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

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

.. _sphx_glr_examples_formulations_plot_sobieski_bilevel_example.py:


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

.. GENERATED FROM PYTHON SOURCE LINES 24-40

.. code-block:: Python


    from __future__ import annotations

    from copy import deepcopy
    from logging import WARNING

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import execute_post
    from gemseo.algos.opt.nlopt.settings.nlopt_cobyla_settings import NLOPT_COBYLA_Settings
    from gemseo.algos.opt.scipy_local.settings.slsqp import SLSQP_Settings
    from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 41-48

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 48-55

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 56-64

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 64-66

.. code-block:: Python

    design_space = SobieskiDesignSpace()








.. GENERATED FROM PYTHON SOURCE LINES 67-70

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

.. GENERATED FROM PYTHON SOURCE LINES 70-89

.. code-block:: Python


    slsqp_settings = SLSQP_Settings(
        max_iter=30,
        xtol_rel=1e-7,
        xtol_abs=1e-7,
        ftol_rel=1e-7,
        ftol_abs=1e-7,
        ineq_tolerance=1e-4,
    )

    cobyla_settings = NLOPT_COBYLA_Settings(
        max_iter=50,
        xtol_rel=1e-7,
        xtol_abs=1e-7,
        ftol_rel=1e-7,
        ftol_abs=1e-7,
        ineq_tolerance=1e-4,
    )








.. GENERATED FROM PYTHON SOURCE LINES 90-93

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

.. GENERATED FROM PYTHON SOURCE LINES 93-103

.. code-block:: Python

    sc_prop = create_scenario(
        propu,
        "y_34",
        design_space.filter("x_3", copy=True),
        name="PropulsionScenario",
        formulation_name="DisciplinaryOpt",
    )
    sc_prop.set_algorithm(slsqp_settings)
    sc_prop.add_constraint("g_3", constraint_type="ineq")








.. GENERATED FROM PYTHON SOURCE LINES 104-107

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

.. GENERATED FROM PYTHON SOURCE LINES 107-118

.. 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",
    )
    sc_aero.set_algorithm(slsqp_settings)
    sc_aero.add_constraint("g_2", constraint_type="ineq")








.. GENERATED FROM PYTHON SOURCE LINES 119-123

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 123-134

.. code-block:: Python

    sc_str = create_scenario(
        struct,
        "y_11",
        design_space.filter("x_1", copy=True),
        name="StructureScenario",
        maximize_objective=True,
        formulation_name="DisciplinaryOpt",
    )
    sc_str.add_constraint("g_1", constraint_type="ineq")
    sc_str.set_algorithm(slsqp_settings)








.. GENERATED FROM PYTHON SOURCE LINES 135-139

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 139-153

.. code-block:: Python

    system_scenario = create_scenario(
        [sc_prop, sc_aero, sc_str, mission],
        "y_4",
        design_space.filter("x_shared", copy=True),
        apply_cstr_tosub_scenarios=False,
        parallel_scenarios=False,
        multithread_scenarios=True,
        main_mda_settings={"tolerance": 1e-14, "max_mda_iter": 30},
        maximize_objective=True,
        sub_scenarios_log_level=WARNING,
        formulation_name="BiLevel",
    )
    system_scenario.add_constraint(["g_1", "g_2", "g_3"], constraint_type="ineq")





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

 .. code-block:: none

     WARNING - 11:48:27: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
     WARNING - 11:48:27: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.




.. GENERATED FROM PYTHON SOURCE LINES 154-164

.. 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``.

.. GENERATED FROM PYTHON SOURCE LINES 166-173

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 173-175

.. code-block:: Python

    system_scenario.xdsmize(save_html=False, pdf_build=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": "Optimizer",
            "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": [
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            "from": "_U_",
            "to": "Opt",
            "name": "x_shared^(0)"
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            "from": "Opt",
            "to": "_U_",
            "name": "-y_4^*, g_1_g_2_g_3^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_shared"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_1, g_2, g_3"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x_shared"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g_3"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "x_shared"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "g_2"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_shared"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1"
          },
          {
            "from": "Opt",
            "to": "Dis8",
            "name": "x_shared"
          },
          {
            "from": "Dis8",
            "to": "Opt",
            "name": "g_1, g_2, g_3"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x_shared"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g_3"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "x_shared"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "g_2"
          },
          {
            "from": "Opt",
            "to": "Dis4",
            "name": "x_shared"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1"
          },
          {
            "from": "Opt",
            "to": "Dis12",
            "name": "x_shared"
          },
          {
            "from": "Dis12",
            "to": "Opt",
            "name": "y_4"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "y_32^*, y_31^*, y_3^*, y_34^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g_3"
          },
          {
            "from": "Dis3",
            "to": "_U_",
            "name": "y_21^*, y_23^*, y_24^*, y_2^*"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "g_2"
          },
          {
            "from": "Dis4",
            "to": "_U_",
            "name": "y_1^*, y_11^*, y_14^*, y_12^*"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "y_32^*, y_31^*, y_3^*, y_34^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g_3"
          },
          {
            "from": "Dis3",
            "to": "_U_",
            "name": "y_21^*, y_23^*, y_24^*, y_2^*"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "g_2"
          },
          {
            "from": "Dis4",
            "to": "_U_",
            "name": "y_1^*, y_11^*, y_14^*, y_12^*"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "g_1"
          },
          {
            "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)"
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          {
            "from": "Opt",
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            "name": "y_34^*, g_3^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_3"
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          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_3, y_34"
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        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": ""
      },
      "AerodynamicsScenario_scn-1-2": {
        "nodes": [
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            "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)"
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          {
            "from": "Opt",
            "to": "_U_",
            "name": "-y_24^*, g_2^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_2"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_2, y_24"
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          {
            "from": "Dis1",
            "to": "_U_",
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        ],
        "workflow": [
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        ],
        "optpb": ""
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        "nodes": [
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            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
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            "name": "SobieskiStructure",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
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            "to": "Opt",
            "name": "x_1^(0)"
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            "to": "Dis1",
            "name": "x_1"
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            "to": "Opt",
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            "to": "_U_",
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            "from": "Dis1",
            "to": "Opt",
            "name": "y_11, g_1"
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            [
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          ]
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      }
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              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 176-178

Execute the main scenario
^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 178-180

.. code-block:: Python

    system_scenario.execute(cobyla_settings)





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

 .. code-block:: none

        INFO - 11:48:27: *** Start MDOScenario execution ***
        INFO - 11:48:27: MDOScenario
        INFO - 11:48:27:    Disciplines: AerodynamicsScenario PropulsionScenario SobieskiMission StructureScenario
        INFO - 11:48:27:    MDO formulation: BiLevel
        INFO - 11:48:27: Optimization problem:
        INFO - 11:48:27:    minimize -y_4(x_shared)
        INFO - 11:48:27:    with respect to x_shared
        INFO - 11:48:27:    subject to constraints:
        INFO - 11:48:27:       g_1_g_2_g_3(x_shared) <= 0
        INFO - 11:48:27:    over the design space:
        INFO - 11:48:27:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:48:27:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 11:48:27:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:48:27:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 11:48:27:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 11:48:27:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 11:48:27:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 11:48:27:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 11:48:27:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 11:48:27:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:48:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 11:48:27:      2%|▏         | 1/50 [00:00<00:07,  6.51 it/sec, obj=-553]
     WARNING - 11:48:27: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:27:       The solution is not feasible.
        INFO - 11:48:27:      4%|▍         | 2/50 [00:00<00:07,  6.59 it/sec, obj=-574]
     WARNING - 11:48:27: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:27:       The solution is not feasible.
        INFO - 11:48:27:      6%|▌         | 3/50 [00:00<00:07,  6.68 it/sec, obj=-813]
     WARNING - 11:48:28: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:28:       The solution is not feasible.
        INFO - 11:48:28:      8%|▊         | 4/50 [00:00<00:07,  6.51 it/sec, obj=-751]
     WARNING - 11:48:28: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:28:       The solution is not feasible.
        INFO - 11:48:28:     10%|█         | 5/50 [00:00<00:07,  5.93 it/sec, obj=-734]
     WARNING - 11:48:28: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:28:       The solution is not feasible.
        INFO - 11:48:28:     12%|█▏        | 6/50 [00:00<00:07,  6.11 it/sec, obj=-977]
     WARNING - 11:48:28: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:28:       The solution is not feasible.
        INFO - 11:48:28:     14%|█▍        | 7/50 [00:01<00:07,  5.90 it/sec, obj=-1.05e+3]
     WARNING - 11:48:28: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:28:       The solution is not feasible.
        INFO - 11:48:28:     16%|█▌        | 8/50 [00:01<00:07,  5.84 it/sec, obj=-1.67e+3]
        INFO - 11:48:29:     18%|█▊        | 9/50 [00:01<00:07,  5.83 it/sec, obj=-1.73e+3]
     WARNING - 11:48:29: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:29:       The solution is not feasible.
        INFO - 11:48:29:     20%|██        | 10/50 [00:01<00:06,  5.76 it/sec, obj=-2.59e+3]
        INFO - 11:48:29:     22%|██▏       | 11/50 [00:01<00:06,  5.76 it/sec, obj=-2.94e+3]
     WARNING - 11:48:29: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:29:       The solution is not feasible.
        INFO - 11:48:29:     24%|██▍       | 12/50 [00:02<00:06,  5.67 it/sec, obj=-2.39e+3]
        INFO - 11:48:29:     26%|██▌       | 13/50 [00:02<00:06,  5.67 it/sec, obj=-2.66e+3]
     WARNING - 11:48:29: MDAJacobi has reached its maximum number of iterations, but the normalized residual norm 4.00581977874369e-13 is still above the tolerance 1e-14.
        INFO - 11:48:30:     28%|██▊       | 14/50 [00:02<00:06,  5.64 it/sec, obj=-2.54e+3]
     WARNING - 11:48:30: MDAJacobi has reached its maximum number of iterations, but the normalized residual norm 2.6870836615612218e-14 is still above the tolerance 1e-14.
        INFO - 11:48:30:     30%|███       | 15/50 [00:02<00:06,  5.51 it/sec, obj=-2.51e+3]
     WARNING - 11:48:30: MDAJacobi has reached its maximum number of iterations, but the normalized residual norm 2.6870836615612218e-14 is still above the tolerance 1e-14.
        INFO - 11:48:30:     32%|███▏      | 16/50 [00:02<00:06,  5.47 it/sec, obj=-2.2e+3]
        INFO - 11:48:30:     34%|███▍      | 17/50 [00:03<00:06,  5.50 it/sec, obj=-2.76e+3]
        INFO - 11:48:30:     36%|███▌      | 18/50 [00:03<00:05,  5.46 it/sec, obj=-2.47e+3]
     WARNING - 11:48:30: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:30:       The solution is not feasible.
        INFO - 11:48:31:     38%|███▊      | 19/50 [00:03<00:05,  5.46 it/sec, obj=-2.97e+3]
        INFO - 11:48:31:     40%|████      | 20/50 [00:03<00:05,  5.51 it/sec, obj=-2.51e+3]
        INFO - 11:48:31:     42%|████▏     | 21/50 [00:03<00:05,  5.57 it/sec, obj=-2.85e+3]
        INFO - 11:48:31:     44%|████▍     | 22/50 [00:03<00:05,  5.57 it/sec, obj=-2.99e+3]
        INFO - 11:48:31:     46%|████▌     | 23/50 [00:04<00:04,  5.62 it/sec, obj=-2.7e+3]
        INFO - 11:48:31:     48%|████▊     | 24/50 [00:04<00:04,  5.64 it/sec, obj=-3.1e+3]
        INFO - 11:48:31:     50%|█████     | 25/50 [00:04<00:04,  5.71 it/sec, obj=-2.8e+3]
        INFO - 11:48:32:     52%|█████▏    | 26/50 [00:04<00:04,  5.68 it/sec, obj=-3.07e+3]
        INFO - 11:48:32:     54%|█████▍    | 27/50 [00:04<00:04,  5.74 it/sec, obj=-3.15e+3]
     WARNING - 11:48:32: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:32:       The solution is not feasible.
        INFO - 11:48:32:     56%|█████▌    | 28/50 [00:04<00:03,  5.68 it/sec, obj=-2.8e+3]
     WARNING - 11:48:32: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:32:       The solution is not feasible.
     WARNING - 11:48:32: MDAJacobi has reached its maximum number of unsuccessful iterations, but the normalized residual norm 2.6870836615612218e-14 is still above the tolerance 1e-14.
        INFO - 11:48:32:     58%|█████▊    | 29/50 [00:05<00:03,  5.69 it/sec, obj=-3.14e+3]
     WARNING - 11:48:32: Optimization found no feasible point; the least infeasible point is selected.
     WARNING - 11:48:32:       The solution is not feasible.
        INFO - 11:48:32:     60%|██████    | 30/50 [00:05<00:03,  5.74 it/sec, obj=-3.12e+3]
     WARNING - 11:48:32: MDAJacobi has reached its maximum number of unsuccessful iterations, but the normalized residual norm 1.7359275648513364e-14 is still above the tolerance 1e-14.
        INFO - 11:48:32:     62%|██████▏   | 31/50 [00:05<00:03,  5.79 it/sec, obj=-3.12e+3]
     WARNING - 11:48:33: MDAJacobi has reached its maximum number of unsuccessful iterations, but the normalized residual norm 2.6870836615612218e-14 is still above the tolerance 1e-14.
        INFO - 11:48:33:     64%|██████▍   | 32/50 [00:05<00:03,  5.83 it/sec, obj=-3.12e+3]
        INFO - 11:48:33:     66%|██████▌   | 33/50 [00:05<00:02,  5.88 it/sec, obj=-3.22e+3]
        INFO - 11:48:33:     68%|██████▊   | 34/50 [00:05<00:02,  5.93 it/sec, obj=-3.12e+3]
        INFO - 11:48:33:     70%|███████   | 35/50 [00:05<00:02,  5.96 it/sec, obj=-3.13e+3]
        INFO - 11:48:33:     72%|███████▏  | 36/50 [00:05<00:02,  6.01 it/sec, obj=-3.11e+3]
        INFO - 11:48:33:     74%|███████▍  | 37/50 [00:06<00:02,  6.06 it/sec, obj=-3.14e+3]
        INFO - 11:48:33:     76%|███████▌  | 38/50 [00:06<00:01,  6.10 it/sec, obj=-3.16e+3]
        INFO - 11:48:33:     78%|███████▊  | 39/50 [00:06<00:01,  6.13 it/sec, obj=-3.2e+3]
     WARNING - 11:48:33: MDAJacobi has reached its maximum number of unsuccessful iterations, but the normalized residual norm 1.7359275648513364e-14 is still above the tolerance 1e-14.
        INFO - 11:48:34:     80%|████████  | 40/50 [00:06<00:01,  6.17 it/sec, obj=-3.16e+3]
        INFO - 11:48:34:     82%|████████▏ | 41/50 [00:06<00:01,  6.21 it/sec, obj=-3.16e+3]
        INFO - 11:48:34:     84%|████████▍ | 42/50 [00:06<00:01,  6.25 it/sec, obj=-3.15e+3]
        INFO - 11:48:34:     86%|████████▌ | 43/50 [00:06<00:01,  6.29 it/sec, obj=-3.17e+3]
        INFO - 11:48:34:     88%|████████▊ | 44/50 [00:06<00:00,  6.32 it/sec, obj=-3.18e+3]
        INFO - 11:48:34:     90%|█████████ | 45/50 [00:07<00:00,  6.36 it/sec, obj=-3.19e+3]
     WARNING - 11:48:34: MDAJacobi has reached its maximum number of unsuccessful iterations, but the normalized residual norm 1.7359275648513364e-14 is still above the tolerance 1e-14.
        INFO - 11:48:34:     92%|█████████▏| 46/50 [00:07<00:00,  6.37 it/sec, obj=-3.2e+3]
        INFO - 11:48:34:     94%|█████████▍| 47/50 [00:07<00:00,  6.40 it/sec, obj=-3.21e+3]
        INFO - 11:48:34:     96%|█████████▌| 48/50 [00:07<00:00,  6.43 it/sec, obj=-3.22e+3]
     WARNING - 11:48:35: MDAJacobi has reached its maximum number of iterations, but the normalized residual norm 2.6870836615612218e-14 is still above the tolerance 1e-14.
        INFO - 11:48:35:     98%|█████████▊| 49/50 [00:07<00:00,  6.44 it/sec, obj=-3.23e+3]
        INFO - 11:48:35:    100%|██████████| 50/50 [00:07<00:00,  6.47 it/sec, obj=-3.24e+3]
        INFO - 11:48:35: Optimization result:
        INFO - 11:48:35:    Optimizer info:
        INFO - 11:48:35:       Status: None
        INFO - 11:48:35:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
        INFO - 11:48:35:       Number of calls to the objective function by the optimizer: 52
        INFO - 11:48:35:    Solution:
        INFO - 11:48:35:       The solution is feasible.
        INFO - 11:48:35:       Objective: -3238.8281256729097
        INFO - 11:48:35:       Standardized constraints:
        INFO - 11:48:35:          g_1_g_2_g_3 = [-3.41837669e-12 -1.26719778e-02 -2.55059750e-02 -3.52857360e-02
        INFO - 11:48:35:  -4.26719778e-02 -1.80140386e-01 -5.98596144e-02  0.00000000e+00
        INFO - 11:48:35:  -7.67083754e-01 -2.32916246e-01  0.00000000e+00 -1.83208648e-01]
        INFO - 11:48:35:       Design space:
        INFO - 11:48:35:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 11:48:35:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 11:48:35:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 11:48:35:          | x_shared[0] |     0.01    | 0.05999999999999999 |     0.09    | float |
        INFO - 11:48:35:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 11:48:35:          | x_shared[2] |     1.4     |  1.400356170737944  |     1.8     | float |
        INFO - 11:48:35:          | x_shared[3] |     2.5     |  3.729810789921248  |     8.5     | float |
        INFO - 11:48:35:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 11:48:35:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 11:48:35:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 11:48:35: *** End MDOScenario execution (time: 0:00:07.733525) ***




.. GENERATED FROM PYTHON SOURCE LINES 181-184

Plot the history of the MDA residuals
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
For the first MDA:

.. GENERATED FROM PYTHON SOURCE LINES 184-186

.. code-block:: Python

    system_scenario.formulation.mda1.plot_residual_history(save=False, show=True)




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_001.png
   :alt: MDAJacobi: residual plot
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 187-188

For the second MDA:

.. GENERATED FROM PYTHON SOURCE LINES 188-190

.. code-block:: Python

    system_scenario.formulation.mda2.plot_residual_history(save=False, show=True)




.. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_002.png
   :alt: MDAJacobi: residual plot
   :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 191-193

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

.. GENERATED FROM PYTHON SOURCE LINES 193-195

.. 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_sobieski_bilevel_example_003.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_004.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_005.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_006.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_006.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7048fb9950a0>



.. GENERATED FROM PYTHON SOURCE LINES 196-198

Plot the structure optimization histories of the 2 first iterations
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 198-206

.. 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)

    for disc in [propu, aero, mission, struct]:
        print(f"{disc.name}: {disc.execution_statistics.n_executions} calls.")



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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_007.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_008.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_009.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_009.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_010.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_010.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_011.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_011.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_012.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_012.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_013.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_013.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_014.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_014.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    SobieskiPropulsion: 1637 calls.
    SobieskiAerodynamics: 1760 calls.
    SobieskiMission: 50 calls.
    SobieskiStructure: 1941 calls.





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

   **Total running time of the script:** (0 minutes 10.731 seconds)


.. _sphx_glr_download_examples_formulations_plot_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_sobieski_bilevel_example.ipynb <plot_sobieski_bilevel_example.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_sobieski_bilevel_example.py <plot_sobieski_bilevel_example.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

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


.. only:: html

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

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