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

.. only:: html

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

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

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

.. _sphx_glr_examples_mdo_plot_opt_as_mdo.py:


Make a monodisciplinary optimization problem multidisciplinary
==============================================================

Introduction
------------

The :class:`.OptAsMDOScenario` is a class
to make a monodisciplinary optimization problem multidisciplinary :cite:`AzizAlaoui2025`.
The only requirement is that
the discipline has at least three scalar inputs and at least one output.
This scenario can be used to enrich a catalog of benchmark MDO problems,
based on the observation that
MDO benchmark problems are far less numerous than optimization problems.

This example illustrates it
in the case of the minimization of the 3-dimensional Rosenbrock function

.. math::

   f(z) = 100(z_2-z_1^2)^2 + (1-z_1)^2 + 100(z_1-z_0^2)^2 + (1-z_0)^2

over the hypercube :math:`[-1,1]^3`.

The unique solution of this minimization problem is
the design point :math:`z^*=(1,1,1)` at which :math:`f` is zero.

.. GENERATED FROM PYTHON SOURCE LINES 43-57

.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo import configure_logger
    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import generate_coupling_graph
    from gemseo.problems.mdo.opt_as_mdo_scenario import OptAsMDOScenario

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 58-62

Material
--------
First,
we create the discipline implementing the Rosenbrock function:

.. GENERATED FROM PYTHON SOURCE LINES 62-67

.. code-block:: Python

    discipline = create_discipline(
        "AnalyticDiscipline",
        expressions={"f": "100*(z_2-z_1**2)**2+(1-z_1)**2+100*(z_1-z_0**2)**2+(1-z_0)**2"},
        name="Rosenbrock",
    )







.. GENERATED FROM PYTHON SOURCE LINES 68-69

as well as the design space:

.. GENERATED FROM PYTHON SOURCE LINES 69-73

.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("z_0", lower_bound=-1, upper_bound=1)
    design_space.add_variable("z_1", lower_bound=-1, upper_bound=1)
    design_space.add_variable("z_2", lower_bound=-1, upper_bound=1)







.. GENERATED FROM PYTHON SOURCE LINES 74-76

and choose :math:`x^{(0)}=(-0.25, 0.75, -0.9)`
as the starting point of the optimization:

.. GENERATED FROM PYTHON SOURCE LINES 76-79

.. code-block:: Python

    initial_point = array([-0.25, 0.75, -0.9])
    design_space.set_current_value(initial_point)








.. GENERATED FROM PYTHON SOURCE LINES 80-84

Optimization problem
--------------------
Then,
we define the optimization problem:

.. GENERATED FROM PYTHON SOURCE LINES 84-87

.. code-block:: Python

    opt_scenario = create_scenario(
        [discipline], "f", design_space, formulation_name="DisciplinaryOpt"
    )







.. GENERATED FROM PYTHON SOURCE LINES 88-89

and solve it using the SLSQP algorithm:

.. GENERATED FROM PYTHON SOURCE LINES 89-90

.. code-block:: Python

    opt_scenario.execute(algo_name="NLOPT_SLSQP", max_iter=100)




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

 .. code-block:: none

        INFO - 20:38:26: *** Start MDOScenario execution ***
        INFO - 20:38:26: MDOScenario
        INFO - 20:38:26:    Disciplines: Rosenbrock
        INFO - 20:38:26:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:26: Optimization problem:
        INFO - 20:38:26:    minimize f(z_0, z_1, z_2)
        INFO - 20:38:26:    with respect to z_0, z_1, z_2
        INFO - 20:38:26:    over the design space:
        INFO - 20:38:26:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:26:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:26:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:26:       | z_0  |      -1     | -0.25 |      1      | float |
        INFO - 20:38:26:       | z_1  |      -1     |  0.75 |      1      | float |
        INFO - 20:38:26:       | z_2  |      -1     |  -0.9 |      1      | float |
        INFO - 20:38:26:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:26: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 20:38:26:      1%|          | 1/100 [00:00<00:00, 404.78 it/sec, obj=263]
        INFO - 20:38:26:      2%|▏         | 2/100 [00:00<00:00, 568.95 it/sec, obj=408]
        INFO - 20:38:26:      3%|▎         | 3/100 [00:00<00:00, 815.33 it/sec, obj=20.2]
        INFO - 20:38:26:      4%|▍         | 4/100 [00:00<00:00, 824.84 it/sec, obj=168]
        INFO - 20:38:26:      5%|▌         | 5/100 [00:00<00:00, 1003.71 it/sec, obj=8.91]
        INFO - 20:38:26:      6%|▌         | 6/100 [00:00<00:00, 992.54 it/sec, obj=395]
        INFO - 20:38:26:      7%|▋         | 7/100 [00:00<00:00, 1133.29 it/sec, obj=4.06]
        INFO - 20:38:26:      8%|▊         | 8/100 [00:00<00:00, 1109.05 it/sec, obj=151]
        INFO - 20:38:26:      9%|▉         | 9/100 [00:00<00:00, 1226.17 it/sec, obj=3.31]
        INFO - 20:38:26:     10%|█         | 10/100 [00:00<00:00, 1183.66 it/sec, obj=2.09]
        INFO - 20:38:26:     11%|█         | 11/100 [00:00<00:00, 1218.95 it/sec, obj=2.02]
        INFO - 20:38:26:     12%|█▏        | 12/100 [00:00<00:00, 1254.43 it/sec, obj=1.97]
        INFO - 20:38:26:     13%|█▎        | 13/100 [00:00<00:00, 1283.63 it/sec, obj=1.92]
        INFO - 20:38:26:     14%|█▍        | 14/100 [00:00<00:00, 1311.22 it/sec, obj=1.85]
        INFO - 20:38:26:     15%|█▌        | 15/100 [00:00<00:00, 1336.62 it/sec, obj=1.73]
        INFO - 20:38:26:     16%|█▌        | 16/100 [00:00<00:00, 1358.78 it/sec, obj=1.3]
        INFO - 20:38:26:     17%|█▋        | 17/100 [00:00<00:00, 1378.53 it/sec, obj=0.995]
        INFO - 20:38:26:     18%|█▊        | 18/100 [00:00<00:00, 1396.50 it/sec, obj=0.721]
        INFO - 20:38:26:     19%|█▉        | 19/100 [00:00<00:00, 1416.59 it/sec, obj=0.625]
        INFO - 20:38:26:     20%|██        | 20/100 [00:00<00:00, 1438.87 it/sec, obj=6.19]
        INFO - 20:38:26:     21%|██        | 21/100 [00:00<00:00, 1498.20 it/sec, obj=0.491]
        INFO - 20:38:26:     22%|██▏       | 22/100 [00:00<00:00, 1461.75 it/sec, obj=5.86]
        INFO - 20:38:26:     23%|██▎       | 23/100 [00:00<00:00, 1515.62 it/sec, obj=0.403]
        INFO - 20:38:26:     24%|██▍       | 24/100 [00:00<00:00, 1482.00 it/sec, obj=0.87]
        INFO - 20:38:26:     25%|██▌       | 25/100 [00:00<00:00, 1532.00 it/sec, obj=0.279]
        INFO - 20:38:26:     26%|██▌       | 26/100 [00:00<00:00, 1494.46 it/sec, obj=0.243]
        INFO - 20:38:26:     27%|██▋       | 27/100 [00:00<00:00, 1509.04 it/sec, obj=0.244]
        INFO - 20:38:26:     28%|██▊       | 28/100 [00:00<00:00, 1554.60 it/sec, obj=0.224]
        INFO - 20:38:26:     29%|██▉       | 29/100 [00:00<00:00, 1519.62 it/sec, obj=0.171]
        INFO - 20:38:26:     30%|███       | 30/100 [00:00<00:00, 1534.30 it/sec, obj=0.276]
        INFO - 20:38:26:     31%|███       | 31/100 [00:00<00:00, 1574.46 it/sec, obj=0.117]
        INFO - 20:38:26:     32%|███▏      | 32/100 [00:00<00:00, 1539.99 it/sec, obj=0.0792]
        INFO - 20:38:26:     33%|███▎      | 33/100 [00:00<00:00, 1547.92 it/sec, obj=0.0624]
        INFO - 20:38:26:     34%|███▍      | 34/100 [00:00<00:00, 1554.24 it/sec, obj=0.0366]
        INFO - 20:38:26:     35%|███▌      | 35/100 [00:00<00:00, 1562.14 it/sec, obj=0.0298]
        INFO - 20:38:26:     36%|███▌      | 36/100 [00:00<00:00, 1568.60 it/sec, obj=0.0164]
        INFO - 20:38:26:     37%|███▋      | 37/100 [00:00<00:00, 1576.60 it/sec, obj=0.0103]
        INFO - 20:38:26:     38%|███▊      | 38/100 [00:00<00:00, 1583.07 it/sec, obj=0.00429]
        INFO - 20:38:26:     39%|███▉      | 39/100 [00:00<00:00, 1590.62 it/sec, obj=0.00128]
        INFO - 20:38:26:     40%|████      | 40/100 [00:00<00:00, 1596.69 it/sec, obj=0.000368]
        INFO - 20:38:26:     41%|████      | 41/100 [00:00<00:00, 1603.21 it/sec, obj=2.77e-5]
        INFO - 20:38:26:     42%|████▏     | 42/100 [00:00<00:00, 1607.34 it/sec, obj=6.38e-7]
        INFO - 20:38:26:     43%|████▎     | 43/100 [00:00<00:00, 1612.69 it/sec, obj=1.32e-9]
        INFO - 20:38:26:     44%|████▍     | 44/100 [00:00<00:00, 1618.53 it/sec, obj=9.1e-12]
        INFO - 20:38:26:     45%|████▌     | 45/100 [00:00<00:00, 1623.69 it/sec, obj=6.58e-14]
        INFO - 20:38:26:     46%|████▌     | 46/100 [00:00<00:00, 1629.56 it/sec, obj=1.58e-21]
        INFO - 20:38:26:     47%|████▋     | 47/100 [00:00<00:00, 1632.21 it/sec, obj=Not evaluated]
        INFO - 20:38:26: Optimization result:
        INFO - 20:38:26:    Optimizer info:
        INFO - 20:38:26:       Status: None
        INFO - 20:38:26:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:38:26:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:26:    Solution:
        INFO - 20:38:26:       Objective: 1.584054020051718e-21
        INFO - 20:38:26:       Design space:
        INFO - 20:38:26:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:38:26:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:38:26:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:38:26:          | z_0  |      -1     |         1          |      1      | float |
        INFO - 20:38:26:          | z_1  |      -1     | 0.9999999999996698 |      1      | float |
        INFO - 20:38:26:          | z_2  |      -1     | 0.9999999999953735 |      1      | float |
        INFO - 20:38:26:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:38:26: *** End MDOScenario execution ***




.. GENERATED FROM PYTHON SOURCE LINES 91-101

We can see that the numerical solution corresponds to the analytical one.

MDO problem
-----------
Now,
we use the :class:`.OptAsMDOScenario` to rewrite this optimization problem
as an MDO problem with two strongly coupled disciplines.

First,
we reset the design space to the initial point:

.. GENERATED FROM PYTHON SOURCE LINES 101-102

.. code-block:: Python

    design_space.set_current_value(initial_point)







.. GENERATED FROM PYTHON SOURCE LINES 103-105

and create the :class:`.OptAsMDOScenario`,
orchestrated by an MDF formulation:

.. GENERATED FROM PYTHON SOURCE LINES 105-106

.. code-block:: Python

    mdo_scenario = OptAsMDOScenario(discipline, "f", design_space, formulation_name="MDF")







.. GENERATED FROM PYTHON SOURCE LINES 107-109

Then,
we can see that the design variables have been renamed:

.. GENERATED FROM PYTHON SOURCE LINES 109-110

.. code-block:: Python

    design_space





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='margin: 1em;'>Design space:<br/><table>
        <thead>
            <tr>
                <th>Name</th>
                <th>Lower bound</th>
                <th>Value</th>
                <th>Upper bound</th>
                <th>Type</th>
            </tr>
        </thead>
        <tbody>
            <tr>
                <td>x_0</td>
                <td>-1</td>
                <td>-0.25</td>
                <td>1</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_1</td>
                <td>-1</td>
                <td>0.75</td>
                <td>1</td>
                <td>float</td>
            </tr>
            <tr>
                <td>x_2</td>
                <td>-1</td>
                <td>-0.9</td>
                <td>1</td>
                <td>float</td>
            </tr>
        </tbody>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 111-119

This renaming is based on the convention:

- the first design variable is the global design variable and is named :math:`x_0`,
- the :math:`(1+i)`-th design variable is the local design variable
  specific to the :math:`i`-th strongly coupled discipline
  and is named :math:`x_{1+i}`.

We can also have a look to the coupling graph:

.. GENERATED FROM PYTHON SOURCE LINES 119-120

.. code-block:: Python

    generate_coupling_graph(mdo_scenario.disciplines, file_path="")





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <?xml version="1.0" encoding="UTF-8" standalone="no"?>
    <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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    <text text-anchor="middle" x="69.54" y="-188.3" font-family="Times,serif" font-size="14.00">L</text>
    </g>
    <!-- Rosenbrock -->
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    <title>Rosenbrock</title>
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    <text text-anchor="middle" x="69.54" y="-101.3" font-family="Times,serif" font-size="14.00">Rosenbrock</text>
    </g>
    <!-- L&#45;&gt;Rosenbrock -->
    <g id="edge1" class="edge">
    <title>L&#45;&gt;Rosenbrock</title>
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    <g id="a_edge1&#45;label"><a xlink:title="Global name, Name in discipline &#39;L&#39;, Name in discipline &#39;Rosenbrock&#39;&#10;&#10;z_2, z_2, z_2&#10;z_0, z_0, z_0&#10;z_1, z_1, z_1">
    <text text-anchor="middle" x="113.54" y="-144.8" font-family="Times,serif" font-size="14.00">z_0, z_1, z_2</text>
    </a>
    </g>
    </g>
    <!-- _Rosenbrock -->
    <!-- Rosenbrock&#45;&gt;_Rosenbrock -->
    <g id="edge6" class="edge">
    <title>Rosenbrock&#45;&gt;_Rosenbrock</title>
    <path fill="none" stroke="black" d="M69.54,-86.8C69.54,-75.16 69.54,-59.55 69.54,-46.24"/>
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    </g>
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    <!-- D1 -->
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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 121-131

and see that there are two strongly coupled disciplines :math:`D_1` and :math:`D_2`,
connected by the coupling variables :math:`y_1` and :math:`y_2`.
These disciplines are weakly coupled to a downstream link discipline :math:`L`,
which is weakly coupled to the downstream original discipline.
Let us note that the link discipline computes
the values of the design variables in the original optimization problem
from the values of the design and coupling variables in the MDO problem.

Lastly,
we solve this scenario using the SLSQP algorithm:

.. GENERATED FROM PYTHON SOURCE LINES 131-133

.. code-block:: Python

    mdo_scenario.set_differentiation_method(method="finite_differences")
    mdo_scenario.execute(algo_name="NLOPT_SLSQP", max_iter=100)




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

 .. code-block:: none

        INFO - 20:38:26: *** Start OptAsMDOScenario execution ***
        INFO - 20:38:26: OptAsMDOScenario
        INFO - 20:38:26:    Disciplines: D1 D2 L Rosenbrock
        INFO - 20:38:26:    MDO formulation: MDF
        INFO - 20:38:26: Optimization problem:
        INFO - 20:38:26:    minimize f(x_0, x_1, x_2)
        INFO - 20:38:26:    with respect to x_0, x_1, x_2
        INFO - 20:38:26:    over the design space:
        INFO - 20:38:26:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:26:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:26:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:26:       | x_0  |      -1     | -0.25 |      1      | float |
        INFO - 20:38:26:       | x_1  |      -1     |  0.75 |      1      | float |
        INFO - 20:38:26:       | x_2  |      -1     |  -0.9 |      1      | float |
        INFO - 20:38:26:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:26: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 20:38:26:      1%|          | 1/100 [00:00<00:00, 104.55 it/sec, obj=263]
        INFO - 20:38:26:      2%|▏         | 2/100 [00:00<00:01, 64.44 it/sec, obj=408]
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     WARNING - 20:38:26: All components of the normalized vector should be between 0 and 1; upper bounds violated: [1.000001].
     WARNING - 20:38:26: All components of the normalized vector should be between 0 and 1; upper bounds violated: [1.000001].
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     WARNING - 20:38:26: All components of the normalized vector should be between 0 and 1; upper bounds violated: [1.000001].
        INFO - 20:38:26:      8%|▊         | 8/100 [00:00<00:01, 84.14 it/sec, obj=151]
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     WARNING - 20:38:26: All components of the normalized vector should be between 0 and 1; upper bounds violated: [1.000001].
        INFO - 20:38:26:     19%|█▉        | 19/100 [00:00<00:00, 83.03 it/sec, obj=0.6]
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        INFO - 20:38:26:     39%|███▉      | 39/100 [00:00<00:00, 85.11 it/sec, obj=9.5e-7]
        INFO - 20:38:26:     40%|████      | 40/100 [00:00<00:00, 85.08 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     41%|████      | 41/100 [00:00<00:00, 86.24 it/sec, obj=6.45e-7]
        INFO - 20:38:26:     42%|████▏     | 42/100 [00:00<00:00, 88.30 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     43%|████▎     | 43/100 [00:00<00:00, 89.87 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     44%|████▍     | 44/100 [00:00<00:00, 91.41 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     45%|████▌     | 45/100 [00:00<00:00, 92.94 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     46%|████▌     | 46/100 [00:00<00:00, 94.46 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     47%|████▋     | 47/100 [00:00<00:00, 95.96 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     48%|████▊     | 48/100 [00:00<00:00, 97.45 it/sec, obj=6.41e-7]
        INFO - 20:38:26:     49%|████▉     | 49/100 [00:00<00:00, 98.89 it/sec, obj=6.41e-7]
        INFO - 20:38:26: Optimization result:
        INFO - 20:38:26:    Optimizer info:
        INFO - 20:38:26:       Status: None
        INFO - 20:38:26:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:38:26:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:26:    Solution:
        INFO - 20:38:26:       Objective: 6.40943911289712e-07
        INFO - 20:38:26:       Design space:
        INFO - 20:38:26:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:38:26:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:38:26:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:38:26:          | x_0  |      -1     | 0.9996445136827841 |      1      | float |
        INFO - 20:38:26:          | x_1  |      -1     | 0.999284303839403  |      1      | float |
        INFO - 20:38:26:          | x_2  |      -1     | 0.9985690703536887 |      1      | float |
        INFO - 20:38:26:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:38:26: *** End OptAsMDOScenario execution ***




.. GENERATED FROM PYTHON SOURCE LINES 134-135

We can see that the numerical solution corresponds to the analytical one.


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

   **Total running time of the script:** (0 minutes 0.852 seconds)


.. _sphx_glr_download_examples_mdo_plot_opt_as_mdo.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_opt_as_mdo.zip <plot_opt_as_mdo.zip>`


.. only:: html

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

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