.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/exterior_penalty/plot_exterior_penalty_sobieski.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_exterior_penalty_plot_exterior_penalty_sobieski.py>`
        to download the full example code.

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

.. _sphx_glr_examples_exterior_penalty_plot_exterior_penalty_sobieski.py:


Example for exterior penalty applied to the Sobieski test case.
===============================================================

.. GENERATED FROM PYTHON SOURCE LINES 22-54

This section describes how to set up and solve the MDO problem relative to the
:ref:`Sobieski test case <sobieski_problem>` with |g| applying external penalty.

.. seealso::

   To start with a simpler MDO problem, and for a detailed description
   of how to plug a test case into |g|, see :ref:`sellar_mdo`.


.. _sobieski_use_case:

Solving with an :ref:`MDF formulation <mdf_formulation>`
--------------------------------------------------------

In this example, we solve the range optimization using the following
:ref:`MDF formulation <mdf_formulation>`:

- The :ref:`MDF formulation <mdf_formulation>` couples all the disciplines
  during the :ref:`mda` at each optimization iteration.
- All the :term:`design variables` are equally treated, concatenated in a
  single vector and given to a single :term:`optimization algorithm` as the
  unknowns of the problem.
- There is no specific :term:`constraint` due to the :ref:`MDF formulation
  <mdf_formulation>`.
- Only the design :term:`constraints` :math:`g\_1`, :math:`g\_2` and
  :math:`g\_3` are added to the problem.
- The :term:`objective function` is the range (the :math:`y\_4` variable in
  the model), computed after the :ref:`mda`.

Imports
-------
All the imports needed for the tutorials are performed here.

.. GENERATED FROM PYTHON SOURCE LINES 54-67

.. code-block:: Python

    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import get_available_formulations
    from gemseo.disciplines.utils import get_all_inputs
    from gemseo.disciplines.utils import get_all_outputs
    from gemseo.formulations.mdf_settings import MDF_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 68-74

Step 1: Creation of :class:`.Discipline`
-------------------------------------------

To build the scenario, we first instantiate the disciplines. Here, the
disciplines themselves have already been
developed and interfaced with |g| (see :ref:`benchmark_problems`).

.. GENERATED FROM PYTHON SOURCE LINES 74-82

.. code-block:: Python


    disciplines = create_discipline([
        "SobieskiPropulsion",
        "SobieskiAerodynamics",
        "SobieskiMission",
        "SobieskiStructure",
    ])








.. GENERATED FROM PYTHON SOURCE LINES 83-90

.. tip::

   For the disciplines that are not interfaced with |g|, the |g|'s
   :mod:`~gemseo` eases the creation of disciplines without having
   to import them.

   See :ref:`api`.

.. GENERATED FROM PYTHON SOURCE LINES 92-108

Step 2: Creation of :class:`.Scenario`
--------------------------------------

The scenario delegates the creation of the optimization problem to the
:ref:`MDO formulation <mdo_formulations>`.

Therefore, it needs the list of ``disciplines``, the name of the formulation
(or its settings model), the name of the objective function and the design space.

- The ``design_space`` (shown below for reference)
  defines the unknowns of the optimization problem, and their bounds. It contains
  all the design variables needed by the :ref:`MDF formulation <mdf_formulation>`.
  It can be imported from a text file, or created from scratch with the methods
  :func:`.create_design_space` and
  :meth:`~gemseo.algos.design_space.DesignSpace.add_variable`. In this case,
  we will use ``SobieskiDesignSpace`` already defined in |g|.

.. GENERATED FROM PYTHON SOURCE LINES 108-110

.. code-block:: Python

    design_space = SobieskiDesignSpace()
    x_0 = design_space.get_current_value(as_dict=True)







.. GENERATED FROM PYTHON SOURCE LINES 111-142

.. code::

     name      lower_bound      value      upper_bound  type
     x_shared      0.01          0.05          0.09     float
     x_shared    30000.0       45000.0       60000.0    float
     x_shared      1.4           1.6           1.8      float
     x_shared      2.5           5.5           8.5      float
     x_shared      40.0          55.0          70.0     float
     x_shared     500.0         1000.0        1500.0    float
     x_1           0.1           0.25          0.4      float
     x_1           0.75          1.0           1.25     float
     x_2           0.75          1.0           1.25     float
     x_3           0.1           0.5           1.0      float
     y_14        24850.0    50606.9741711    77100.0    float
     y_14        -7700.0    7306.20262124    45000.0    float
     y_32         0.235       0.50279625      0.795     float
     y_31         2960.0    6354.32430691    10185.0    float
     y_24          0.44       4.15006276      11.13     float
     y_34          0.44       1.10754577       1.98     float
     y_23         3365.0    12194.2671934    26400.0    float
     y_21        24850.0    50606.9741711    77250.0    float
     y_12        24850.0      50606.9742     77250.0    float
     y_12          0.45          0.95          1.5      float

- The available :ref:`MDO formulations <mdo_formulations>` are located in the
  **gemseo.formulations** package, see :ref:`extending-gemseo` for extending
  GEMSEO with other formulations.
- The ``formulation`` name (here, ``"MDF"``) shall be passed to
  the scenario to select them.
- The list of available formulations can be obtained by using
  :func:`.get_available_formulations`.

.. GENERATED FROM PYTHON SOURCE LINES 142-143

.. code-block:: Python

    get_available_formulations()




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

 .. code-block:: none


    ['BiLevel', 'DisciplinaryOpt', 'IDF', 'MDF']



.. GENERATED FROM PYTHON SOURCE LINES 144-148

- :math:`y\_4` corresponds to the ``objective_name``. This name must be one
  of the disciplines outputs, here the ``SobieskiMission`` discipline. The list of
  all outputs of the disciplines can be obtained by using
  :meth:`~gemseo.disciplines.utils.get_all_outputs`:

.. GENERATED FROM PYTHON SOURCE LINES 148-150

.. code-block:: Python

    get_all_outputs(disciplines)
    get_all_inputs(disciplines)




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

 .. code-block:: none


    ['c_0', 'c_1', 'c_2', 'c_3', 'c_4', 'x_1', 'x_2', 'x_3', 'x_shared', 'y_12', 'y_14', 'y_21', 'y_23', 'y_24', 'y_31', 'y_32', 'y_34']



.. GENERATED FROM PYTHON SOURCE LINES 151-154

From these :class:`~gemseo.core.discipline.Discipline`, design space,
:ref:`MDO formulation <mdo_formulations>` name and objective function name,
we build the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 154-162

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "y_4",
        design_space,
        maximize_objective=True,
        formulation_name="MDF",
    )





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

 .. code-block:: none

     WARNING - 02:41:20: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
     WARNING - 02:41:20: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.




.. GENERATED FROM PYTHON SOURCE LINES 163-165

Note that both the formulation settings passed to :func:`.create_scenario` can be provided
via a Pydantic model. For more information, see :ref:`formulation_settings`.

.. GENERATED FROM PYTHON SOURCE LINES 167-181

The range function (:math:`y\_4`) should be maximized. However, optimizers
minimize functions by default. Which is why, when creating the scenario, the argument
``maximize_objective`` shall be set to ``True``.

Differentiation method
~~~~~~~~~~~~~~~~~~~~~~

We may choose the way derivatives are computed:


**Function derivatives.** As analytical disciplinary derivatives are
available for the Sobieski test-case, they can be used instead of computing
the derivatives with finite-differences or with the complex-step method.
The easiest way to set a method is to let the optimizer determine it:

.. GENERATED FROM PYTHON SOURCE LINES 181-182

.. code-block:: Python

    scenario.set_differentiation_method()







.. GENERATED FROM PYTHON SOURCE LINES 183-208

The default behavior of the optimizer triggers :term:`finite differences`.
It corresponds to:

.. code::

  scenario.set_differentiation_method("finite_differences",1e-7)

It is also possible to differentiate functions by means of the
:term:`complex step` method:

.. code::

  scenario.set_differentiation_method("complex_step",1e-30j)

Constraints
~~~~~~~~~~~

Similarly to the objective function, the constraints names are a subset
of the disciplines' outputs. They can be obtained by using
:meth:`~gemseo.disciplines.utils.get_all_outputs`.

The formulation has a powerful feature to automatically dispatch the constraints
(:math:`g\_1, g\_2, g\_3`) and plug them to the optimizers depending on
the formulation. To do that, we use the method
:meth:`~gemseo.scenarios.scenario.Scenario.add_constraint`:

.. GENERATED FROM PYTHON SOURCE LINES 209-211

.. code-block:: Python

    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, constraint_type="ineq")







.. GENERATED FROM PYTHON SOURCE LINES 212-214

Step 3: Apply the exterior penalty and execute the scenario
-----------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 214-217

.. code-block:: Python

    scenario.formulation.optimization_problem.apply_exterior_penalty(
        objective_scale=10.0, scale_inequality=10.0
    )







.. GENERATED FROM PYTHON SOURCE LINES 218-220

In this way the L-BFGS-B algorithm can be used to solve the optimization problem.
Note that this algorithm is not suited for constrained optimization problems.

.. GENERATED FROM PYTHON SOURCE LINES 220-222

.. code-block:: Python

    scenario.execute(algo_name="L-BFGS-B", max_iter=10)





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

 .. code-block:: none

        INFO - 02:41:20:  
        INFO - 02:41:20: *** Start MDOScenario execution ***
        INFO - 02:41:20: MDOScenario
        INFO - 02:41:20:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 02:41:20:    MDO formulation: MDF
        INFO - 02:41:20: Optimization problem:
        INFO - 02:41:20:    minimize [[[[-y_4/10.0]+pos_sum_g_1]+pos_sum_g_2]+pos_sum_g_3](x_1, x_2, x_3, x_shared) = -y_4(x_shared, x_1, x_2, x_3)/10.0+sum(heaviside()***2)+sum(heaviside()***2)+sum(heaviside()***2)
        INFO - 02:41:20:    with respect to x_1, x_2, x_3, x_shared
        INFO - 02:41:20:    over the design space:
        INFO - 02:41:20:       +-------------+-------------+-------+-------------+-------+
        INFO - 02:41:20:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 02:41:20:       +-------------+-------------+-------+-------------+-------+
        INFO - 02:41:20:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 02:41:20:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 02:41:20:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 02:41:20:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 02:41:20:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 02:41:20:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 02:41:20:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 02:41:20:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 02:41:20:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 02:41:20:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 02:41:20:       +-------------+-------------+-------+-------------+-------+
        INFO - 02:41:20: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 02:41:20:     10%|█         | 1/10 [00:00<00:00, 21.56 it/sec, obj=-53.3]
        INFO - 02:41:20:     20%|██        | 2/10 [00:00<00:00, 16.37 it/sec, obj=-401]
        INFO - 02:41:20:     30%|███       | 3/10 [00:00<00:00, 16.05 it/sec, obj=103]
        INFO - 02:41:20:     40%|████      | 4/10 [00:00<00:00, 15.28 it/sec, obj=-488]
        INFO - 02:41:20:     50%|█████     | 5/10 [00:00<00:00, 14.73 it/sec, obj=-489]
        INFO - 02:41:20:     60%|██████    | 6/10 [00:00<00:00, 14.41 it/sec, obj=-489]
        INFO - 02:41:20:     70%|███████   | 7/10 [00:00<00:00, 14.18 it/sec, obj=-489]
        INFO - 02:41:20:     80%|████████  | 8/10 [00:00<00:00, 14.06 it/sec, obj=-489]
        INFO - 02:41:20:     90%|█████████ | 9/10 [00:00<00:00, 13.96 it/sec, obj=-489]
        INFO - 02:41:20:    100%|██████████| 10/10 [00:00<00:00, 13.87 it/sec, obj=-489]
        INFO - 02:41:20: Optimization result:
        INFO - 02:41:20:    Optimizer info:
        INFO - 02:41:20:       Status: None
        INFO - 02:41:20:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
        INFO - 02:41:20:       Number of calls to the objective function by the optimizer: 12
        INFO - 02:41:20:    Solution:
        INFO - 02:41:20:       Objective: -489.2416290389579
        INFO - 02:41:20:       Design space:
        INFO - 02:41:20:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 02:41:20:          | Name        | Lower bound |       Value        | Upper bound | Type  |
        INFO - 02:41:20:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 02:41:20:          | x_shared[0] |     0.01    |        0.09        |     0.09    | float |
        INFO - 02:41:20:          | x_shared[1] |    30000    |       60000        |    60000    | float |
        INFO - 02:41:20:          | x_shared[2] |     1.4     |        1.4         |     1.8     | float |
        INFO - 02:41:20:          | x_shared[3] |     2.5     |        2.5         |     8.5     | float |
        INFO - 02:41:20:          | x_shared[4] |      40     |         70         |      70     | float |
        INFO - 02:41:20:          | x_shared[5] |     500     |        1500        |     1500    | float |
        INFO - 02:41:20:          | x_1[0]      |     0.1     | 0.2486534942780023 |     0.4     | float |
        INFO - 02:41:20:          | x_1[1]      |     0.75    |        0.75        |     1.25    | float |
        INFO - 02:41:20:          | x_2         |     0.75    |        0.75        |     1.25    | float |
        INFO - 02:41:20:          | x_3         |     0.1     | 0.258406178367566  |      1      | float |
        INFO - 02:41:20:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 02:41:20: *** End MDOScenario execution (time: 0:00:00.757958) ***




.. GENERATED FROM PYTHON SOURCE LINES 223-225

Note that the algorithm settings passed to :class:`~.BaseDriverLibrary.execute` can be provided via a
Pydantic model. For more information, :ref:`algorithm_settings`.

.. GENERATED FROM PYTHON SOURCE LINES 227-231

Post-processing options
~~~~~~~~~~~~~~~~~~~~~~~
To visualize the optimization history of the constraint violation one can use the
:class:`.BasicHistory`:

.. GENERATED FROM PYTHON SOURCE LINES 231-237

.. code-block:: Python

    scenario.post_process(
        post_name="BasicHistory",
        variable_names=["g_1", "g_2", "g_3"],
        save=False,
        show=True,
    )



.. image-sg:: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_001.png
   :alt: History plot
   :srcset: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7f8560375070>



.. GENERATED FROM PYTHON SOURCE LINES 238-243

This solution is almost feasible.
The solution can better approximate the original problem solution increasing the value
of `objective_scale` and  `scale_inequality` parameters.
Step 4: Rerun the scenario with increased penalty and objective scaling.
------------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 243-245

.. code-block:: Python

    design_space.set_current_value(x_0)








.. GENERATED FROM PYTHON SOURCE LINES 246-249

Here, we use the :class:`.MDF_Settings` model to define the formulation instead of passing
the settings one by one as we did the first time. Both ways of defining the settings
are equally valid.

.. GENERATED FROM PYTHON SOURCE LINES 249-264

.. code-block:: Python


    scenario_2 = create_scenario(
        disciplines,
        "y_4",
        design_space,
        formulation_settings_model=MDF_Settings(),
        maximize_objective=True,
    )
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario_2.add_constraint(constraint, constraint_type="ineq")
    scenario_2.set_differentiation_method()
    scenario_2.formulation.optimization_problem.apply_exterior_penalty(
        objective_scale=1000.0, scale_inequality=1000.0
    )





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

 .. code-block:: none

     WARNING - 02:41:21: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
     WARNING - 02:41:21: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.




.. GENERATED FROM PYTHON SOURCE LINES 265-268

Here, we use the :class:`.L_BFGS_B_Settings` model to define the algorithm settings instead of
passing them one by one as we did the first time. Both ways of defining the settings
are equally valid.

.. GENERATED FROM PYTHON SOURCE LINES 268-275

.. code-block:: Python

    from gemseo.settings.opt import L_BFGS_B_Settings  # noqa: E402

    scenario_2.execute(L_BFGS_B_Settings(max_iter=1000))
    scenario_2.post_process(
        post_name="BasicHistory", variable_names=["-y_4"], save=False, show=True
    )




.. image-sg:: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_002.png
   :alt: History plot
   :srcset: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 02:41:21:  
        INFO - 02:41:21: *** Start MDOScenario execution ***
        INFO - 02:41:21: MDOScenario
        INFO - 02:41:21:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 02:41:21:    MDO formulation: MDF
        INFO - 02:41:21: Optimization problem:
        INFO - 02:41:21:    minimize [[[[-y_4/1000.0]+pos_sum_g_1]+pos_sum_g_2]+pos_sum_g_3](x_1, x_2, x_3, x_shared) = -y_4(x_shared, x_1, x_2, x_3)/1000.0+sum(heaviside()***2)+sum(heaviside()***2)+sum(heaviside()***2)
        INFO - 02:41:21:    with respect to x_1, x_2, x_3, x_shared
        INFO - 02:41:21:    over the design space:
        INFO - 02:41:21:       +-------------+-------------+-------+-------------+-------+
        INFO - 02:41:21:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 02:41:21:       +-------------+-------------+-------+-------------+-------+
        INFO - 02:41:21:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 02:41:21:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 02:41:21:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 02:41:21:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 02:41:21:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 02:41:21:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 02:41:21:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 02:41:21:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 02:41:21:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 02:41:21:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 02:41:21:       +-------------+-------------+-------+-------------+-------+
        INFO - 02:41:21: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 02:41:21:      1%|          | 6/1000 [00:00<01:03, 15.53 it/sec, obj=-0.428]
        INFO - 02:41:21:      1%|          | 7/1000 [00:00<01:03, 15.64 it/sec, obj=-0.504]
        INFO - 02:41:21:      1%|          | 8/1000 [00:00<01:02, 15.81 it/sec, obj=-0.413]
        INFO - 02:41:21:      1%|          | 9/1000 [00:00<01:02, 15.96 it/sec, obj=-0.521]
        INFO - 02:41:21:      1%|          | 10/1000 [00:00<01:01, 16.16 it/sec, obj=-0.537]
        INFO - 02:41:21:      1%|          | 11/1000 [00:00<01:00, 16.33 it/sec, obj=-0.54]
        INFO - 02:41:22:      1%|          | 12/1000 [00:00<00:59, 16.47 it/sec, obj=-0.541]
        INFO - 02:41:22:      1%|▏         | 13/1000 [00:00<00:59, 16.59 it/sec, obj=-0.521]
        INFO - 02:41:22:      1%|▏         | 14/1000 [00:00<00:59, 16.70 it/sec, obj=-0.541]
        INFO - 02:41:22:      2%|▏         | 15/1000 [00:00<00:58, 16.70 it/sec, obj=4.92]
        INFO - 02:41:22:      2%|▏         | 16/1000 [00:00<00:58, 16.79 it/sec, obj=-0.542]
        INFO - 02:41:22:      2%|▏         | 17/1000 [00:01<00:58, 16.88 it/sec, obj=-0.542]
        INFO - 02:41:22:      2%|▏         | 18/1000 [00:01<00:58, 16.91 it/sec, obj=0.751]
        INFO - 02:41:22:      2%|▏         | 19/1000 [00:01<00:57, 16.98 it/sec, obj=-0.542]
        INFO - 02:41:22:      2%|▏         | 20/1000 [00:01<00:57, 16.99 it/sec, obj=-0.589]
        INFO - 02:41:22:      2%|▏         | 21/1000 [00:01<00:57, 16.91 it/sec, obj=28.5]
        INFO - 02:41:22:      2%|▏         | 22/1000 [00:01<00:57, 16.92 it/sec, obj=-0.601]
        INFO - 02:41:22:      2%|▏         | 23/1000 [00:01<00:57, 16.93 it/sec, obj=-0.609]
        INFO - 02:41:22:      2%|▏         | 24/1000 [00:01<00:57, 16.90 it/sec, obj=2.4]
        INFO - 02:41:22:      2%|▎         | 25/1000 [00:01<00:57, 16.88 it/sec, obj=-0.625]
        INFO - 02:41:22:      3%|▎         | 26/1000 [00:01<00:57, 16.86 it/sec, obj=-0.639]
        INFO - 02:41:22:      3%|▎         | 27/1000 [00:01<00:57, 16.84 it/sec, obj=-0.311]
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        INFO - 02:41:28:     11%|█         | 109/1000 [00:07<01:01, 14.41 it/sec, obj=-4.41]
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        INFO - 02:41:29:     11%|█         | 111/1000 [00:07<01:01, 14.38 it/sec, obj=-4.41]
        INFO - 02:41:29:     11%|█         | 112/1000 [00:07<01:01, 14.36 it/sec, obj=-4.41]
        INFO - 02:41:29:     11%|█▏        | 113/1000 [00:07<01:01, 14.35 it/sec, obj=-4.41]
        INFO - 02:41:29:     11%|█▏        | 114/1000 [00:07<01:01, 14.33 it/sec, obj=-4.41]
        INFO - 02:41:29:     12%|█▏        | 115/1000 [00:08<01:01, 14.32 it/sec, obj=-4.41]
        INFO - 02:41:29:     12%|█▏        | 116/1000 [00:08<01:01, 14.31 it/sec, obj=-4.41]
        INFO - 02:41:29: Optimization result:
        INFO - 02:41:29:    Optimizer info:
        INFO - 02:41:29:       Status: 0
        INFO - 02:41:29:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
        INFO - 02:41:29:       Number of calls to the objective function by the optimizer: 118
        INFO - 02:41:29:    Solution:
        INFO - 02:41:29:       Objective: -4.4116962873840135
        INFO - 02:41:29:       Design space:
        INFO - 02:41:29:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 02:41:29:          | Name        | Lower bound |       Value        | Upper bound | Type  |
        INFO - 02:41:29:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 02:41:29:          | x_shared[0] |     0.01    |        0.09        |     0.09    | float |
        INFO - 02:41:29:          | x_shared[1] |    30000    |       60000        |    60000    | float |
        INFO - 02:41:29:          | x_shared[2] |     1.4     |        1.4         |     1.8     | float |
        INFO - 02:41:29:          | x_shared[3] |     2.5     |        2.5         |     8.5     | float |
        INFO - 02:41:29:          | x_shared[4] |      40     |         70         |      70     | float |
        INFO - 02:41:29:          | x_shared[5] |     500     |        1500        |     1500    | float |
        INFO - 02:41:29:          | x_1[0]      |     0.1     |        0.4         |     0.4     | float |
        INFO - 02:41:29:          | x_1[1]      |     0.75    |        0.75        |     1.25    | float |
        INFO - 02:41:29:          | x_2         |     0.75    |        0.75        |     1.25    | float |
        INFO - 02:41:29:          | x_3         |     0.1     | 0.1563542074363522 |      1      | float |
        INFO - 02:41:29:          +-------------+-------------+--------------------+-------------+-------+
        INFO - 02:41:29: *** End MDOScenario execution (time: 0:00:08.146409) ***

    <gemseo.post.basic_history.BasicHistory object at 0x7f855d19ea50>



.. GENERATED FROM PYTHON SOURCE LINES 276-279

Here, we use the :class:`.BasicHistory_Settings` model to define the post-processor settings
instead of passing them one by one as we did the first time.
Both ways of defining the settings are equally valid.

.. GENERATED FROM PYTHON SOURCE LINES 279-288

.. code-block:: Python

    from gemseo.settings.post import BasicHistory_Settings  # noqa: E402

    scenario_2.post_process(
        BasicHistory_Settings(
            variable_names=["g_1", "g_2", "g_3"],
            save=False,
            show=True,
        )
    )



.. image-sg:: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_003.png
   :alt: History plot
   :srcset: /examples/exterior_penalty/images/sphx_glr_plot_exterior_penalty_sobieski_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7f855d0b5850>



.. GENERATED FROM PYTHON SOURCE LINES 289-291

The solution feasibility was improved but this comes with a much higher number of
iterations.


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

   **Total running time of the script:** (0 minutes 9.813 seconds)


.. _sphx_glr_download_examples_exterior_penalty_plot_exterior_penalty_sobieski.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

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

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

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

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


.. only:: html

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

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