.. 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 35-49

.. code-block:: Python


    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 50-52

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

.. GENERATED FROM PYTHON SOURCE LINES 52-56

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 57-59

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

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: Python

    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 62-64

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

.. GENERATED FROM PYTHON SOURCE LINES 64-67

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 10:53:53:  
        INFO - 10:53:53: *** Start MDOScenario execution ***
        INFO - 10:53:53: MDOScenario
        INFO - 10:53:53:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
        INFO - 10:53:53:    MDO formulation: MDF
        INFO - 10:53:53: Optimization problem:
        INFO - 10:53:53:    minimize f(x_0, x_1, x_2)
        INFO - 10:53:53:    with respect to x_0, x_1, x_2
        INFO - 10:53:53:    subject to constraints:
        INFO - 10:53:53:       c_1(x_0, x_1, x_2) <= 0.0
        INFO - 10:53:53:       c_2(x_0, x_1, x_2) <= 0.0
        INFO - 10:53:53:    over the design space:
        INFO - 10:53:53:       +--------+-------------+-------+-------------+-------+
        INFO - 10:53:53:       | Name   | Lower bound | Value | Upper bound | Type  |
        INFO - 10:53:53:       +--------+-------------+-------+-------------+-------+
        INFO - 10:53:53:       | x_0    |      0      |  0.5  |      1      | float |
        INFO - 10:53:53:       | x_1    |      0      |  0.5  |      1      | float |
        INFO - 10:53:53:       | x_2[0] |      0      |  0.5  |      1      | float |
        INFO - 10:53:53:       | x_2[1] |      0      |  0.5  |      1      | float |
        INFO - 10:53:53:       | x_2[2] |      0      |  0.5  |      1      | float |
        INFO - 10:53:53:       +--------+-------------+-------+-------------+-------+
        INFO - 10:53:53: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:53:53:      1%|          | 1/100 [00:00<00:05, 18.62 it/sec, obj=3.07]
     WARNING - 10:53:54: MDAJacobi has reached its maximum number of iterations but the normed residual 2.1168696116299354e-06 is still above the tolerance 1e-06.
        INFO - 10:53:54:      2%|▏         | 2/100 [00:00<00:12,  7.63 it/sec, obj=1.21]
        INFO - 10:53:54:      3%|▎         | 3/100 [00:00<00:11,  8.74 it/sec, obj=0.991]
        INFO - 10:53:54:      4%|▍         | 4/100 [00:00<00:10,  9.48 it/sec, obj=0.986]
        INFO - 10:53:54:      5%|▌         | 5/100 [00:00<00:09,  9.97 it/sec, obj=0.982]
        INFO - 10:53:54:      6%|▌         | 6/100 [00:00<00:09, 10.31 it/sec, obj=0.971]
        INFO - 10:53:54:      7%|▋         | 7/100 [00:00<00:08, 10.53 it/sec, obj=0.97]
        INFO - 10:53:54:      8%|▊         | 8/100 [00:00<00:08, 10.75 it/sec, obj=0.969]
        INFO - 10:53:54:      9%|▉         | 9/100 [00:00<00:08, 10.90 it/sec, obj=0.969]
        INFO - 10:53:54:     10%|█         | 10/100 [00:00<00:08, 11.02 it/sec, obj=0.969]
        INFO - 10:53:54:     11%|█         | 11/100 [00:00<00:07, 12.11 it/sec, obj=Not evaluated]
        INFO - 10:53:54: Optimization result:
        INFO - 10:53:54:    Optimizer info:
        INFO - 10:53:54:       Status: None
        INFO - 10:53:54:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 10:53:54:       Number of calls to the objective function by the optimizer: 11
        INFO - 10:53:54:    Solution:
        INFO - 10:53:54:       The solution is feasible.
        INFO - 10:53:54:       Objective: 0.9692177673322132
        INFO - 10:53:54:       Standardized constraints:
        INFO - 10:53:54:          c_1 = [-0.68664086 -0.21340455]
        INFO - 10:53:54:          c_2 = [-7.31227816e-01 -1.68967484e-01 -2.32695971e-01  1.19959598e-12]
        INFO - 10:53:54:       Design space:
        INFO - 10:53:54:          +--------+-------------+-----------------------+-------------+-------+
        INFO - 10:53:54:          | Name   | Lower bound |         Value         | Upper bound | Type  |
        INFO - 10:53:54:          +--------+-------------+-----------------------+-------------+-------+
        INFO - 10:53:54:          | x_0    |      0      |   0.7071349698120486  |      1      | float |
        INFO - 10:53:54:          | x_1    |      0      |   0.999999999999994   |      1      | float |
        INFO - 10:53:54:          | x_2[0] |      0      | 1.149355539667889e-15 |      1      | float |
        INFO - 10:53:54:          | x_2[1] |      0      |   0.5233175560073939  |      1      | float |
        INFO - 10:53:54:          | x_2[2] |      0      | 7.693613505196677e-16 |      1      | float |
        INFO - 10:53:54:          +--------+-------------+-----------------------+-------------+-------+
        INFO - 10:53:54: *** End MDOScenario execution (time: 0:00:00.925638) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 68-70

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

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    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 0x7efd344dc220>



.. GENERATED FROM PYTHON SOURCE LINES 73-75

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

.. GENERATED FROM PYTHON SOURCE LINES 75-78

.. code-block:: Python

    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 - 10:53:55: Optimization problem:
        INFO - 10:53:55:    minimize f = 0.5x'Qx + c'x + d
        INFO - 10:53:55:    with respect to x
        INFO - 10:53:55:    subject to constraints:
        INFO - 10:53:55:       g: Ax-b <= 0 <= 0.0
        INFO - 10:53:55:    over the design space:
        INFO - 10:53:55:       +------+-------------+-------+-------------+-------+
        INFO - 10:53:55:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 10:53:55:       +------+-------------+-------+-------------+-------+
        INFO - 10:53:55:       | x[0] |      0      |  0.5  |      1      | float |
        INFO - 10:53:55:       | x[1] |      0      |  0.5  |      1      | float |
        INFO - 10:53:55:       | x[2] |      0      |  0.5  |      1      | float |
        INFO - 10:53:55:       | x[3] |      0      |  0.5  |      1      | float |
        INFO - 10:53:55:       | x[4] |      0      |  0.5  |      1      | float |
        INFO - 10:53:55:       +------+-------------+-------+-------------+-------+
        INFO - 10:53:55: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:53:55:      1%|          | 1/100 [00:00<00:00, 2098.20 it/sec, obj=3.07]
        INFO - 10:53:55:      2%|▏         | 2/100 [00:00<00:00, 530.76 it/sec, obj=1.21]
        INFO - 10:53:55:      3%|▎         | 3/100 [00:00<00:00, 534.44 it/sec, obj=0.991]
        INFO - 10:53:55:      4%|▍         | 4/100 [00:00<00:00, 547.88 it/sec, obj=0.986]
        INFO - 10:53:55:      5%|▌         | 5/100 [00:00<00:00, 553.98 it/sec, obj=0.982]
        INFO - 10:53:55:      6%|▌         | 6/100 [00:00<00:00, 555.92 it/sec, obj=0.971]
        INFO - 10:53:55:      7%|▋         | 7/100 [00:00<00:00, 552.47 it/sec, obj=0.97]
       ERROR - 10:53:55: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.2.0/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.2.0/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 10:53:55:      8%|▊         | 8/100 [00:00<00:00, 533.36 it/sec, obj=0.969]
        INFO - 10:53:55: Optimization result:
        INFO - 10:53:55:    Optimizer info:
        INFO - 10:53:55:       Status: None
        INFO - 10:53:55:       Message:  GEMSEO Stopped the driver
        INFO - 10:53:55:       Number of calls to the objective function by the optimizer: 9
        INFO - 10:53:55:    Solution:
        INFO - 10:53:55:       The solution is feasible.
        INFO - 10:53:55:       Objective: 0.9692176254005034
        INFO - 10:53:55:       Standardized constraints:
        INFO - 10:53:55:          g = [-6.86640980e-01 -2.13404451e-01 -7.31227677e-01 -1.68967471e-01
        INFO - 10:53:55:  -2.32695870e-01 -2.22044605e-15]
        INFO - 10:53:55:       Design space:
        INFO - 10:53:55:          +------+-------------+--------------------+-------------+-------+
        INFO - 10:53:55:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 10:53:55:          +------+-------------+--------------------+-------------+-------+
        INFO - 10:53:55:          | x[0] |      0      | 0.7071348743877915 |      1      | float |
        INFO - 10:53:55:          | x[1] |      0      |         1          |      1      | float |
        INFO - 10:53:55:          | x[2] |      0      |         0          |      1      | float |
        INFO - 10:53:55:          | x[3] |      0      | 0.5233180438726639 |      1      | float |
        INFO - 10:53:55:          | x[4] |      0      |         0          |      1      | float |
        INFO - 10:53:55:          +------+-------------+--------------------+-------------+-------+


.. 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: [0.70713487 1.         0.         0.52331804 0.        ]</li><li>Objective function: 0.9692176254005034</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 79-81

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

.. GENERATED FROM PYTHON SOURCE LINES 81-82

.. code-block:: Python

    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 0x7efd341af1f0>




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

   **Total running time of the script:** (0 minutes 3.857 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-jupyter

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

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

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


.. only:: html

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

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