.. 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 24-36

.. code-block:: default

    from __future__ import annotations

    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

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 37-44

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

.. GENERATED FROM PYTHON SOURCE LINES 44-53

.. code-block:: default

    propu, aero, mission, struct = create_discipline(
        [
            "SobieskiPropulsion",
            "SobieskiAerodynamics",
            "SobieskiMission",
            "SobieskiStructure",
        ]
    )








.. GENERATED FROM PYTHON SOURCE LINES 54-62

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 62-64

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 65-68

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 68-77

.. 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 78-81

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

.. GENERATED FROM PYTHON SOURCE LINES 81-89

.. 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 90-93

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

.. GENERATED FROM PYTHON SOURCE LINES 93-102

.. 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 103-107

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 107-116

.. 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 117-121

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 121-133

.. 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 134-138

.. 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 138-142

.. code-block:: default


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








.. GENERATED FROM PYTHON SOURCE LINES 143-148

.. 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 148-152

.. 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 153-158

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 160-170

.. 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 170-180

.. 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

 .. code-block:: none

        INFO - 16:58:02:  
        INFO - 16:58:02: *** Start DOEScenario execution ***
        INFO - 16:58:02: DOEScenario
        INFO - 16:58:02:    Disciplines: AerodynamicsScenario PropulsionScenario SobieskiMission StructureScenario
        INFO - 16:58:02:    MDO formulation: BiLevel
        INFO - 16:58:02: Optimization problem:
        INFO - 16:58:02:    minimize y_4(x_shared)
        INFO - 16:58:02:    with respect to x_shared
        INFO - 16:58:02:    over the design space:
        INFO - 16:58:02:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:58:02:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 16:58:02:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:58:02:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:58:02:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:58:02:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:58:02:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:58:02:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:58:02:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:58:02:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:58:02: Solving optimization problem with algorithm lhs:
        INFO - 16:58:02: ...   0%|          | 0/30 [00:00<?, ?it]
        INFO - 16:58:02: Running DOE in parallel on n_processes = 4
       ERROR - 16:58:03: Failed to execute task indexed 0
       ERROR - 16:58:03: math domain error
        INFO - 16:58:03: ...   3%|▎         | 1/30 [00:00<00:25,  1.13 it/sec, obj=485]
        INFO - 16:58:03: ...   7%|▋         | 2/30 [00:01<00:15,  1.84 it/sec, obj=388]
        INFO - 16:58:04: ...  10%|█         | 3/30 [00:01<00:09,  2.70 it/sec, obj=350]
        INFO - 16:58:04: ...  13%|█▎        | 4/30 [00:01<00:08,  3.12 it/sec, obj=621]
        INFO - 16:58:04: ...  17%|█▋        | 5/30 [00:01<00:07,  3.46 it/sec, obj=495]
        INFO - 16:58:04: ...  20%|██        | 6/30 [00:01<00:05,  4.00 it/sec, obj=458]
        INFO - 16:58:04: ...  23%|██▎       | 7/30 [00:01<00:05,  4.31 it/sec, obj=549]
        INFO - 16:58:04: ...  27%|██▋       | 8/30 [00:01<00:04,  4.70 it/sec, obj=367]
        INFO - 16:58:04: ...  30%|███       | 9/30 [00:01<00:04,  4.91 it/sec, obj=892]
        INFO - 16:58:04: ...  33%|███▎      | 10/30 [00:02<00:04,  4.90 it/sec, obj=918]
        INFO - 16:58:04: ...  37%|███▋      | 11/30 [00:02<00:03,  5.37 it/sec, obj=1.27e+3]
        INFO - 16:58:05: ...  40%|████      | 12/30 [00:02<00:03,  5.36 it/sec, obj=415]
        INFO - 16:58:05: ...  43%|████▎     | 13/30 [00:02<00:02,  5.70 it/sec, obj=354]
        INFO - 16:58:05: ...  47%|████▋     | 14/30 [00:02<00:02,  5.79 it/sec, obj=337]
        INFO - 16:58:05: ...  50%|█████     | 15/30 [00:02<00:02,  6.16 it/sec, obj=1.2e+3]
        INFO - 16:58:05: ...  53%|█████▎    | 16/30 [00:02<00:02,  5.99 it/sec, obj=2.27e+3]
        INFO - 16:58:05: ...  57%|█████▋    | 17/30 [00:02<00:02,  5.86 it/sec, obj=380]
        INFO - 16:58:05: ...  60%|██████    | 18/30 [00:02<00:01,  6.19 it/sec, obj=829]
        INFO - 16:58:05: ...  63%|██████▎   | 19/30 [00:02<00:01,  6.52 it/sec, obj=394]
        INFO - 16:58:05: ...  67%|██████▋   | 20/30 [00:02<00:01,  6.70 it/sec, obj=832]
        INFO - 16:58:06: ...  70%|███████   | 21/30 [00:03<00:01,  6.30 it/sec, obj=640]
        INFO - 16:58:06: ...  73%|███████▎  | 22/30 [00:03<00:01,  6.59 it/sec, obj=1.21e+3]
        INFO - 16:58:06: ...  77%|███████▋  | 23/30 [00:03<00:01,  6.84 it/sec, obj=1.04e+3]
        INFO - 16:58:06: ...  80%|████████  | 24/30 [00:03<00:00,  6.98 it/sec, obj=1.19e+3]
        INFO - 16:58:06: ...  83%|████████▎ | 25/30 [00:03<00:00,  6.69 it/sec, obj=484]
        INFO - 16:58:06: ...  87%|████████▋ | 26/30 [00:03<00:00,  6.82 it/sec, obj=470]
        INFO - 16:58:06: ...  90%|█████████ | 27/30 [00:03<00:00,  7.05 it/sec, obj=647]
        INFO - 16:58:06: ...  93%|█████████▎| 28/30 [00:03<00:00,  7.26 it/sec, obj=293]
        INFO - 16:58:06: ...  97%|█████████▋| 29/30 [00:03<00:00,  7.39 it/sec, obj=952]
        INFO - 16:58:06: Optimization result:
        INFO - 16:58:06:    Optimizer info:
        INFO - 16:58:06:       Status: None
        INFO - 16:58:06:       Message: None
        INFO - 16:58:06:       Number of calls to the objective function by the optimizer: 30
        INFO - 16:58:06:    Solution:
        INFO - 16:58:06:       Objective: 292.91178826079175
        INFO - 16:58:06:       Design space: 
        INFO - 16:58:06:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:58:06:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 16:58:06:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:58:06:       | x_shared[0] |     0.01    | 0.04666883227502976 |     0.09    | float |
        INFO - 16:58:06:       | x_shared[1] |    30000    |  37789.27932845149  |    60000    | float |
        INFO - 16:58:06:       | x_shared[2] |     1.4     |  1.667044086506944  |     1.8     | float |
        INFO - 16:58:06:       | x_shared[3] |     2.5     |   8.29772323088249  |     8.5     | float |
        INFO - 16:58:06:       | x_shared[4] |      40     |  42.41730480236713  |      70     | float |
        INFO - 16:58:06:       | x_shared[5] |     500     |  724.9388551459947  |     1500    | float |
        INFO - 16:58:06:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:58:06: *** End DOEScenario execution (time: 0:00:03.972317) ***
        INFO - 16:58:06: Scenario Execution Statistics
        INFO - 16:58:06:    Discipline: PropulsionScenario
        INFO - 16:58:06:       Executions number: 30
        INFO - 16:58:06:       Execution time: 0.8666399659978197 s
        INFO - 16:58:06:       Linearizations number: 0
        INFO - 16:58:06:    Discipline: AerodynamicsScenario
        INFO - 16:58:06:       Executions number: 30
        INFO - 16:58:06:       Execution time: 1.116203335002865 s
        INFO - 16:58:06:       Linearizations number: 0
        INFO - 16:58:06:    Discipline: StructureScenario
        INFO - 16:58:06:       Executions number: 30
        INFO - 16:58:06:       Execution time: 4.326108792000923 s
        INFO - 16:58:06:       Linearizations number: 0
        INFO - 16:58:06:    Discipline: SobieskiMission
        INFO - 16:58:06:       Executions number: 29
        INFO - 16:58:06:       Execution time: 0.0017370240020682104 s
        INFO - 16:58:06:       Linearizations number: 0
        INFO - 16:58:06:    Total number of executions calls: 119
        INFO - 16:58:06:    Total number of linearizations: 0




.. GENERATED FROM PYTHON SOURCE LINES 181-187

.. 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 189-196

Exporting the problem data.
^^^^^^^^^^^^^^^^^^^^^^^^^^^
After the execution of the scenario, you may want to export your data to use it
elsewhere. The method :meth:`.Scenario.export_to_dataset` will allow you to export
your results to a :class:`.Dataset`, the basic |g| class to store data.
From a dataset, you can even obtain a Pandas dataframe with the method
:meth:`~.Dataset.export_to_dataframe`:

.. GENERATED FROM PYTHON SOURCE LINES 196-199

.. code-block:: default

    dataset = system_scenario.export_to_dataset("a_name_for_my_dataset")
    dataframe = dataset.export_to_dataframe()








.. GENERATED FROM PYTHON SOURCE LINES 200-202

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

.. GENERATED FROM PYTHON SOURCE LINES 202-204

.. code-block:: default

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




.. 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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7fbc391f6550>



.. GENERATED FROM PYTHON SOURCE LINES 205-207

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

.. GENERATED FROM PYTHON SOURCE LINES 207-214

.. code-block:: default

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




.. 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

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7fbc3932ac70>



.. GENERATED FROM PYTHON SOURCE LINES 215-217

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

.. GENERATED FROM PYTHON SOURCE LINES 217-219

.. code-block:: default

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




.. 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

 .. code-block:: none


    <gemseo.post.para_coord.ParallelCoordinates object at 0x7fbc3932a640>



.. GENERATED FROM PYTHON SOURCE LINES 220-222

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

.. GENERATED FROM PYTHON SOURCE LINES 222-223

.. code-block:: default

    system_scenario.post_process("Correlations", save=False, show=True)




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

 .. code-block:: none

        INFO - 16:58:09: Detected 0 correlations > 0.95

    <gemseo.post.correlations.Correlations object at 0x7fbc6b4c94c0>




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

   **Total running time of the script:** ( 0 minutes  7.130 seconds)


.. _sphx_glr_download_examples_formulations_plot_doe_sobieski_bilevel_example.py:

.. only:: html

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