.. 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 24-38

.. 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.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 39-46

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 46-53

.. code-block:: Python

    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:: Python

    design_space = SobieskiDesignSpace()








.. 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 68-76

.. code-block:: Python

    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 77-80

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

.. GENERATED FROM PYTHON SOURCE LINES 80-90

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 91-94

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

.. GENERATED FROM PYTHON SOURCE LINES 94-105

.. code-block:: Python

    sc_aero = create_scenario(
        aero,
        "DisciplinaryOpt",
        "y_24",
        design_space.filter("x_2", copy=True),
        name="AerodynamicsScenario",
        maximize_objective=True,
    )
    sc_aero.default_inputs = sub_sc_opts
    sc_aero.add_constraint("g_2", constraint_type="ineq")








.. GENERATED FROM PYTHON SOURCE LINES 106-110

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 110-121

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 122-126

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 126-141

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 142-149

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 149-151

.. 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": "Optimizer",
            "type": "optimization"
          },
          {
            "id": "Dis1",
            "name": "MDAJacobi",
            "type": "mda"
          },
          {
            "id": "Dis2",
            "name": "SobieskiPropulsion",
            "type": "analysis"
          },
          {
            "id": "Dis3",
            "name": "SobieskiAerodynamics",
            "type": "analysis"
          },
          {
            "id": "Dis4",
            "name": "SobieskiStructure",
            "type": "analysis"
          },
          {
            "id": "Dis5",
            "name": "PropulsionScenario_scn-1-1",
            "type": "mdo",
            "subxdsm": "PropulsionScenario_scn-1-1"
          },
          {
            "id": "Dis6",
            "name": "AerodynamicsScenario_scn-1-2",
            "type": "mdo",
            "subxdsm": "AerodynamicsScenario_scn-1-2"
          },
          {
            "id": "Dis7",
            "name": "StructureScenario_scn-1-3",
            "type": "mdo",
            "subxdsm": "StructureScenario_scn-1-3"
          },
          {
            "id": "Dis8",
            "name": "MDAJacobi",
            "type": "mda"
          },
          {
            "id": "Dis12",
            "name": "SobieskiMission",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_shared^(0)"
          },
          {
            "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": "Optimization problem:\n   minimize -y_4(x_shared)\n   with respect to x_shared\n   subject to constraints:\n      g_1_g_2_g_3(x_shared) <= 0.0"
      },
      "PropulsionScenario_scn-1-1": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization"
          },
          {
            "id": "Dis1",
            "name": "SobieskiPropulsion",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_3^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "y_34^*, g_3^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_3"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_3, y_34"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_32^*, y_31^*, y_3^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_3, y_34"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": "Optimization problem:\n   minimize y_34(x_3)\n   with respect to x_3\n   subject to constraints:\n      g_3(x_3) <= 0.0"
      },
      "AerodynamicsScenario_scn-1-2": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization"
          },
          {
            "id": "Dis1",
            "name": "SobieskiAerodynamics",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_2^(0)"
          },
          {
            "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"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_21^*, y_23^*, y_2^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_24, g_2"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": "Optimization problem:\n   minimize -y_24(x_2)\n   with respect to x_2\n   subject to constraints:\n      g_2(x_2) <= 0.0"
      },
      "StructureScenario_scn-1-3": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization"
          },
          {
            "id": "Dis1",
            "name": "SobieskiStructure",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x_1^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "-y_11^*, g_1^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x_1"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "g_1, y_11"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "y_1^*, y_14^*, y_12^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "y_11, g_1"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": "Optimization problem:\n   minimize -y_11(x_1)\n   with respect to x_1\n   subject to constraints:\n      g_1(x_1) <= 0.0"
      }
    };
              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 152-154

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

.. GENERATED FROM PYTHON SOURCE LINES 154-160

.. code-block:: Python

    system_scenario.execute({
        "max_iter": 50,
        "algo": "NLOPT_COBYLA",
        "algo_options": algo_options,
    })





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

 .. code-block:: none

        INFO - 08:56:50:  
        INFO - 08:56:50: *** Start MDOScenario execution ***
        INFO - 08:56:50: MDOScenario
        INFO - 08:56:50:    Disciplines: AerodynamicsScenario PropulsionScenario SobieskiMission StructureScenario
        INFO - 08:56:50:    MDO formulation: BiLevel
        INFO - 08:56:50: Optimization problem:
        INFO - 08:56:50:    minimize -y_4(x_shared)
        INFO - 08:56:50:    with respect to x_shared
        INFO - 08:56:50:    subject to constraints:
        INFO - 08:56:50:       g_1_g_2_g_3(x_shared) <= 0.0
        INFO - 08:56:50:    over the design space:
        INFO - 08:56:50:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:56:50:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 08:56:50:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:56:50:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 08:56:50:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 08:56:50:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 08:56:50:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 08:56:50:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 08:56:50:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 08:56:50:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:56:50: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 08:56:50:      2%|▏         | 1/50 [00:00<00:16,  3.03 it/sec, obj=-553]
     WARNING - 08:56:50: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:50:       The solution is not feasible.
        INFO - 08:56:50:      4%|▍         | 2/50 [00:00<00:13,  3.45 it/sec, obj=-574]
     WARNING - 08:56:51: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:51:       The solution is not feasible.
        INFO - 08:56:51:      6%|▌         | 3/50 [00:00<00:12,  3.69 it/sec, obj=-813]
     WARNING - 08:56:51: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:51:       The solution is not feasible.
        INFO - 08:56:51:      8%|▊         | 4/50 [00:01<00:12,  3.78 it/sec, obj=-751]
     WARNING - 08:56:51: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:51:       The solution is not feasible.
        INFO - 08:56:51:     10%|█         | 5/50 [00:01<00:12,  3.57 it/sec, obj=-734]
     WARNING - 08:56:51: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:51:       The solution is not feasible.
        INFO - 08:56:51:     12%|█▏        | 6/50 [00:01<00:11,  3.70 it/sec, obj=-977]
     WARNING - 08:56:52: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:52:       The solution is not feasible.
        INFO - 08:56:52:     14%|█▍        | 7/50 [00:01<00:11,  3.69 it/sec, obj=-1.05e+3]
     WARNING - 08:56:52: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:52:       The solution is not feasible.
        INFO - 08:56:52:     16%|█▌        | 8/50 [00:02<00:11,  3.67 it/sec, obj=-1.67e+3]
        INFO - 08:56:52:     18%|█▊        | 9/50 [00:02<00:11,  3.68 it/sec, obj=-1.73e+3]
     WARNING - 08:56:52: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:52:       The solution is not feasible.
        INFO - 08:56:53:     20%|██        | 10/50 [00:02<00:11,  3.62 it/sec, obj=-2.59e+3]
        INFO - 08:56:53:     22%|██▏       | 11/50 [00:03<00:10,  3.63 it/sec, obj=-2.94e+3]
     WARNING - 08:56:53: MDAJacobi has reached its maximum number of iterations but the normed residual 2.189447656198491e-13 is still above the tolerance 1e-14.
        INFO - 08:56:53:     24%|██▍       | 12/50 [00:03<00:10,  3.51 it/sec, obj=-2.64e+3]
     WARNING - 08:56:53: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:53:       The solution is not feasible.
        INFO - 08:56:54:     26%|██▌       | 13/50 [00:03<00:10,  3.56 it/sec, obj=-2.85e+3]
     WARNING - 08:56:54: MDAJacobi has reached its maximum number of iterations but the normed residual 1.8505396985126146e-13 is still above the tolerance 1e-14.
        INFO - 08:56:54:     28%|██▊       | 14/50 [00:03<00:10,  3.54 it/sec, obj=-2.79e+3]
     WARNING - 08:56:54: MDAJacobi has reached its maximum number of iterations but the normed residual 3.0145345591022575e-14 is still above the tolerance 1e-14.
     WARNING - 08:56:54: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:54:       The solution is not feasible.
        INFO - 08:56:54:     30%|███       | 15/50 [00:04<00:10,  3.45 it/sec, obj=-2.4e+3]
        INFO - 08:56:54:     32%|███▏      | 16/50 [00:04<00:09,  3.50 it/sec, obj=-3.07e+3]
     WARNING - 08:56:55: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:55:       The solution is not feasible.
        INFO - 08:56:55:     34%|███▍      | 17/50 [00:04<00:09,  3.55 it/sec, obj=-3.01e+3]
        INFO - 08:56:55:     36%|███▌      | 18/50 [00:05<00:08,  3.59 it/sec, obj=-3.39e+3]
        INFO - 08:56:55:     38%|███▊      | 19/50 [00:05<00:08,  3.64 it/sec, obj=-3.84e+3]
     WARNING - 08:56:55: MDAJacobi has reached its maximum number of iterations but the normed residual 3.8877123894689336e-14 is still above the tolerance 1e-14.
        INFO - 08:56:55:     40%|████      | 20/50 [00:05<00:08,  3.64 it/sec, obj=-3.58e+3]
        INFO - 08:56:56:     42%|████▏     | 21/50 [00:05<00:07,  3.68 it/sec, obj=-3.66e+3]
        INFO - 08:56:56:     44%|████▍     | 22/50 [00:05<00:07,  3.72 it/sec, obj=-3.77e+3]
     WARNING - 08:56:56: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:56:       The solution is not feasible.
        INFO - 08:56:56:     46%|████▌     | 23/50 [00:06<00:07,  3.75 it/sec, obj=-3.75e+3]
        INFO - 08:56:56:     48%|████▊     | 24/50 [00:06<00:06,  3.76 it/sec, obj=-2.94e+3]
     WARNING - 08:56:56: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:56:       The solution is not feasible.
        INFO - 08:56:56:     50%|█████     | 25/50 [00:06<00:06,  3.77 it/sec, obj=-3.71e+3]
        INFO - 08:56:57:     52%|█████▏    | 26/50 [00:06<00:06,  3.84 it/sec, obj=-3.96e+3]
        INFO - 08:56:57:     54%|█████▍    | 27/50 [00:06<00:05,  3.89 it/sec, obj=-3.87e+3]
     WARNING - 08:56:57: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:57:       The solution is not feasible.
        INFO - 08:56:57:     56%|█████▌    | 28/50 [00:07<00:05,  3.94 it/sec, obj=-3.95e+3]
        INFO - 08:56:57:     58%|█████▊    | 29/50 [00:07<00:05,  3.98 it/sec, obj=-3.93e+3]
     WARNING - 08:56:57: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:57:       The solution is not feasible.
        INFO - 08:56:57:     60%|██████    | 30/50 [00:07<00:04,  4.03 it/sec, obj=-3.97e+3]
        INFO - 08:56:57:     62%|██████▏   | 31/50 [00:07<00:04,  4.06 it/sec, obj=-3.96e+3]
        INFO - 08:56:58:     64%|██████▍   | 32/50 [00:07<00:04,  4.11 it/sec, obj=-3.96e+3]
        INFO - 08:56:58:     66%|██████▌   | 33/50 [00:07<00:04,  4.16 it/sec, obj=-3.95e+3]
        INFO - 08:56:58:     68%|██████▊   | 34/50 [00:08<00:03,  4.22 it/sec, obj=-3.94e+3]
     WARNING - 08:56:58: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:58:       The solution is not feasible.
        INFO - 08:56:58:     70%|███████   | 35/50 [00:08<00:03,  4.26 it/sec, obj=-3.97e+3]
     WARNING - 08:56:58: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:56:58:       The solution is not feasible.
        INFO - 08:56:58:     72%|███████▏  | 36/50 [00:08<00:03,  4.29 it/sec, obj=-3.98e+3]
        INFO - 08:56:58:     74%|███████▍  | 37/50 [00:08<00:03,  4.33 it/sec, obj=-3.96e+3]
        INFO - 08:56:59:     76%|███████▌  | 38/50 [00:08<00:02,  4.39 it/sec, obj=-3.95e+3]
        INFO - 08:56:59:     78%|███████▊  | 39/50 [00:08<00:02,  4.43 it/sec, obj=-3.95e+3]
        INFO - 08:56:59:     80%|████████  | 40/50 [00:08<00:02,  4.47 it/sec, obj=-3.96e+3]
        INFO - 08:56:59:     82%|████████▏ | 41/50 [00:09<00:01,  4.51 it/sec, obj=-3.96e+3]
        INFO - 08:56:59:     84%|████████▍ | 42/50 [00:09<00:01,  4.56 it/sec, obj=-3.96e+3]
        INFO - 08:56:59:     86%|████████▌ | 43/50 [00:09<00:01,  4.58 it/sec, obj=-3.95e+3]
     WARNING - 08:56:59: MDAJacobi has reached its maximum number of iterations but the normed residual 3.8001101574110354e-14 is still above the tolerance 1e-14.
        INFO - 08:56:59:     88%|████████▊ | 44/50 [00:09<00:01,  4.57 it/sec, obj=-3.96e+3]
        INFO - 08:57:00:     90%|█████████ | 45/50 [00:09<00:01,  4.59 it/sec, obj=-3.96e+3]
        INFO - 08:57:00:     92%|█████████▏| 46/50 [00:09<00:00,  4.64 it/sec, obj=-3.96e+3]
        INFO - 08:57:00:     94%|█████████▍| 47/50 [00:10<00:00,  4.67 it/sec, obj=-3.96e+3]
     WARNING - 08:57:00: Optimization found no feasible point !  The least infeasible point is selected.
     WARNING - 08:57:00:       The solution is not feasible.
        INFO - 08:57:00:     96%|█████████▌| 48/50 [00:10<00:00,  4.70 it/sec, obj=-3.96e+3]
        INFO - 08:57:00:     98%|█████████▊| 49/50 [00:10<00:00,  4.74 it/sec, obj=-3.96e+3]
        INFO - 08:57:00:    100%|██████████| 50/50 [00:10<00:00,  4.78 it/sec, obj=-3.96e+3]
        INFO - 08:57:00: Optimization result:
        INFO - 08:57:00:    Optimizer info:
        INFO - 08:57:00:       Status: None
        INFO - 08:57:00:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 08:57:00:       Number of calls to the objective function by the optimizer: 52
        INFO - 08:57:00:    Solution:
        INFO - 08:57:00:       The solution is feasible.
        INFO - 08:57:00:       Objective: -3963.3800122701787
        INFO - 08:57:00:       Standardized constraints:
        INFO - 08:57:00:          g_1_g_2_g_3 = [-0.01805093 -0.03333915 -0.04424381 -0.05182998 -0.05732217 -0.13720865
        INFO - 08:57:00:  -0.10279135  0.         -0.76718646 -0.23281354  0.         -0.183255  ]
        INFO - 08:57:00:       Design space:
        INFO - 08:57:00:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:57:00:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 08:57:00:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:57:00:          | x_shared[0] |     0.01    | 0.05999999999999999 |     0.09    | float |
        INFO - 08:57:00:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 08:57:00:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 08:57:00:          | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 08:57:00:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 08:57:00:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 08:57:00:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:57:00: *** End MDOScenario execution (time: 0:00:10.472100) ***

    {'max_iter': 50, 'algo_options': {'xtol_rel': 1e-07, 'xtol_abs': 1e-07, 'ftol_rel': 1e-07, 'ftol_abs': 1e-07, 'ineq_tolerance': 0.0001}, 'algo': 'NLOPT_COBYLA'}



.. GENERATED FROM PYTHON SOURCE LINES 161-164

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

.. GENERATED FROM PYTHON SOURCE LINES 164-168

.. code-block:: Python

    system_scenario.formulation.mda1.plot_residual_history(save=False, show=True)
    # For the second MDA:
    system_scenario.formulation.mda2.plot_residual_history(save=False, show=True)




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


    *

      .. 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-multi-img

    *

      .. 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-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 169-171

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

.. GENERATED FROM PYTHON SOURCE LINES 171-173

.. code-block:: Python

    system_scenario.post_process("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: 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 0x7f1dae479790>



.. GENERATED FROM PYTHON SOURCE LINES 174-176

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

.. GENERATED FROM PYTHON SOURCE LINES 176-185

.. code-block:: Python


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

    for disc in [propu, aero, mission, struct]:
        print(f"{disc.name}: {disc.n_calls} 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: 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: Hessian diagonal approximation
         :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 inequality constraints
         :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 optimization variables
         :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 objective value
         :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: Distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_014.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_015.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_015.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_016.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_bilevel_example_016.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    SobieskiPropulsion: 1290 calls.
    SobieskiAerodynamics: 1343 calls.
    SobieskiMission: 50 calls.
    SobieskiStructure: 1394 calls.





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

   **Total running time of the script:** (0 minutes 14.663 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>`


.. only:: html

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

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