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

.. only:: html

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

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

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

.. _sphx_glr_examples_scalable_plot_scalable_param_mdf.py:


Parametric scalable MDO problem - MDF
=====================================
We define
a :class:`~.gemseo.problems.scalable.parametric.scalable_problem.ScalableProblem`
with a shared design variable of size 1
and 2 strongly coupled disciplines.
The first one has a local design variable of size 1
and a coupling variable of size 2
while the second one has a local design variable of size 3
and a coupling variable of size 4.

We would like to solve this MDO problem by means of an MDF formulation.

.. GENERATED FROM PYTHON SOURCE LINES 35-48

.. code-block:: default

    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import execute_algo
    from gemseo import execute_post
    from gemseo import generate_n2_plot
    from gemseo.problems.scalable.parametric.core.scalable_discipline_settings import (
        ScalableDisciplineSettings,
    )
    from gemseo.problems.scalable.parametric.scalable_problem import ScalableProblem

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 49-51

Instantiation of the scalable problem
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: default

    problem = ScalableProblem(
        [ScalableDisciplineSettings(1, 2), ScalableDisciplineSettings(3, 4)], 1
    )








.. GENERATED FROM PYTHON SOURCE LINES 56-58

Display the coupling structure
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 58-60

.. code-block:: default

    generate_n2_plot(problem.disciplines, save=False, show=True)




.. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_001.png
   :alt: plot scalable param mdf
   :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 61-63

Solve the MDO using an MDF formulation
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 63-66

.. code-block:: default

    scenario = problem.create_scenario()
    scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})





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

 .. code-block:: none

        INFO - 08:23:54:  
        INFO - 08:23:54: *** Start MDOScenario execution ***
        INFO - 08:23:54: MDOScenario
        INFO - 08:23:54:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
        INFO - 08:23:54:    MDO formulation: MDF
        INFO - 08:23:54: Optimization problem:
        INFO - 08:23:54:    minimize f(x_0, x_1, x_2)
        INFO - 08:23:54:    with respect to x_0, x_1, x_2
        INFO - 08:23:54:    subject to constraints:
        INFO - 08:23:54:       c_1(x_0, x_1, x_2) <= 0.0
        INFO - 08:23:54:       c_2(x_0, x_1, x_2) <= 0.0
        INFO - 08:23:54:    over the design space:
        INFO - 08:23:54:    +--------+-------------+-------+-------------+-------+----------------------+
        INFO - 08:23:54:    | name   | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 08:23:54:    +--------+-------------+-------+-------------+-------+----------------------+
        INFO - 08:23:54:    | x_0    |      0      |  0.5  |      1      | float |                      |
        INFO - 08:23:54:    | x_1    |      0      |  0.5  |      1      | float |                      |
        INFO - 08:23:54:    | x_2[0] |      0      |  0.5  |      1      | float |                      |
        INFO - 08:23:54:    | x_2[1] |      0      |  0.5  |      1      | float |                      |
        INFO - 08:23:54:    | x_2[2] |      0      |  0.5  |      1      | float |                      |
        INFO - 08:23:54:    +--------+-------------+-------+-------------+-------+----------------------+
        INFO - 08:23:54: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 08:23:54: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 08:23:55: ...   1%|          | 1/100 [00:00<00:04, 24.38 it/sec, obj=1]
        INFO - 08:23:55: ...   2%|▏         | 2/100 [00:00<00:08, 11.70 it/sec, obj=0.921]
        INFO - 08:23:55: ...   3%|▎         | 3/100 [00:00<00:05, 17.51 it/sec, obj=0.513]
        INFO - 08:23:55: ...   4%|▍         | 4/100 [00:00<00:08, 11.90 it/sec, obj=0.438]
        INFO - 08:23:55: ...   5%|▌         | 5/100 [00:00<00:07, 12.53 it/sec, obj=0.418]
        INFO - 08:23:55: ...   6%|▌         | 6/100 [00:00<00:07, 13.00 it/sec, obj=0.416]
        INFO - 08:23:55: ...   7%|▋         | 7/100 [00:00<00:06, 13.31 it/sec, obj=0.415]
        INFO - 08:23:55: ...   8%|▊         | 8/100 [00:00<00:06, 13.57 it/sec, obj=0.415]
        INFO - 08:23:55: ...   9%|▉         | 9/100 [00:00<00:06, 13.77 it/sec, obj=0.415]
        INFO - 08:23:55: ...  10%|█         | 10/100 [00:00<00:06, 13.96 it/sec, obj=0.415]
        INFO - 08:23:55: ...  11%|█         | 11/100 [00:00<00:06, 14.11 it/sec, obj=0.415]
        INFO - 08:23:55: ...  12%|█▏        | 12/100 [00:00<00:05, 14.95 it/sec, obj=0.415]
        INFO - 08:23:55: ...  13%|█▎        | 13/100 [00:00<00:05, 16.19 it/sec, obj=0.415]
        INFO - 08:23:55: Optimization result:
        INFO - 08:23:55:    Optimizer info:
        INFO - 08:23:55:       Status: None
        INFO - 08:23:55:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 08:23:55:       Number of calls to the objective function by the optimizer: 15
        INFO - 08:23:55:    Solution:
        INFO - 08:23:55:       The solution is feasible.
        INFO - 08:23:55:       Objective: 0.4147214093889784
        INFO - 08:23:55:       Standardized constraints:
        INFO - 08:23:55:          c_1 = [-0.32430622 -0.43254409]
        INFO - 08:23:55:          c_2 = [ 2.44645415e-11 -2.51297060e-01 -2.35380107e-01 -4.99968067e-01]
        INFO - 08:23:55:       Scalable design space:
        INFO - 08:23:55:       +--------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 08:23:55:       | name   | lower_bound |        value        | upper_bound | type  | Initial distribution |
        INFO - 08:23:55:       +--------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 08:23:55:       | x_0    |      0      |  0.4836326345734573 |      1      | float |                      |
        INFO - 08:23:55:       | x_1    |      0      |  0.9999999999999998 |      1      | float |                      |
        INFO - 08:23:55:       | x_2[0] |      0      | 0.08671679318925574 |      1      | float |                      |
        INFO - 08:23:55:       | x_2[1] |      0      |  0.9085357497327241 |      1      | float |                      |
        INFO - 08:23:55:       | x_2[2] |      0      |  0.2480176751996585 |      1      | float |                      |
        INFO - 08:23:55:       +--------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 08:23:55: *** End MDOScenario execution (time: 0:00:00.819416) ***

    {'max_iter': 100, 'algo': 'NLOPT_SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 67-69

Post-process the results
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 69-71

.. code-block:: default

    scenario.post_process("OptHistoryView", save=False, show=True)




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


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_004.png
         :alt: Distance to the optimum
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_005.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_006.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_006.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f0cbe9cfe20>



.. GENERATED FROM PYTHON SOURCE LINES 72-74

Solve the associated quadratic programming problem
--------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 74-77

.. code-block:: default

    problem = problem.create_quadratic_programming_problem()
    execute_algo(problem, algo_name="NLOPT_SLSQP", max_iter=100)





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

 .. code-block:: none

        INFO - 08:23:56: Optimization problem:
        INFO - 08:23:56:    minimize f = 0.5x'Qx + c'x + d
        INFO - 08:23:56:    with respect to x
        INFO - 08:23:56:    subject to constraints:
        INFO - 08:23:56:       g: Ax-b <= 0 <= 0.0
        INFO - 08:23:56:    over the design space:
        INFO - 08:23:56:    +------+-------------+-------+-------------+-------+
        INFO - 08:23:56:    | name | lower_bound | value | upper_bound | type  |
        INFO - 08:23:56:    +------+-------------+-------+-------------+-------+
        INFO - 08:23:56:    | x[0] |      0      |  0.5  |      1      | float |
        INFO - 08:23:56:    | x[1] |      0      |  0.5  |      1      | float |
        INFO - 08:23:56:    | x[2] |      0      |  0.5  |      1      | float |
        INFO - 08:23:56:    | x[3] |      0      |  0.5  |      1      | float |
        INFO - 08:23:56:    | x[4] |      0      |  0.5  |      1      | float |
        INFO - 08:23:56:    +------+-------------+-------+-------------+-------+
        INFO - 08:23:56: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 08:23:56: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 08:23:56: ...   1%|          | 1/100 [00:00<00:00, 2441.39 it/sec, obj=1]
        INFO - 08:23:56: ...   2%|▏         | 2/100 [00:00<00:00, 563.86 it/sec, obj=0.921]
        INFO - 08:23:56: ...   3%|▎         | 3/100 [00:00<00:00, 791.43 it/sec, obj=0.513]
        INFO - 08:23:56: ...   4%|▍         | 4/100 [00:00<00:00, 548.78 it/sec, obj=0.438]
        INFO - 08:23:56: ...   5%|▌         | 5/100 [00:00<00:00, 506.53 it/sec, obj=0.418]
        INFO - 08:23:56: ...   6%|▌         | 6/100 [00:00<00:00, 498.95 it/sec, obj=0.416]
        INFO - 08:23:56: ...   7%|▋         | 7/100 [00:00<00:00, 513.24 it/sec, obj=0.415]
        INFO - 08:23:56: ...   8%|▊         | 8/100 [00:00<00:00, 523.37 it/sec, obj=0.415]
        INFO - 08:23:56: ...   9%|▉         | 9/100 [00:00<00:00, 532.63 it/sec, obj=0.415]
        INFO - 08:23:56: ...  10%|█         | 10/100 [00:00<00:00, 539.93 it/sec, obj=0.415]
        INFO - 08:23:56: ...  11%|█         | 11/100 [00:00<00:00, 543.57 it/sec, obj=0.415]
        INFO - 08:23:56: ...  12%|█▏        | 12/100 [00:00<00:00, 549.96 it/sec, obj=0.415]
        INFO - 08:23:56: ...  13%|█▎        | 13/100 [00:00<00:00, 588.78 it/sec, obj=0.415]
        INFO - 08:23:56: Optimization result:
        INFO - 08:23:56:    Optimizer info:
        INFO - 08:23:56:       Status: None
        INFO - 08:23:56:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 08:23:56:       Number of calls to the objective function by the optimizer: 15
        INFO - 08:23:56:    Solution:
        INFO - 08:23:56:       The solution is feasible.
        INFO - 08:23:56:       Objective: 0.414721553468123
        INFO - 08:23:56:       Standardized constraints:
        INFO - 08:23:56:          g = [-3.24306238e-01 -4.32544172e-01 -4.44089210e-16 -2.51297007e-01
        INFO - 08:23:56:  -2.35380057e-01 -4.99968031e-01]
        INFO - 08:23:56:       Design space:
        INFO - 08:23:56:       +------+-------------+---------------------+-------------+-------+
        INFO - 08:23:56:       | name | lower_bound |        value        | upper_bound | type  |
        INFO - 08:23:56:       +------+-------------+---------------------+-------------+-------+
        INFO - 08:23:56:       | x[0] |      0      |  0.4836327595359132 |      1      | float |
        INFO - 08:23:56:       | x[1] |      0      |  0.9999999999999998 |      1      | float |
        INFO - 08:23:56:       | x[2] |      0      | 0.08671677713547089 |      1      | float |
        INFO - 08:23:56:       | x[3] |      0      |  0.9085357909356101 |      1      | float |
        INFO - 08:23:56:       | x[4] |      0      |  0.2480176979962943 |      1      | float |
        INFO - 08:23:56:       +------+-------------+---------------------+-------------+-------+


.. 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: [0.48363276 1.         0.08671678 0.90853579 0.2480177 ]</li><li>Objective function: 0.414721553468123</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 78-80

Post-process the results
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 80-81

.. code-block:: default

    execute_post(problem, "OptHistoryView", save=False, show=True)



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


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_007.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_008.png
         :alt: Evolution of the objective value
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_009.png
         :alt: Distance to the optimum
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_009.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_010.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_010.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_011.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/scalable/images/sphx_glr_plot_scalable_param_mdf_011.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f0cbeafc370>




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

   **Total running time of the script:** (0 minutes 3.621 seconds)


.. _sphx_glr_download_examples_scalable_plot_scalable_param_mdf.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_scalable_param_mdf.py <plot_scalable_param_mdf.py>`

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

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


.. only:: html

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

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