.. 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 - 16:25:34:  
        INFO - 16:25:34: *** Start MDOScenario execution ***
        INFO - 16:25:34: MDOScenario
        INFO - 16:25:34:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
        INFO - 16:25:34:    MDO formulation: MDF
        INFO - 16:25:34: Optimization problem:
        INFO - 16:25:34:    minimize f(x_0, x_1, x_2)
        INFO - 16:25:34:    with respect to x_0, x_1, x_2
        INFO - 16:25:34:    subject to constraints:
        INFO - 16:25:34:       c_1(x_0, x_1, x_2) <= 0.0
        INFO - 16:25:34:       c_2(x_0, x_1, x_2) <= 0.0
        INFO - 16:25:34:    over the design space:
        INFO - 16:25:34:    |                             Parameter space                             |
        INFO - 16:25:34:    +------+-------------+-------+-------------+-------+----------------------+
        INFO - 16:25:34:    | name | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 16:25:34:    +------+-------------+-------+-------------+-------+----------------------+
        INFO - 16:25:34:    | x_0  |      0      |  0.5  |      1      | float |                      |
        INFO - 16:25:34:    | x_1  |      0      |  0.5  |      1      | float |                      |
        INFO - 16:25:34:    | x_2  |      0      |  0.5  |      1      | float |                      |
        INFO - 16:25:34:    | x_2  |      0      |  0.5  |      1      | float |                      |
        INFO - 16:25:34:    | x_2  |      0      |  0.5  |      1      | float |                      |
        INFO - 16:25:34:    +------+-------------+-------+-------------+-------+----------------------+
        INFO - 16:25:34: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 16:25:34: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 16:25:34: ...   1%|          | 1/100 [00:00<00:04, 20.73 it/sec, obj=1]
        INFO - 16:25:34: ...   2%|▏         | 2/100 [00:00<00:09, 10.16 it/sec, obj=0.921]
        INFO - 16:25:34: ...   3%|▎         | 3/100 [00:00<00:06, 15.19 it/sec, obj=0.513]
        INFO - 16:25:34: ...   4%|▍         | 4/100 [00:00<00:09, 10.31 it/sec, obj=0.438]
        INFO - 16:25:34: ...   5%|▌         | 5/100 [00:00<00:08, 10.95 it/sec, obj=0.418]
        INFO - 16:25:34: ...   6%|▌         | 6/100 [00:00<00:08, 11.37 it/sec, obj=0.416]
        INFO - 16:25:34: ...   7%|▋         | 7/100 [00:00<00:07, 11.68 it/sec, obj=0.415]
        INFO - 16:25:35: ...   8%|▊         | 8/100 [00:00<00:07, 11.90 it/sec, obj=0.415]
        INFO - 16:25:35: ...   9%|▉         | 9/100 [00:00<00:07, 12.09 it/sec, obj=0.415]
        INFO - 16:25:35: ...  10%|█         | 10/100 [00:00<00:07, 12.23 it/sec, obj=0.415]
        INFO - 16:25:35: ...  11%|█         | 11/100 [00:00<00:07, 12.36 it/sec, obj=0.415]
        INFO - 16:25:35: ...  12%|█▏        | 12/100 [00:00<00:07, 12.47 it/sec, obj=0.415]
        INFO - 16:25:35: ...  13%|█▎        | 13/100 [00:01<00:06, 12.55 it/sec, obj=0.415]
        INFO - 16:25:35: ...  14%|█▍        | 14/100 [00:01<00:06, 13.50 it/sec, obj=Not evaluated]
        INFO - 16:25:35: Optimization result:
        INFO - 16:25:35:    Optimizer info:
        INFO - 16:25:35:       Status: None
        INFO - 16:25:35:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 16:25:35:       Number of calls to the objective function by the optimizer: 15
        INFO - 16:25:35:    Solution:
        INFO - 16:25:35:       The solution is feasible.
        INFO - 16:25:35:       Objective: 0.4147214934939104
        INFO - 16:25:35:       Standardized constraints:
        INFO - 16:25:35:          c_1 = [-0.32430624 -0.43254418]
        INFO - 16:25:35:          c_2 = [-1.11022302e-16 -2.51297019e-01 -2.35380057e-01 -4.99967998e-01]
        INFO - 16:25:35:       +---------------------------------------------------------------------------------------+
        INFO - 16:25:35:       |                                    Parameter space                                    |
        INFO - 16:25:35:       +------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 16:25:35:       | name | lower_bound |        value        | upper_bound | type  | Initial distribution |
        INFO - 16:25:35:       +------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 16:25:35:       | x_0  |      0      |  0.4836327085400906 |      1      | float |                      |
        INFO - 16:25:35:       | x_1  |      0      |  0.9999999999999998 |      1      | float |                      |
        INFO - 16:25:35:       | x_2  |      0      | 0.08671672721432457 |      1      | float |                      |
        INFO - 16:25:35:       | x_2  |      0      |  0.9085358010297667 |      1      | float |                      |
        INFO - 16:25:35:       | x_2  |      0      |  0.2480176715968743 |      1      | float |                      |
        INFO - 16:25:35:       +------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 16:25:35: *** End MDOScenario execution (time: 0:00:01.056727) ***

    {'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

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.0/lib/python3.9/site-packages/genson/schema/strategies/base.py:42: UserWarning: Schema incompatible. Keyword 'description' has conflicting values ('The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.' vs. 'The width and height of the figure in inches, e.g. `(w, h)`.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'). Using 'The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'
      warn(('Schema incompatible. Keyword {0!r} has conflicting '

    <gemseo.post.opt_history_view.OptHistoryView object at 0x7fea489c2760>



.. 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 - 16:25:36: Optimization problem:
        INFO - 16:25:36:    minimize f = 0.5x'Qx + c'x + d
        INFO - 16:25:36:    with respect to x
        INFO - 16:25:36:    subject to constraints:
        INFO - 16:25:36:       g: Ax-b <= 0 <= 0.0
        INFO - 16:25:36:    over the design space:
        INFO - 16:25:36:    +------+-------------+-------+-------------+-------+
        INFO - 16:25:36:    | name | lower_bound | value | upper_bound | type  |
        INFO - 16:25:36:    +------+-------------+-------+-------------+-------+
        INFO - 16:25:36:    | x[0] |      0      |  0.5  |      1      | float |
        INFO - 16:25:36:    | x[1] |      0      |  0.5  |      1      | float |
        INFO - 16:25:36:    | x[2] |      0      |  0.5  |      1      | float |
        INFO - 16:25:36:    | x[3] |      0      |  0.5  |      1      | float |
        INFO - 16:25:36:    | x[4] |      0      |  0.5  |      1      | float |
        INFO - 16:25:36:    +------+-------------+-------+-------------+-------+
        INFO - 16:25:36: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 16:25:36: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 16:25:36: ...   1%|          | 1/100 [00:00<00:00, 2056.03 it/sec, obj=1]
        INFO - 16:25:36: ...   2%|▏         | 2/100 [00:00<00:00, 522.13 it/sec, obj=0.921]
        INFO - 16:25:36: ...   3%|▎         | 3/100 [00:00<00:00, 732.93 it/sec, obj=0.513]
        INFO - 16:25:36: ...   4%|▍         | 4/100 [00:00<00:00, 509.34 it/sec, obj=0.438]
        INFO - 16:25:36: ...   5%|▌         | 5/100 [00:00<00:00, 520.82 it/sec, obj=0.418]
        INFO - 16:25:36: ...   6%|▌         | 6/100 [00:00<00:00, 526.42 it/sec, obj=0.416]
        INFO - 16:25:36: ...   7%|▋         | 7/100 [00:00<00:00, 533.06 it/sec, obj=0.415]
        INFO - 16:25:36: ...   8%|▊         | 8/100 [00:00<00:00, 538.75 it/sec, obj=0.415]
        INFO - 16:25:36: ...   9%|▉         | 9/100 [00:00<00:00, 541.53 it/sec, obj=0.415]
        INFO - 16:25:36: ...  10%|█         | 10/100 [00:00<00:00, 545.80 it/sec, obj=0.415]
        INFO - 16:25:36: ...  11%|█         | 11/100 [00:00<00:00, 548.18 it/sec, obj=0.415]
        INFO - 16:25:36: ...  12%|█▏        | 12/100 [00:00<00:00, 549.95 it/sec, obj=0.415]
        INFO - 16:25:36: ...  13%|█▎        | 13/100 [00:00<00:00, 589.06 it/sec, obj=0.415]
        INFO - 16:25:36: Optimization result:
        INFO - 16:25:36:    Optimizer info:
        INFO - 16:25:36:       Status: None
        INFO - 16:25:36:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 16:25:36:       Number of calls to the objective function by the optimizer: 15
        INFO - 16:25:36:    Solution:
        INFO - 16:25:36:       The solution is feasible.
        INFO - 16:25:36:       Objective: 0.414721553468123
        INFO - 16:25:36:       Standardized constraints:
        INFO - 16:25:36:          g = [-3.24306238e-01 -4.32544172e-01 -4.44089210e-16 -2.51297007e-01
        INFO - 16:25:36:  -2.35380057e-01 -4.99968031e-01]
        INFO - 16:25:36:       Design space: 
        INFO - 16:25:36:       +------+-------------+---------------------+-------------+-------+
        INFO - 16:25:36:       | name | lower_bound |        value        | upper_bound | type  |
        INFO - 16:25:36:       +------+-------------+---------------------+-------------+-------+
        INFO - 16:25:36:       | x[0] |      0      |  0.4836327595359132 |      1      | float |
        INFO - 16:25:36:       | x[1] |      0      |  0.9999999999999998 |      1      | float |
        INFO - 16:25:36:       | x[2] |      0      | 0.08671677713547089 |      1      | float |
        INFO - 16:25:36:       | x[3] |      0      |  0.9085357909356101 |      1      | float |
        INFO - 16:25:36:       | x[4] |      0      |  0.2480176979962943 |      1      | float |
        INFO - 16:25:36:       +------+-------------+---------------------+-------------+-------+

    Optimization result:
       Design variables: [0.48363276 1.         0.08671678 0.90853579 0.2480177 ]
       Objective function: 0.414721553468123
       Feasible solution: True



.. 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 0x7fea48558040>




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

   **Total running time of the script:** ( 0 minutes  4.217 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>`_