.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/formulations/plot_doe_sobieski_bilevel_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_bilevel_example.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_formulations_plot_doe_sobieski_bilevel_example.py:


BiLevel-based DOE on the Sobieski SSBJ test case
================================================

.. GENERATED FROM PYTHON SOURCE LINES 24-35

.. code-block:: default

    from copy import deepcopy
    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 36-43

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 43-52

.. code-block:: default

    propu, aero, mission, struct = 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().design_space








.. GENERATED FROM PYTHON SOURCE LINES 64-67

Then, we build a sub-scenario for each strongly coupled disciplines,
using the following algorithm, maximum number of iterations and
algorithm options:

.. GENERATED FROM PYTHON SOURCE LINES 67-75

.. code-block:: default

    algo_options = {
        "xtol_rel": 1e-7,
        "xtol_abs": 1e-7,
        "ftol_rel": 1e-7,
        "ftol_abs": 1e-7,
        "ineq_tolerance": 1e-4,
    }
    sub_sc_opts = {"max_iter": 30, "algo": "SLSQP", "algo_options": algo_options}







.. GENERATED FROM PYTHON SOURCE LINES 76-79

Build a sub-scenario for Propulsion
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This sub-scenario will minimize SFC.

.. GENERATED FROM PYTHON SOURCE LINES 79-87

.. code-block:: default

    sc_prop = create_scenario(
        propu,
        "DisciplinaryOpt",
        "y_34",
        design_space=deepcopy(design_space).filter("x_3"),
        name="PropulsionScenario",
    )








.. GENERATED FROM PYTHON SOURCE LINES 88-91

Build a sub-scenario for Aerodynamics
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This sub-scenario will minimize L/D.

.. GENERATED FROM PYTHON SOURCE LINES 91-100

.. code-block:: default

    sc_aero = create_scenario(
        aero,
        "DisciplinaryOpt",
        "y_24",
        deepcopy(design_space).filter("x_2"),
        name="AerodynamicsScenario",
        maximize_objective=True,
    )








.. GENERATED FROM PYTHON SOURCE LINES 101-105

Build a sub-scenario for Structure
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This sub-scenario will maximize
log(aircraft total weight / (aircraft total weight - fuel weight)).

.. GENERATED FROM PYTHON SOURCE LINES 105-114

.. code-block:: default

    sc_str = create_scenario(
        struct,
        "DisciplinaryOpt",
        "y_11",
        deepcopy(design_space).filter("x_1"),
        name="StructureScenario",
        maximize_objective=True,
    )








.. GENERATED FROM PYTHON SOURCE LINES 115-119

Build a scenario for Mission
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This scenario is based on the three previous sub-scenarios and on the
Mission and aims to maximize the range (Breguet).

.. GENERATED FROM PYTHON SOURCE LINES 119-131

.. code-block:: default

    sub_disciplines = [sc_prop, sc_aero, sc_str] + [mission]
    design_space = deepcopy(design_space).filter("x_shared")
    system_scenario = create_scenario(
        sub_disciplines,
        "BiLevel",
        "y_4",
        design_space,
        parallel_scenarios=False,
        reset_x0_before_opt=True,
        scenario_type="DOE",
    )








.. GENERATED FROM PYTHON SOURCE LINES 132-136

.. note::

   Setting :code:`reset_x0_before_opt=True` is mandatory when doing a DOE
   in parallel. If we want reproducible results, don't reuse previous xopt.

.. GENERATED FROM PYTHON SOURCE LINES 136-140

.. code-block:: default


    system_scenario.formulation.mda1.warm_start = False
    system_scenario.formulation.mda2.warm_start = False








.. GENERATED FROM PYTHON SOURCE LINES 141-146

.. note::

   This is mandatory when doing a DOE in parallel if we want always exactly
   the same results, don't warm start mda1 to have exactly the same
   process whatever the execution order and process dispatch.

.. GENERATED FROM PYTHON SOURCE LINES 146-150

.. code-block:: default


    for sub_sc in sub_disciplines[0:3]:
        sub_sc.default_inputs = {"max_iter": 20, "algo": "L-BFGS-B"}








.. GENERATED FROM PYTHON SOURCE LINES 151-156

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 158-168

.. warning::
   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 168-178

.. code-block:: default

    system_scenario.execute(
        {
            "n_samples": 30,
            "algo": "lhs",
            "algo_options": {"n_processes": 1 if os_name == "nt" else 4},
        }
    )

    system_scenario.print_execution_metrics()





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

 Out:

 .. code-block:: none

        INFO - 10:05:20:  
        INFO - 10:05:20: *** Start DOEScenario execution ***
        INFO - 10:05:20: DOEScenario
        INFO - 10:05:20:    Disciplines: PropulsionScenario AerodynamicsScenario StructureScenario SobieskiMission
        INFO - 10:05:20:    MDO formulation: BiLevel
        INFO - 10:05:20: Optimization problem:
        INFO - 10:05:20:    minimize y_4(x_shared)
        INFO - 10:05:20:    with respect to x_shared
        INFO - 10:05:20:    over the design space:
        INFO - 10:05:20:    +----------+-------------+-------+-------------+-------+
        INFO - 10:05:20:    | name     | lower_bound | value | upper_bound | type  |
        INFO - 10:05:20:    +----------+-------------+-------+-------------+-------+
        INFO - 10:05:20:    | x_shared |     0.01    |  0.05 |     0.09    | float |
        INFO - 10:05:20:    | x_shared |    30000    | 45000 |    60000    | float |
        INFO - 10:05:20:    | x_shared |     1.4     |  1.6  |     1.8     | float |
        INFO - 10:05:20:    | x_shared |     2.5     |  5.5  |     8.5     | float |
        INFO - 10:05:20:    | x_shared |      40     |   55  |      70     | float |
        INFO - 10:05:20:    | x_shared |     500     |  1000 |     1500    | float |
        INFO - 10:05:20:    +----------+-------------+-------+-------------+-------+
        INFO - 10:05:20: Solving optimization problem with algorithm lhs:
        INFO - 10:05:20: ...   0%|          | 0/30 [00:00<?, ?it]
        INFO - 10:05:20: Running DOE in parallel on n_processes = 4
       ERROR - 10:05:21: Failed to execute task indexed 0
       ERROR - 10:05:21: math domain error
        INFO - 10:05:21: ...   3%|▎         | 1/30 [00:00<00:00, 31.02 it/sec, obj=485]
        INFO - 10:05:21: ...   7%|▋         | 2/30 [00:01<00:01, 27.63 it/sec, obj=388]
        INFO - 10:05:21: ...  10%|█         | 3/30 [00:01<00:01, 25.27 it/sec, obj=350]
        INFO - 10:05:21: ...  13%|█▎        | 4/30 [00:01<00:01, 22.14 it/sec, obj=621]
        INFO - 10:05:22: ...  17%|█▋        | 5/30 [00:01<00:01, 18.42 it/sec, obj=458]
        INFO - 10:05:22: ...  27%|██▋       | 8/30 [00:01<00:01, 16.14 it/sec, obj=549]
        INFO - 10:05:22: ...  30%|███       | 9/30 [00:02<00:01, 14.48 it/sec, obj=918]
        INFO - 10:05:22: ...  37%|███▋      | 11/30 [00:02<00:01, 13.19 it/sec, obj=1.27e+3]
        INFO - 10:05:23: ...  40%|████      | 12/30 [00:02<00:01, 12.38 it/sec, obj=354]
        INFO - 10:05:23: ...  47%|████▋     | 14/30 [00:02<00:01, 11.22 it/sec, obj=1.2e+3]
        INFO - 10:05:23: ...  53%|█████▎    | 16/30 [00:02<00:01, 10.26 it/sec, obj=2.27e+3]
        INFO - 10:05:23: ...  60%|██████    | 18/30 [00:03<00:01,  9.48 it/sec, obj=380]
        INFO - 10:05:23: ...  67%|██████▋   | 20/30 [00:03<00:01,  8.84 it/sec, obj=832]
        INFO - 10:05:24: ...  70%|███████   | 21/30 [00:03<00:01,  8.46 it/sec, obj=1.04e+3]
        INFO - 10:05:24: ...  73%|███████▎  | 22/30 [00:03<00:00,  8.18 it/sec, obj=1.21e+3]
        INFO - 10:05:24: ...  80%|████████  | 24/30 [00:03<00:00,  7.59 it/sec, obj=470]
        INFO - 10:05:24: ...  87%|████████▋ | 26/30 [00:04<00:00,  7.03 it/sec, obj=484]
        INFO - 10:05:24: ...  97%|█████████▋| 29/30 [00:04<00:00,  6.85 it/sec, obj=647]
        INFO - 10:05:24: Optimization result:
        INFO - 10:05:24:    Optimizer info:
        INFO - 10:05:24:       Status: None
        INFO - 10:05:24:       Message: None
        INFO - 10:05:24:       Number of calls to the objective function by the optimizer: 30
        INFO - 10:05:24:    Solution:
        INFO - 10:05:24:       Objective: 292.91178826079175
        INFO - 10:05:24:       Design space:
        INFO - 10:05:24:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:05:24:       | name     | lower_bound |        value        | upper_bound | type  |
        INFO - 10:05:24:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:05:24:       | x_shared |     0.01    | 0.04666883227502976 |     0.09    | float |
        INFO - 10:05:24:       | x_shared |    30000    |  37789.27932845149  |    60000    | float |
        INFO - 10:05:24:       | x_shared |     1.4     |  1.667044086506944  |     1.8     | float |
        INFO - 10:05:24:       | x_shared |     2.5     |   8.29772323088249  |     8.5     | float |
        INFO - 10:05:24:       | x_shared |      40     |  42.41730480236713  |      70     | float |
        INFO - 10:05:24:       | x_shared |     500     |  724.9388551459947  |     1500    | float |
        INFO - 10:05:24:       +----------+-------------+---------------------+-------------+-------+
        INFO - 10:05:24: *** End DOEScenario execution (time: 0:00:04.389215) ***
        INFO - 10:05:24: Scenario Execution Statistics
        INFO - 10:05:24:    Discipline: PropulsionScenario
        INFO - 10:05:24:       Executions number: 30
        INFO - 10:05:24:       Execution time: 0.9347774299967568 s
        INFO - 10:05:24:       Linearizations number: 0
        INFO - 10:05:24:    Discipline: AerodynamicsScenario
        INFO - 10:05:24:       Executions number: 30
        INFO - 10:05:24:       Execution time: 1.1256235389882931 s
        INFO - 10:05:24:       Linearizations number: 0
        INFO - 10:05:24:    Discipline: StructureScenario
        INFO - 10:05:24:       Executions number: 30
        INFO - 10:05:24:       Execution time: 4.6455857699984335 s
        INFO - 10:05:24:       Linearizations number: 0
        INFO - 10:05:24:    Discipline: SobieskiMission
        INFO - 10:05:24:       Executions number: 29
        INFO - 10:05:24:       Execution time: 0.0017069160239771008 s
        INFO - 10:05:24:       Linearizations number: 0
        INFO - 10:05:24:    Total number of executions calls: 119
        INFO - 10:05:24:    Total number of linearizations: 0




.. GENERATED FROM PYTHON SOURCE LINES 179-185

.. 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 187-189

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

.. GENERATED FROM PYTHON SOURCE LINES 189-191

.. code-block:: default

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




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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_001.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_002.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_003.png
         :alt: Distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_003.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7fdbe18cd6a0>



.. GENERATED FROM PYTHON SOURCE LINES 192-194

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

.. GENERATED FROM PYTHON SOURCE LINES 194-198

.. code-block:: default

    system_scenario.post_process(
        "ScatterPlotMatrix", show=False, save=False, variable_names=["y_4", "x_shared"]
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_004.png
   :alt: plot doe sobieski bilevel example
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_004.png
   :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7fdbf81057c0>



.. GENERATED FROM PYTHON SOURCE LINES 199-201

Plot parallel coordinates
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 201-203

.. code-block:: default

    system_scenario.post_process("ParallelCoordinates", show=False, save=False)




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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_005.png
         :alt: Design variables history colored by 'y_4' value
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_006.png
         :alt: Objective function and constraints history colored by 'y_4' value.
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_bilevel_example_006.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none


    <gemseo.post.para_coord.ParallelCoordinates object at 0x7fdbf8230d30>



.. GENERATED FROM PYTHON SOURCE LINES 204-206

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

.. GENERATED FROM PYTHON SOURCE LINES 206-209

.. code-block:: default

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




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

 Out:

 .. code-block:: none

        INFO - 10:05:28: Detected 0 correlations > 0.95





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

   **Total running time of the script:** ( 0 minutes  7.529 seconds)


.. _sphx_glr_download_examples_formulations_plot_doe_sobieski_bilevel_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_bilevel_example.py <plot_doe_sobieski_bilevel_example.py>`



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

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


.. only:: html

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

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