.. 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

        :ref:`Go to the end <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:: Python


    from __future__ import annotations

    from copy import deepcopy
    from os import name as os_name

    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import execute_post
    from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace








.. GENERATED FROM PYTHON SOURCE LINES 36-43

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 43-50

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 51-59

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 59-61

.. code-block:: Python

    design_space = SobieskiDesignSpace()








.. GENERATED FROM PYTHON SOURCE LINES 62-63

Then, we build a sub-scenario for each strongly coupled disciplines.

.. GENERATED FROM PYTHON SOURCE LINES 65-68

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

.. GENERATED FROM PYTHON SOURCE LINES 68-76

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 77-80

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

.. GENERATED FROM PYTHON SOURCE LINES 80-89

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 90-94

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 94-103

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 104-108

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 108-121

.. code-block:: Python

    sub_disciplines = [sc_prop, sc_aero, sc_str, mission]
    system_scenario = create_scenario(
        sub_disciplines,
        "y_4",
        design_space.filter("x_shared", copy=True),
        parallel_scenarios=False,
        reset_x0_before_opt=True,
        scenario_type="DOE",
        formulation_name="BiLevel",
        save_opt_history="True",
        naming="UUID",
    )








.. GENERATED FROM PYTHON SOURCE LINES 122-126

.. note::

   Setting ``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 128-143

.. tip::

   When running BiLevel scenarios, it is interesting to access the optimization
   history of the sub-scenarios for each system iteration. By default, the setting
   ``keep_opt_history`` is set to ``True``. This allows you to store in memory the
   databases of the sub-scenarios (see the last section of this example for more
   details).
   In some cases, storing the databases in memory can take up too much space and cause
   performance issues. In these cases, set ``keep_opt_history=False`` and save the
   databases to the disk using ``save_opt_history=True``. If your sub-scenarios are
   running in parallel, and you are saving the optimization histories to the disk, set
   the ``naming`` setting to ``"UUID"``, which is multiprocessing-safe.
   The setting ``keep_opt_history`` will not work if the sub-scenarios are running in
   parallel because the databases are not copied from the sub-processes to the main
   process. In this case you shall always save the optimization history to the disk.

.. GENERATED FROM PYTHON SOURCE LINES 143-147

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 148-153

.. 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 153-157

.. code-block:: Python


    for sub_sc in sub_disciplines[0:3]:
        sub_sc.set_algorithm(algo_name="L-BFGS-B", max_iter=20)








.. GENERATED FROM PYTHON SOURCE LINES 158-165

Visualize the XDSM
^^^^^^^^^^^^^^^^^^
Generate the XDSM on the fly:

- ``log_workflow_status=True`` will log the status of the workflow  in the console,
- ``save_html`` (default ``True``) will generate a self-contained HTML file,
  that can be automatically opened using ``show_html=True``.

.. GENERATED FROM PYTHON SOURCE LINES 165-167

.. code-block:: Python

    system_scenario.xdsmize(save_html=False)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

        <script type="text/javascript">
            document.addEventListener('DOMContentLoaded', () => {
              const mdo = {
      "root": {
        "nodes": [
          {
            "id": "Opt",
            "name": "DOE",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "MDAJacobi",
            "type": "mda",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "SobieskiPropulsion",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis3",
            "name": "SobieskiAerodynamics",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis4",
            "name": "SobieskiStructure",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis5",
            "name": "PropulsionScenario_scn-1-1",
            "type": "mdo",
            "subxdsm": "PropulsionScenario_scn-1-1",
            "status": "DONE"
          },
          {
            "id": "Dis6",
            "name": "AerodynamicsScenario_scn-1-2",
            "type": "mdo",
            "subxdsm": "AerodynamicsScenario_scn-1-2",
            "status": "DONE"
          },
          {
            "id": "Dis7",
            "name": "StructureScenario_scn-1-3",
            "type": "mdo",
            "subxdsm": "StructureScenario_scn-1-3",
            "status": "DONE"
          },
          {
            "id": "Dis8",
            "name": "MDAJacobi",
            "type": "mda",
            "status": "DONE"
          },
          {
            "id": "Dis12",
            "name": "SobieskiMission",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_shared^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "y_4^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis8",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_shared"
          },
          {
            "from": "Opt",
            "to": "Dis12",
            "name": "x_shared"
          },
          {
            "from": "Dis12",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "y_32^*, y_31^*, g_3^*, y_3^*, y_34^*"
          },
          {
            "from": "Dis3",
            "to": "_U_",
            "name": "y_21^*, y_23^*, y_24^*, g_2^*, y_2^*"
          },
          {
            "from": "Dis4",
            "to": "_U_",
            "name": "y_1^*, y_11^*, y_14^*, g_1^*, y_12^*"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "y_32^*, y_31^*, g_3^*, y_3^*, y_34^*"
          },
          {
            "from": "Dis3",
            "to": "_U_",
            "name": "y_21^*, y_23^*, y_24^*, g_2^*, y_2^*"
          },
          {
            "from": "Dis4",
            "to": "_U_",
            "name": "y_1^*, y_11^*, y_14^*, g_1^*, y_12^*"
          },
          {
            "from": "Dis12",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Dis1",
            "to": "Dis5",
            "name": "y_23"
          },
          {
            "from": "Dis1",
            "to": "Dis6",
            "name": "y_12, y_32"
          },
          {
            "from": "Dis1",
            "to": "Dis7",
            "name": "y_21, y_31"
          },
          {
            "from": "Dis1",
            "to": "Dis8",
            "name": "y_12, y_21, y_23, y_31, y_32"
          },
          {
            "from": "Dis1",
            "to": "Dis12",
            "name": "y_14, y_24, y_34"
          },
          {
            "from": "Dis5",
            "to": "Dis1",
            "name": "x_3, y_31, y_32"
          },
          {
            "from": "Dis5",
            "to": "Dis6",
            "name": "y_32"
          },
          {
            "from": "Dis5",
            "to": "Dis7",
            "name": "y_31"
          },
          {
            "from": "Dis5",
            "to": "Dis8",
            "name": "x_3, y_31, y_32"
          },
          {
            "from": "Dis5",
            "to": "Dis12",
            "name": "y_34"
          },
          {
            "from": "Dis6",
            "to": "Dis1",
            "name": "x_2, y_21, y_23"
          },
          {
            "from": "Dis6",
            "to": "Dis5",
            "name": "y_23"
          },
          {
            "from": "Dis6",
            "to": "Dis7",
            "name": "y_21"
          },
          {
            "from": "Dis6",
            "to": "Dis8",
            "name": "x_2, y_21, y_23"
          },
          {
            "from": "Dis6",
            "to": "Dis12",
            "name": "y_24"
          },
          {
            "from": "Dis7",
            "to": "Dis1",
            "name": "x_1, y_12"
          },
          {
            "from": "Dis7",
            "to": "Dis6",
            "name": "y_12"
          },
          {
            "from": "Dis7",
            "to": "Dis8",
            "name": "x_1, y_12"
          },
          {
            "from": "Dis7",
            "to": "Dis12",
            "name": "y_14"
          },
          {
            "from": "Dis8",
            "to": "Dis1",
            "name": "y_12, y_21, y_23, y_31, y_32"
          },
          {
            "from": "Dis8",
            "to": "Dis5",
            "name": "y_23"
          },
          {
            "from": "Dis8",
            "to": "Dis6",
            "name": "y_12, y_32"
          },
          {
            "from": "Dis8",
            "to": "Dis7",
            "name": "y_21, y_31"
          },
          {
            "from": "Dis8",
            "to": "Dis12",
            "name": "y_14, y_24, y_34"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "y_23"
          },
          {
            "from": "Dis2",
            "to": "Dis1",
            "name": "y_31, y_32"
          },
          {
            "from": "Dis1",
            "to": "Dis3",
            "name": "y_12, y_32"
          },
          {
            "from": "Dis3",
            "to": "Dis1",
            "name": "y_21, y_23"
          },
          {
            "from": "Dis1",
            "to": "Dis4",
            "name": "y_21, y_31"
          },
          {
            "from": "Dis4",
            "to": "Dis1",
            "name": "y_12"
          },
          {
            "from": "Dis8",
            "to": "Dis2",
            "name": "y_23"
          },
          {
            "from": "Dis2",
            "to": "Dis8",
            "name": "y_31, y_32"
          },
          {
            "from": "Dis8",
            "to": "Dis3",
            "name": "y_12, y_32"
          },
          {
            "from": "Dis3",
            "to": "Dis8",
            "name": "y_21, y_23"
          },
          {
            "from": "Dis8",
            "to": "Dis4",
            "name": "y_21, y_31"
          },
          {
            "from": "Dis4",
            "to": "Dis8",
            "name": "y_12"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              [
                {
                  "parallel": [
                    "Dis2",
                    "Dis3",
                    "Dis4"
                  ]
                }
              ],
              "Dis5",
              "Dis6",
              "Dis7",
              "Dis8",
              [
                {
                  "parallel": [
                    "Dis2",
                    "Dis3",
                    "Dis4"
                  ]
                }
              ],
              "Dis12"
            ]
          ]
        ],
        "optpb": ""
      },
      "PropulsionScenario_scn-1-1": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "SobieskiPropulsion",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_3^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "y_34^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_3"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_34"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_32^*, y_31^*, g_3^*, y_3^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_34"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": ""
      },
      "AerodynamicsScenario_scn-1-2": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "SobieskiAerodynamics",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_2^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "-y_24^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_2"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_24"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_21^*, y_23^*, g_2^*, y_2^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_24"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": ""
      },
      "StructureScenario_scn-1-3": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "SobieskiStructure",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_1^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "-y_11^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_1"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_11"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_1^*, y_14^*, g_1^*, y_12^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_11"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": ""
      }
    };
              const config = {
                labelizer: {
                    ellipsis: 5,
                    subSupScript: false,
                    showLinkNbOnly: false,
                },
                layout: {
                    origin: { x: 50, y: 20 },
                    cellsize: { w: 150, h: 50 },
                    padding: 10,
                },
                withDefaultDriver: true,
                withTitleTooltip: true,
              };
              xdsmjs.XDSMjs(config).createXdsm(mdo);
            });
        </script>
        <div class='xdsm-toolbar'></div><div class='xdsm2'></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 168-173

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 175-182

.. warning::
   The multiprocessing option has some limitations on Windows.
   Due to problems with sphinx, we disable it in this example.
   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 182-187

.. code-block:: Python

    n_processes = 1 if os_name == "nt" else 4
    system_scenario.execute(algo_name="PYDOE_LHS", n_samples=30, n_processes=n_processes)

    system_scenario.print_execution_metrics()





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

 .. code-block:: none

        INFO - 16:24:06: *** Start DOEScenario execution ***
        INFO - 16:24:06: DOEScenario
        INFO - 16:24:06:    Disciplines: AerodynamicsScenario PropulsionScenario SobieskiMission StructureScenario
        INFO - 16:24:06:    MDO formulation: BiLevel
        INFO - 16:24:06: Optimization problem:
        INFO - 16:24:06:    minimize y_4(x_shared)
        INFO - 16:24:06:    with respect to x_shared
        INFO - 16:24:06:    over the design space:
        INFO - 16:24:06:       +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:06:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 16:24:06:       +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:06:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:24:06:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:24:06:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:24:06:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:24:06:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:24:06:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:24:06:       +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:06: Solving optimization problem with algorithm PYDOE_LHS:
        INFO - 16:24:06: Running DOE in parallel on n_processes = 4
        INFO - 16:24:06:      3%|▎         | 1/30 [00:00<00:06,  4.78 it/sec, feas=True, obj=247]
        INFO - 16:24:06:      7%|▋         | 2/30 [00:00<00:03,  7.83 it/sec, feas=True, obj=485]
        INFO - 16:24:06:     10%|█         | 3/30 [00:00<00:02, 10.51 it/sec, feas=True, obj=388]
        INFO - 16:24:06:     13%|█▎        | 4/30 [00:00<00:01, 13.33 it/sec, feas=True, obj=350]
        INFO - 16:24:06:     17%|█▋        | 5/30 [00:00<00:01, 14.83 it/sec, feas=True, obj=621]
        INFO - 16:24:06:     20%|██        | 6/30 [00:00<00:01, 14.68 it/sec, feas=True, obj=458]
        INFO - 16:24:06:     23%|██▎       | 7/30 [00:00<00:01, 16.47 it/sec, feas=True, obj=495]
        INFO - 16:24:07:     27%|██▋       | 8/30 [00:00<00:01, 16.52 it/sec, feas=True, obj=549]
        INFO - 16:24:07:     30%|███       | 9/30 [00:00<00:01, 18.15 it/sec, feas=True, obj=367]
        INFO - 16:24:07:     33%|███▎      | 10/30 [00:00<00:01, 17.67 it/sec, feas=True, obj=892]
        INFO - 16:24:07:     37%|███▋      | 11/30 [00:00<00:00, 19.26 it/sec, feas=True, obj=918]
        INFO - 16:24:07:     40%|████      | 12/30 [00:00<00:00, 18.89 it/sec, feas=True, obj=1.27e+3]
        INFO - 16:24:07:     43%|████▎     | 13/30 [00:00<00:00, 19.35 it/sec, feas=True, obj=354]
        INFO - 16:24:07:     47%|████▋     | 14/30 [00:00<00:00, 20.20 it/sec, feas=True, obj=415]
        INFO - 16:24:07:     50%|█████     | 15/30 [00:00<00:00, 19.91 it/sec, feas=True, obj=337]
        INFO - 16:24:07:     53%|█████▎    | 16/30 [00:00<00:00, 20.14 it/sec, feas=True, obj=2.27e+3]
        INFO - 16:24:07:     57%|█████▋    | 17/30 [00:00<00:00, 21.31 it/sec, feas=True, obj=1.2e+3]
        INFO - 16:24:07:     60%|██████    | 18/30 [00:00<00:00, 20.85 it/sec, feas=True, obj=380]
        INFO - 16:24:07:     63%|██████▎   | 19/30 [00:00<00:00, 21.21 it/sec, feas=True, obj=394]
        INFO - 16:24:07:     67%|██████▋   | 20/30 [00:00<00:00, 21.82 it/sec, feas=True, obj=829]
        INFO - 16:24:07:     70%|███████   | 21/30 [00:00<00:00, 22.14 it/sec, feas=True, obj=832]
        INFO - 16:24:07:     73%|███████▎  | 22/30 [00:01<00:00, 21.80 it/sec, feas=True, obj=1.04e+3]
        INFO - 16:24:07:     77%|███████▋  | 23/30 [00:01<00:00, 22.48 it/sec, feas=True, obj=1.21e+3]
        INFO - 16:24:07:     80%|████████  | 24/30 [00:01<00:00, 22.56 it/sec, feas=True, obj=640]
        INFO - 16:24:07:     83%|████████▎ | 25/30 [00:01<00:00, 21.95 it/sec, feas=True, obj=1.19e+3]
        INFO - 16:24:07:     87%|████████▋ | 26/30 [00:01<00:00, 21.96 it/sec, feas=True, obj=470]
        INFO - 16:24:07:     90%|█████████ | 27/30 [00:01<00:00, 22.58 it/sec, feas=True, obj=293]
        INFO - 16:24:07:     93%|█████████▎| 28/30 [00:01<00:00, 23.39 it/sec, feas=True, obj=484]
        INFO - 16:24:07:     97%|█████████▋| 29/30 [00:01<00:00, 23.48 it/sec, feas=True, obj=647]
        INFO - 16:24:07:    100%|██████████| 30/30 [00:01<00:00, 23.69 it/sec, feas=True, obj=952]
        INFO - 16:24:07: Optimization result:
        INFO - 16:24:07:    Optimizer info:
        INFO - 16:24:07:       Status: None
        INFO - 16:24:07:       Message: None
        INFO - 16:24:07:    Solution:
        INFO - 16:24:07:       Objective: 246.89549262432172
        INFO - 16:24:07:       Design space:
        INFO - 16:24:07:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:07:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 16:24:07:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:07:          | x_shared[0] |     0.01    | 0.01316336056367379 |     0.09    | float |
        INFO - 16:24:07:          | x_shared[1] |    30000    |  39053.36254511708  |    60000    | float |
        INFO - 16:24:07:          | x_shared[2] |     1.4     |  1.759600266521177  |     1.8     | float |
        INFO - 16:24:07:          | x_shared[3] |     2.5     |  8.352983911532561  |     8.5     | float |
        INFO - 16:24:07:          | x_shared[4] |      40     |  66.23984775914758  |      70     | float |
        INFO - 16:24:07:          | x_shared[5] |     500     |  1232.319858277323  |     1500    | float |
        INFO - 16:24:07:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:07: *** End DOEScenario execution ***
        INFO - 16:24:07: The discipline counters are disabled.




.. GENERATED FROM PYTHON SOURCE LINES 188-194

.. 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 196-201

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.to_dataset` will allow you to export
your results to a :class:`.Dataset`, the basic |g| class to store data.

.. GENERATED FROM PYTHON SOURCE LINES 201-203

.. code-block:: Python

    dataset = system_scenario.to_dataset("a_name_for_my_dataset")








.. GENERATED FROM PYTHON SOURCE LINES 204-206

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

.. GENERATED FROM PYTHON SOURCE LINES 206-208

.. code-block:: Python

    system_scenario.post_process(post_name="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: Evolution of the 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 0x72a4d56037a0>



.. GENERATED FROM PYTHON SOURCE LINES 209-211

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

.. GENERATED FROM PYTHON SOURCE LINES 211-218

.. code-block:: Python

    system_scenario.post_process(
        post_name="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_plot_matrix.ScatterPlotMatrix object at 0x72a4d8779250>



.. GENERATED FROM PYTHON SOURCE LINES 219-221

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

.. GENERATED FROM PYTHON SOURCE LINES 221-223

.. code-block:: Python

    system_scenario.post_process(post_name="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.parallel_coordinates.ParallelCoordinates object at 0x72a4d5ba7080>



.. GENERATED FROM PYTHON SOURCE LINES 224-226

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

.. GENERATED FROM PYTHON SOURCE LINES 226-228

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 16:24:09: Detected 0 correlations > 0.95

    <gemseo.post.correlations.Correlations object at 0x72a4e3c95880>



.. GENERATED FROM PYTHON SOURCE LINES 229-237

Plot the structure optimization histories of the 2 first iterations
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The code below will not work if you ran the system scenario with ``n_processes`` > 1.
Indeed, parallel execution of sub-scenarios prevents us to save the databases from
each sub-process to the main process. If you ran the system scenario with many
processes, you can still save the databases to the disk with
``save_opt_history=True`` and ``naming="UUID"``. Refer to the formulation settings for
more information.

.. GENERATED FROM PYTHON SOURCE LINES 237-242

.. code-block:: Python

    struct_databases = system_scenario.formulation.scenario_adapters[2].databases
    for database in struct_databases[:2]:
        opt_problem = deepcopy(sc_str.formulation.optimization_problem)
        opt_problem.database = database
        execute_post(opt_problem, post_name="OptHistoryView", save=False, show=True)








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

   **Total running time of the script:** (0 minutes 2.759 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-jupyter

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

    .. 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-zip

      :download:`Download zipped: plot_doe_sobieski_bilevel_example.zip <plot_doe_sobieski_bilevel_example.zip>`


.. only:: html

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

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