYTHON SOURCE LINES 121-123

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

.. GENERATED FROM PYTHON SOURCE LINES 123-126

.. 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 - 09:24:56: Detected 10 correlations > 0.95





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

   **Total running time of the script:** ( 0 minutes  8.856 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>`_