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

.. only:: html

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

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

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

.. _sphx_glr_examples_post_process_algorithms_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 28-36

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo.algos.doe.doe_factory import DOEFactory
    from gemseo.post.post_factory import PostFactory
    from gemseo.problems.analytical.binh_korn import BinhKorn








.. GENERATED FROM PYTHON SOURCE LINES 37-40

Import
------
The first step is to import a high-level function for logging.

.. GENERATED FROM PYTHON SOURCE LINES 40-44

.. code-block:: Python


    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-48

Import the optimization problem
-------------------------------
Then, we instantiate the Binh and Korn optimization problem (see :class:`.BinhKorn`).

.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. code-block:: Python


    problem = BinhKorn()








.. GENERATED FROM PYTHON SOURCE LINES 52-57

Create and execute scenario
---------------------------
Then,
we instantiate the design of experiment factory,
and we request the execution of a 100-length LHS optimized by simulated annealing.

.. GENERATED FROM PYTHON SOURCE LINES 57-60

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 13:58:42: Optimization problem:
        INFO - 13:58:42:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
        INFO - 13:58:42:    with respect to x, y
        INFO - 13:58:42:    subject to constraints:
        INFO - 13:58:42:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 13:58:42:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 13:58:42:    over the design space:
        INFO - 13:58:42:       +------+-------------+-------+-------------+-------+
        INFO - 13:58:42:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:58:42:       +------+-------------+-------+-------------+-------+
        INFO - 13:58:42:       | x    |      0      |   1   |      5      | float |
        INFO - 13:58:42:       | y    |      0      |   1   |      3      | float |
        INFO - 13:58:42:       +------+-------------+-------+-------------+-------+
        INFO - 13:58:42: Solving optimization problem with algorithm OT_OPT_LHS:
        INFO - 13:58:42:      1%|          | 1/100 [00:00<00:00, 2442.81 it/sec, obj=[98.50728236 17.96432773]]
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        INFO - 13:58:42:    100%|██████████| 100/100 [00:00<00:00, 1932.71 it/sec, obj=[52.02690192 12.02601654]]
        INFO - 13:58:42: Optimization result:
        INFO - 13:58:42:    Optimizer info:
        INFO - 13:58:42:       Status: None
        INFO - 13:58:42:       Message: None
        INFO - 13:58:42:       Number of calls to the objective function by the optimizer: 100
        INFO - 13:58:42:    Solution:
        INFO - 13:58:42:       The solution is feasible.
        INFO - 13:58:42:       Objective: 30.39964825035985
        INFO - 13:58:42:       Standardized constraints:
        INFO - 13:58:42:          ineq1 = [-11.77907222]
        INFO - 13:58:42:          ineq2 = [-38.26307397]
        INFO - 13:58:42:       Design space:
        INFO - 13:58:42:          +------+-------------+-------------------+-------------+-------+
        INFO - 13:58:42:          | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 13:58:42:          +------+-------------+-------------------+-------------+-------+
        INFO - 13:58:42:          | x    |      0      | 1.542975634014225 |      5      | float |
        INFO - 13:58:42:          | y    |      0      | 1.269910308585573 |      3      | float |
        INFO - 13:58:42:          +------+-------------+-------------------+-------------+-------+


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>Optimization result:<br/><ul><li>Design variables: [1.54297563 1.26991031]</li><li>Objective function: 30.39964825035985</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 61-69

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 denote non-feasible points. Note that the user
can avoid the display of the non-feasible points.

.. GENERATED FROM PYTHON SOURCE LINES 69-88

.. code-block:: Python


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

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



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


    *

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

    *

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


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

 .. code-block:: none


    <gemseo.post.pareto_front.ParetoFront object at 0x7f28ccb4f700>




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

   **Total running time of the script:** (0 minutes 0.486 seconds)


.. _sphx_glr_download_examples_post_process_algorithms_plot_pareto_front_binhkorn.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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