.. 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_binhkorn.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_binhkorn.py>`
        to download the full example code

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

.. _sphx_glr_examples_post_process_plot_pareto_front_binhkorn.py:


Pareto front on Binh and Korn problem
=====================================

In this example, we illustrate the use of the :class:`.ParetoFront` plot
on the Binh and Korn multi-objective problem.

.. GENERATED FROM PYTHON SOURCE LINES 28-34

.. code-block:: default

    from gemseo.algos.doe.doe_factory import DOEFactory
    from gemseo.api import configure_logger
    from gemseo.post.post_factory import PostFactory
    from gemseo.problems.analytical.binh_korn import BinhKorn
    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 35-39

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 39-43

.. code-block:: default


    configure_logger()






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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 44-47

Import the optimization problem
-------------------------------
Then, we instantiate the BinkKorn optimization problem.

.. GENERATED FROM PYTHON SOURCE LINES 47-50

.. code-block:: default


    problem = BinhKorn()








.. GENERATED FROM PYTHON SOURCE LINES 51-55

Create and execute scenario
---------------------------
Then, we create a Design of Experiment factory,
and we request the execution a a full-factorial DOE using 100 samples

.. GENERATED FROM PYTHON SOURCE LINES 55-58

.. code-block:: default

    doe_factory = DOEFactory()
    doe_factory.execute(problem, algo_name="OT_OPT_LHS", n_samples=100)





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

 Out:

 .. code-block:: none

        INFO - 10:02:57: Optimization problem:
        INFO - 10:02:57:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
        INFO - 10:02:57:    with respect to x, y
        INFO - 10:02:57:    subject to constraints:
        INFO - 10:02:57:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 10:02:57:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 10:02:57:    over the design space:
        INFO - 10:02:57:    +------+-------------+-------+-------------+-------+
        INFO - 10:02:57:    | name | lower_bound | value | upper_bound | type  |
        INFO - 10:02:57:    +------+-------------+-------+-------------+-------+
        INFO - 10:02:57:    | x    |      0      |   1   |      5      | float |
        INFO - 10:02:57:    | y    |      0      |   1   |      3      | float |
        INFO - 10:02:57:    +------+-------------+-------+-------------+-------+
        INFO - 10:02:57: Solving optimization problem with algorithm OT_OPT_LHS:
        INFO - 10:02:57: Generation of OT_OPT_LHS DOE with OpenTURNS
        INFO - 10:02:57: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:02:57: ... 100%|██████████| 100/100 [00:00<00:00, 4901.38 it/sec]
        INFO - 10:02:57: Optimization result:
        INFO - 10:02:57:    Optimizer info:
        INFO - 10:02:57:       Status: None
        INFO - 10:02:57:       Message: None
        INFO - 10:02:57:       Number of calls to the objective function by the optimizer: 100
        INFO - 10:02:57:    Solution:
        INFO - 10:02:57:       The solution is feasible.
        INFO - 10:02:57:       Objective: 30.39964825035985
        INFO - 10:02:57:       Standardized constraints:
        INFO - 10:02:57:          ineq1 = [-11.77907222]
        INFO - 10:02:57:          ineq2 = [-38.26307397]
        INFO - 10:02:57:       Design space:
        INFO - 10:02:57:       +------+-------------+-------------------+-------------+-------+
        INFO - 10:02:57:       | name | lower_bound |       value       | upper_bound | type  |
        INFO - 10:02:57:       +------+-------------+-------------------+-------------+-------+
        INFO - 10:02:57:       | x    |      0      | 1.542975634014225 |      5      | float |
        INFO - 10:02:57:       | y    |      0      | 1.269910308585573 |      3      | float |
        INFO - 10:02:57:       +------+-------------+-------------------+-------------+-------+

    Optimization result:
       Design variables: [1.54297563 1.26991031]
       Objective function: 30.39964825035985
       Feasible solution: True



.. GENERATED FROM PYTHON SOURCE LINES 59-67

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.ParetoFront`
plot which generates a plot or a matrix of plots if there are more than
2 objectives, plots in blue the locally non dominated points for the current
two objectives, plots in green the globally (all objectives) Pareto optimal
points. The plots in green denotes non-feasible points. Note that the user
can avoid the display of the non-feasible points.

.. GENERATED FROM PYTHON SOURCE LINES 67-89

.. code-block:: default


    PostFactory().execute(
        problem,
        "ParetoFront",
        save=False,
        show=False,
        show_non_feasible=False,
        objectives=["compute_binhkorn"],
        objectives_labels=["f1", "f2"],
    )

    PostFactory().execute(
        problem,
        "ParetoFront",
        save=False,
        show=False,
        show_non_feasible=True,
        objectives=["compute_binhkorn"],
        objectives_labels=["f1", "f2"],
    )
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



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


    *

      .. image-sg:: /examples/post_process/images/sphx_glr_plot_pareto_front_binhkorn_001.png
         :alt: Pareto front
         :srcset: /examples/post_process/images/sphx_glr_plot_pareto_front_binhkorn_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/images/sphx_glr_plot_pareto_front_binhkorn_002.png
         :alt: Pareto front
         :srcset: /examples/post_process/images/sphx_glr_plot_pareto_front_binhkorn_002.png
         :class: sphx-glr-multi-img






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

   **Total running time of the script:** ( 0 minutes  0.427 seconds)


.. _sphx_glr_download_examples_post_process_plot_pareto_front_binhkorn.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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