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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_post_process_plot_pareto_front.py>`
        to download the full example code

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

.. _sphx_glr_examples_post_process_plot_pareto_front.py:


Pareto front
=============

In this example, we illustrate the use of the :class:`.ParetoFront` plot
on the Sobieski's SSBJ problem.

.. GENERATED FROM PYTHON SOURCE LINES 28-36

.. code-block:: default

    from __future__ import annotations

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.problems.sobieski.core.problem import SobieskiProblem
    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 37-41

Import
------
The first step is to import some functions from the API
and a method to get the design space.

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: default


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-53

Description
-----------

The :class:`~gemseo.post.pareto_front.ParetoFront` post-processing generates
a plot or a matrix of plots (if there are more than
2 objectives). It indicates in red the locally nondominated points for the
current objectives, and in green the globally (all objectives) Pareto optimal
points.

.. GENERATED FROM PYTHON SOURCE LINES 55-59

Create disciplines
------------------
At this point, we instantiate the disciplines of Sobieski's SSBJ problem:
Propulsion, Aerodynamics, Structure and Mission

.. GENERATED FROM PYTHON SOURCE LINES 59-68

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 69-72

Create design space
-------------------
We also read the design space from the :class:`.SobieskiProblem`.

.. GENERATED FROM PYTHON SOURCE LINES 72-74

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 75-82

Create and execute scenario
---------------------------
The next step is to build an MDO scenario in order to maximize the range,
encoded 'y_4', with respect to the design parameters, while satisfying the
inequality constraints 'g_1', 'g_2' and 'g_3'. We can use the MDF formulation,
the SLSQP optimization algorithm
and a maximum number of iterations equal to 100.

.. GENERATED FROM PYTHON SOURCE LINES 82-94

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="MDF",
        objective_name="y_4",
        maximize_objective=True,
        design_space=design_space,
    )
    scenario.set_differentiation_method("user")
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, "ineq")
    scenario.execute({"algo": "SLSQP", "max_iter": 10})





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

 .. code-block:: none

        INFO - 14:43:39:  
        INFO - 14:43:39: *** Start MDOScenario execution ***
        INFO - 14:43:39: MDOScenario
        INFO - 14:43:39:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 14:43:39:    MDO formulation: MDF
        INFO - 14:43:39: Optimization problem:
        INFO - 14:43:39:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 14:43:39:    with respect to x_1, x_2, x_3, x_shared
        INFO - 14:43:39:    subject to constraints:
        INFO - 14:43:39:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:39:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:39:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:39:    over the design space:
        INFO - 14:43:39:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:39:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 14:43:39:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:39:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 14:43:39:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 14:43:39:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 14:43:39:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 14:43:39:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 14:43:39:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 14:43:39:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 14:43:39:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:39:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:39:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 14:43:39:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:39: Solving optimization problem with algorithm SLSQP:
        INFO - 14:43:39: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:43:39: ...  20%|██        | 2/10 [00:00<00:00, 40.65 it/sec, obj=-2.12e+3]
     WARNING - 14:43:39: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
        INFO - 14:43:39: ...  30%|███       | 3/10 [00:00<00:00, 23.55 it/sec, obj=-3.75e+3]
        INFO - 14:43:39: ...  40%|████      | 4/10 [00:00<00:00, 17.18 it/sec, obj=-4.01e+3]
     WARNING - 14:43:39: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
        INFO - 14:43:39: ...  50%|█████     | 5/10 [00:00<00:00, 13.04 it/sec, obj=-4.49e+3]
        INFO - 14:43:40: ...  60%|██████    | 6/10 [00:00<00:00, 11.00 it/sec, obj=-3.4e+3]
        INFO - 14:43:40: ...  80%|████████  | 8/10 [00:01<00:00,  9.36 it/sec, obj=-4.76e+3]
        INFO - 14:43:40: ... 100%|██████████| 10/10 [00:01<00:00,  8.16 it/sec, obj=-4.56e+3]
        INFO - 14:43:40: ... 100%|██████████| 10/10 [00:01<00:00,  8.14 it/sec, obj=-4.56e+3]
        INFO - 14:43:40: Optimization result:
        INFO - 14:43:40:    Optimizer info:
        INFO - 14:43:40:       Status: None
        INFO - 14:43:40:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 14:43:40:       Number of calls to the objective function by the optimizer: 12
        INFO - 14:43:40:    Solution:
        INFO - 14:43:40:       The solution is feasible.
        INFO - 14:43:40:       Objective: -3749.8868975554387
        INFO - 14:43:40:       Standardized constraints:
        INFO - 14:43:40:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
        INFO - 14:43:40:  -0.10219342]
        INFO - 14:43:40:          g_2 = -0.0004062839430756249
        INFO - 14:43:40:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
        INFO - 14:43:40:       Design space: 
        INFO - 14:43:40:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:40:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 14:43:40:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:40:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
        INFO - 14:43:40:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
        INFO - 14:43:40:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 14:43:40:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
        INFO - 14:43:40:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
        INFO - 14:43:40:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
        INFO - 14:43:40:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 14:43:40:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
        INFO - 14:43:40:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
        INFO - 14:43:40:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
        INFO - 14:43:40:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:40: *** End MDOScenario execution (time: 0:00:01.244266) ***

    {'max_iter': 10, 'algo': 'SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 95-98

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.ParetoFront`.

.. GENERATED FROM PYTHON SOURCE LINES 100-108

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the API function
   :meth:`~gemseo.api.get_post_processing_options_schema` to print a table with
   the options for any post-processing algorithm.
   Or refer to our dedicated page:
   :ref:`gen_post_algos`.

.. GENERATED FROM PYTHON SOURCE LINES 108-112

.. code-block:: default


    scenario.post_process("ParetoFront", objectives=["g_3", "-y_4"], save=False, show=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



.. image-sg:: /examples/post_process/images/sphx_glr_plot_pareto_front_001.png
   :alt: Pareto front
   :srcset: /examples/post_process/images/sphx_glr_plot_pareto_front_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  1.936 seconds)


.. _sphx_glr_download_examples_post_process_plot_pareto_front.py:

.. only:: html

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


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

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

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


.. only:: html

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