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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_scalable_scalable_tm.py>`
        to download the full example code

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

.. _sphx_glr_examples_scalable_scalable_tm.py:


Scalable problem of Tedford and Martins, 2010
=============================================

.. GENERATED FROM PYTHON SOURCE LINES 26-41

.. code-block:: default

    from gemseo.api import configure_logger
    from gemseo.api import generate_n2_plot
    from gemseo.problems.scalable.parametric.core.design_space import TMDesignSpace
    from gemseo.problems.scalable.parametric.disciplines import TMMainDiscipline
    from gemseo.problems.scalable.parametric.disciplines import TMSubDiscipline
    from gemseo.problems.scalable.parametric.problem import TMScalableProblem
    from gemseo.problems.scalable.parametric.study import TMParamSS
    from gemseo.problems.scalable.parametric.study import TMParamSSPost
    from gemseo.problems.scalable.parametric.study import TMScalableStudy
    from numpy import array
    from numpy.random import rand

    configure_logger()






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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 42-52

Disciplines
-----------
We define two strongly coupled disciplines and a weakly coupled discipline,
with:

- 2 shared design parameters,
- 2 local design parameters for the first discipline,
- 3 local design parameters for the second discipline,
- 3 coupling variables for the first discipline,
- 2 coupling variables for the second discipline.

.. GENERATED FROM PYTHON SOURCE LINES 52-55

.. code-block:: default

    sizes = {"x_shared": 2, "x_local_0": 2, "x_local_1": 3, "y_0": 3, "y_1": 2}









.. GENERATED FROM PYTHON SOURCE LINES 56-62

We use any values for the coefficients and the default values of the design
parameters and coupling variables.

Strongly coupled disciplines
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Here is the first strongly coupled discipline.

.. GENERATED FROM PYTHON SOURCE LINES 62-77

.. code-block:: default

    default_inputs = {
        "x_shared": rand(sizes["x_shared"]),
        "x_local_0": rand(sizes["x_local_0"]),
        "y_1": rand(sizes["y_1"]),
    }
    index = 0
    c_shared = rand(sizes["y_0"], sizes["x_shared"])
    c_local = rand(sizes["y_0"], sizes["x_local_0"])
    c_coupling = {"y_1": rand(sizes["y_0"], sizes["y_1"])}
    disc0 = TMSubDiscipline(index, c_shared, c_local, c_coupling, default_inputs)

    print(disc0.name)
    print(disc0.get_input_data_names())
    print(disc0.get_output_data_names())





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

 Out:

 .. code-block:: none

    SubModel_0
    KeysView(Grammar name: SubModel_0_input, schema: {
      "$schema": "http://json-schema.org/schema#",
      "type": "object",
      "properties": {
        "x_local_0": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "x_shared": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "y_1": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      },
      "required": [
        "x_local_0",
        "x_shared",
        "y_1"
      ]
    })
    KeysView(Grammar name: SubModel_0_output, schema: {
      "$schema": "http://json-schema.org/schema#",
      "type": "object",
      "properties": {
        "y_0": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      },
      "required": [
        "y_0"
      ]
    })




.. GENERATED FROM PYTHON SOURCE LINES 78-83

.. code-block:: console

   TM_Discipline_0
   dict_keys(['x_shared', 'x_local_0', 'y_1'])
   dict_keys(['y_0'])

.. GENERATED FROM PYTHON SOURCE LINES 86-87

Here is the second one, strongly coupled with the first one.

.. GENERATED FROM PYTHON SOURCE LINES 87-102

.. code-block:: default

    default_inputs = {
        "x_shared": rand(sizes["x_shared"]),
        "x_local_1": rand(sizes["x_local_1"]),
        "y_0": rand(sizes["y_0"]),
    }
    index = 1
    c_shared = rand(sizes["y_1"], sizes["x_shared"])
    c_local = rand(sizes["y_1"], sizes["x_local_1"])
    c_coupling = {"y_0": rand(sizes["y_1"], sizes["y_0"])}
    disc1 = TMSubDiscipline(index, c_shared, c_local, c_coupling, default_inputs)

    print(disc1.name)
    print(disc1.get_input_data_names())
    print(disc1.get_output_data_names())





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

 Out:

 .. code-block:: none

    SubModel_1
    KeysView(Grammar name: SubModel_1_input, schema: {
      "$schema": "http://json-schema.org/schema#",
      "type": "object",
      "properties": {
        "x_local_1": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "x_shared": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "y_0": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      },
      "required": [
        "x_local_1",
        "x_shared",
        "y_0"
      ]
    })
    KeysView(Grammar name: SubModel_1_output, schema: {
      "$schema": "http://json-schema.org/schema#",
      "type": "object",
      "properties": {
        "y_1": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      },
      "required": [
        "y_1"
      ]
    })




.. GENERATED FROM PYTHON SOURCE LINES 103-108

.. code-block:: console

   TM_Discipline_1
   dict_keys(['x_shared', 'x_local_1', 'y_0'])
   dict_keys(['y_1'])

.. GENERATED FROM PYTHON SOURCE LINES 110-113

Weakly coupled discipline
^^^^^^^^^^^^^^^^^^^^^^^^^
Here is the discipline weakly coupled to the previous ones.

.. GENERATED FROM PYTHON SOURCE LINES 113-125

.. code-block:: default

    c_constraint = [array([1.0, 2.0]), array([3.0, 4.0, 5.0])]
    default_inputs = {
        "x_shared": array([0.5]),
        "y_0": array([2.0, 3.0]),
        "y_1": array([4.0, 5.0, 6.0]),
    }
    system = TMMainDiscipline(c_constraint, default_inputs)

    print(system.name)
    print(system.get_input_data_names())
    print(system.get_output_data_names())





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

 Out:

 .. code-block:: none

    MainModel
    KeysView(Grammar name: MainModel_input, schema: {
      "$schema": "http://json-schema.org/schema#",
      "type": "object",
      "properties": {
        "x_shared": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "y_0": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "y_1": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      },
      "required": [
        "x_shared",
        "y_0",
        "y_1"
      ]
    })
    KeysView(Grammar name: MainModel_output, schema: {
      "$schema": "http://json-schema.org/schema#",
      "type": "object",
      "properties": {
        "cstr_0": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "cstr_1": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "obj": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      },
      "required": [
        "cstr_0",
        "cstr_1",
        "obj"
      ]
    })




.. GENERATED FROM PYTHON SOURCE LINES 126-131

.. code-block:: console

   TM_System
   dict_keys(['x_shared', 'y_0', 'y_1'])
   dict_keys(['obj', 'cstr_0', 'cstr_1'])

.. GENERATED FROM PYTHON SOURCE LINES 133-136

Coupling chart
^^^^^^^^^^^^^^
We can represent these three disciplines by means of an N2 chart.

.. GENERATED FROM PYTHON SOURCE LINES 136-138

.. code-block:: default

    generate_n2_plot([disc0, disc1, system], save=False, show=True)




.. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_001.png
   :alt: scalable tm
   :srcset: /examples/scalable/images/sphx_glr_scalable_tm_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 139-140

.. image:: /_images/scalable_tm/N2chart.png

.. GENERATED FROM PYTHON SOURCE LINES 142-146

Design space
------------
We define the design space from the sizes of the shared design parameters,
local parameters and coupling variables.

.. GENERATED FROM PYTHON SOURCE LINES 146-153

.. code-block:: default

    n_shared = sizes["x_shared"]
    n_local = [sizes["x_local_0"], sizes["x_local_1"]]
    n_coupling = [sizes["y_0"], sizes["y_1"]]
    design_space = TMDesignSpace(n_shared, n_local, n_coupling)

    print(design_space)





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

 Out:

 .. code-block:: none

    <gemseo.problems.scalable.parametric.core.design_space.TMDesignSpace object at 0x7fdbe0a60910>




.. GENERATED FROM PYTHON SOURCE LINES 154-173

.. code-block:: console

   Design Space:
   +-----------+-------------+-------+-------------+-------+
   | name      | lower_bound | value | upper_bound | type  |
   +-----------+-------------+-------+-------------+-------+
   | x_local_0 |      0      |  0.5  |      1      | float |
   | x_local_0 |      0      |  0.5  |      1      | float |
   | x_local_1 |      0      |  0.5  |      1      | float |
   | x_local_1 |      0      |  0.5  |      1      | float |
   | x_local_1 |      0      |  0.5  |      1      | float |
   | x_shared  |      0      |  0.5  |      1      | float |
   | x_shared  |      0      |  0.5  |      1      | float |
   | y_0       |      0      |  0.5  |      1      | float |
   | y_0       |      0      |  0.5  |      1      | float |
   | y_0       |      0      |  0.5  |      1      | float |
   | y_1       |      0      |  0.5  |      1      | float |
   | y_1       |      0      |  0.5  |      1      | float |
   +-----------+-------------+-------+-------------+-------+

.. GENERATED FROM PYTHON SOURCE LINES 175-185

Scalable problem
----------------
We define a scalable problem based on two strongly coupled disciplines
and a weakly one, with the following properties:

- 3 shared design parameters,
- 2 local design parameters for the first strongly coupled discipline,
- 2 coupling variables for the first strongly coupled discipline,
- 4 local design parameters for the second strongly coupled discipline,
- 3 coupling variables for the second strongly coupled discipline.

.. GENERATED FROM PYTHON SOURCE LINES 185-193

.. code-block:: default

    problem = TMScalableProblem(3, [2, 4], [2, 3])

    print(problem)

    print(problem.get_design_space())

    print(problem.get_default_inputs())





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

 Out:

 .. code-block:: none

    Scalable problem
    .... MainModel
    ........ Inputs:
    ............ x_shared (3)
    ............ y_0 (2)
    ............ y_1 (3)
    ........ Outputs:
    ............ cstr_0 (2)
    ............ cstr_1 (3)
    ............ obj (1)
    .... SubModel_0
    ........ Inputs:
    ............ x_local_0 (2)
    ............ x_shared (3)
    ............ y_1 (3)
    ........ Outputs:
    ............ y_0 (2)
    .... SubModel_1
    ........ Inputs:
    ............ x_local_1 (4)
    ............ x_shared (3)
    ............ y_0 (2)
    ........ Outputs:
    ............ y_1 (3)
    +------------------------------------------------------------------------------+
    |                               Parameter space                                |
    +-----------+-------------+-------+-------------+-------+----------------------+
    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
    +-----------+-------------+-------+-------------+-------+----------------------+
    | x_local_0 |      0      |  0.5  |      1      | float |                      |
    | x_local_0 |      0      |  0.5  |      1      | float |                      |
    | x_local_1 |      0      |  0.5  |      1      | float |                      |
    | x_local_1 |      0      |  0.5  |      1      | float |                      |
    | x_local_1 |      0      |  0.5  |      1      | float |                      |
    | x_local_1 |      0      |  0.5  |      1      | float |                      |
    | x_shared  |      0      |  0.5  |      1      | float |                      |
    | x_shared  |      0      |  0.5  |      1      | float |                      |
    | x_shared  |      0      |  0.5  |      1      | float |                      |
    | y_0       |      0      |  0.5  |      1      | float |                      |
    | y_0       |      0      |  0.5  |      1      | float |                      |
    | y_1       |      0      |  0.5  |      1      | float |                      |
    | y_1       |      0      |  0.5  |      1      | float |                      |
    | y_1       |      0      |  0.5  |      1      | float |                      |
    +-----------+-------------+-------+-------------+-------+----------------------+
    {'x_shared': array([0.5, 0.5, 0.5]), 'x_local_0': array([0.5, 0.5]), 'y_0': array([0.5, 0.5]), 'cstr_0': array([0.5, 0.5]), 'u_local_0': array([0., 0.]), 'x_local_1': array([0.5, 0.5, 0.5, 0.5]), 'y_1': array([0.5, 0.5, 0.5]), 'cstr_1': array([0.5, 0.5, 0.5]), 'u_local_1': array([0., 0., 0.])}




.. GENERATED FROM PYTHON SOURCE LINES 194-244

.. code-block:: console

    Scalable problem
    > TM_System
       >> Inputs:
          | x_shared (3)
          | y_0 (2)
          | y_1 (3)
       >> Outputs:
          | cstr_0 (2)
          | cstr_1 (3)
          | obj (1)
    > TM_Discipline_0
       >> Inputs:
          | x_local_0 (2)
          | x_shared (3)
          | y_1 (3)
       >> Outputs:
          | y_0 (2)
    > TM_Discipline_1
       >> Inputs:
          | x_local_1 (4)
          | x_shared (3)
          | y_0 (2)
       >> Outputs:
          | y_1 (3)

    Design Space:
    +-----------+-------------+-------+-------------+-------+
    | name      | lower_bound | value | upper_bound | type  |
    +-----------+-------------+-------+-------------+-------+
    | x_local_0 |      0      |  0.5  |      1      | float |
    | x_local_0 |      0      |  0.5  |      1      | float |
    | x_local_1 |      0      |  0.5  |      1      | float |
    | x_local_1 |      0      |  0.5  |      1      | float |
    | x_local_1 |      0      |  0.5  |      1      | float |
    | x_local_1 |      0      |  0.5  |      1      | float |
    | x_shared  |      0      |  0.5  |      1      | float |
    | x_shared  |      0      |  0.5  |      1      | float |
    | x_shared  |      0      |  0.5  |      1      | float |
    | y_0       |      0      |  0.5  |      1      | float |
    | y_0       |      0      |  0.5  |      1      | float |
    | y_1       |      0      |  0.5  |      1      | float |
    | y_1       |      0      |  0.5  |      1      | float |
    | y_1       |      0      |  0.5  |      1      | float |
    +-----------+-------------+-------+-------------+-------+
    {'x_shared': array([0.5, 0.5, 0.5]), 'x_local_0': array([0.5, 0.5]),
    'y_0': array([0.5, 0.5]), 'cstr_0': array([0.5]), 'x_local_1':
    array([0.5, 0.5, 0.5, 0.5]), 'y_1': array([0.5, 0.5, 0.5]), 'cstr_1':
    array([0.5])}

.. GENERATED FROM PYTHON SOURCE LINES 246-254

Scalable study
--------------
We define a scalable study based on two strongly coupled disciplines
and a weakly one, with the following properties:

- 3 shared design parameters,
- 2 local design parameters for each strongly coupled discipline,
- 3 coupling variables for each strongly coupled discipline.

.. GENERATED FROM PYTHON SOURCE LINES 254-257

.. code-block:: default

    study = TMScalableStudy(n_disciplines=2, n_shared=3, n_local=2, n_coupling=3)
    print(study)





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

 Out:

 .. code-block:: none

    Scalable study
    .... 2 disciplines
    .... 3 shared design parameters
    .... 2 local design parameters per discipline
    .... 3 coupling variables per discipline




.. GENERATED FROM PYTHON SOURCE LINES 258-265

.. code-block:: console

   Scalable study
   > 2 disciplines
   > 3 shared design parameters
   > 2 local design parameters per discipline
   > 3 coupling variables per discipline

.. GENERATED FROM PYTHON SOURCE LINES 267-268

Then, we run MDF and IDF formulations:

.. GENERATED FROM PYTHON SOURCE LINES 268-271

.. code-block:: default

    study.run_formulation("MDF", xdsm_pdf=False)
    study.run_formulation("IDF", xdsm_pdf=False)




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


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_002.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_003.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_003.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none

        INFO - 10:04:00: Make the starting point feasible.
        INFO - 10:04:00:  
        INFO - 10:04:00: *** Start MDOScenario execution ***
        INFO - 10:04:00: MDOScenario
        INFO - 10:04:00:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:00:    MDO formulation: MDF
        INFO - 10:04:00: Optimization problem:
        INFO - 10:04:00:    minimize obj(x_local_0, x_local_1, x_shared)
        INFO - 10:04:00:    with respect to x_local_0, x_local_1, x_shared
        INFO - 10:04:00:    subject to constraints:
        INFO - 10:04:00:       cstr_0(x_local_0, x_local_1, x_shared) <= [ 0.65250671 -2.8453087  -4.16343355]
        INFO - 10:04:00:       cstr_1(x_local_0, x_local_1, x_shared) <= [0.85268891 0.52747299 0.62341835]
        INFO - 10:04:00:    over the design space:
        INFO - 10:04:00:    |                               Parameter space                                |
        INFO - 10:04:00:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:00:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 10:04:00:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:00:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:00:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:00: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:00: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:00: ...   2%|▏         | 2/100 [00:00<00:00, 794.69 it/sec]
        INFO - 10:04:00: ...   4%|▍         | 4/100 [00:00<00:00, 386.37 it/sec]
        INFO - 10:04:00: ...   6%|▌         | 6/100 [00:00<00:00, 256.62 it/sec]
        INFO - 10:04:00: ...   8%|▊         | 8/100 [00:00<00:00, 191.56 it/sec]
        INFO - 10:04:00: ...   8%|▊         | 8/100 [00:00<00:00, 191.23 it/sec]
        INFO - 10:04:00: Optimization result:
        INFO - 10:04:00:    Optimizer info:
        INFO - 10:04:00:       Status: None
        INFO - 10:04:00:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:00:       Number of calls to the objective function by the optimizer: 8
        INFO - 10:04:00:    Solution:
        INFO - 10:04:00:       The solution is feasible.
        INFO - 10:04:00:       Objective: 0.28903317159094793
        INFO - 10:04:00:       Standardized constraints:
        INFO - 10:04:00:          cstr_0 + offset = [-1.59418542e+00 -1.77635684e-15 -2.20075451e+01]
        INFO - 10:04:00:          cstr_1 + offset = [-0.62818923 -1.7413806  -1.62123925]
        INFO - 10:04:00:       +--------------------------------------------------------------------------------------------+
        INFO - 10:04:00:       |                                      Parameter space                                       |
        INFO - 10:04:00:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:00:       | name      | lower_bound |        value        | upper_bound | type  | Initial distribution |
        INFO - 10:04:00:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:00:       | x_local_0 |      0      |  0.801127355733839  |      1      | float |                      |
        INFO - 10:04:00:       | x_local_0 |      0      |  0.6239177332508217 |      1      | float |                      |
        INFO - 10:04:00:       | x_local_1 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:00:       | x_local_1 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:00:       | x_shared  |      0      | 0.07024612283000739 |      1      | float |                      |
        INFO - 10:04:00:       | x_shared  |      0      |  0.1762493157624942 |      1      | float |                      |
        INFO - 10:04:00:       | x_shared  |      0      |  0.1499619831353362 |      1      | float |                      |
        INFO - 10:04:00:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:00: *** End MDOScenario execution (time: 0:00:00.537038) ***
        INFO - 10:04:02: Generating HTML XDSM file in : results/coupling/MDF_xdsm.html
        INFO - 10:04:04: Make the starting point feasible.
        INFO - 10:04:04:  
        INFO - 10:04:04: *** Start MDOScenario execution ***
        INFO - 10:04:04: MDOScenario
        INFO - 10:04:04:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:04:    MDO formulation: IDF
        INFO - 10:04:04: Optimization problem:
        INFO - 10:04:04:    minimize obj(x_shared, y_0, y_1)
        INFO - 10:04:04:    with respect to x_local_0, x_local_1, x_shared, y_0, y_1
        INFO - 10:04:04:    subject to constraints:
        INFO - 10:04:04:       cstr_0(x_shared, y_0, y_1) <= [ 0.65250671  0.23093826 -4.16343355]
        INFO - 10:04:04:       cstr_1(x_shared, y_0, y_1) <= [ 0.85268891 -1.36263503  0.62341835]
        INFO - 10:04:04:       y_0: y_0(x_local_0, x_shared, y_1): y_0(x_local_0, x_shared, y_1) - y_0 == 0.0
        INFO - 10:04:04:       y_1: y_1(x_local_1, x_shared, y_0): y_1(x_local_1, x_shared, y_0) - y_1 == 0.0
        INFO - 10:04:04:    over the design space:
        INFO - 10:04:04:    |                               Parameter space                                |
        INFO - 10:04:04:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:04:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 10:04:04:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:04:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:04:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:04: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:04: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:04: ...  10%|█         | 10/100 [00:00<00:00, 1482.83 it/sec]
        INFO - 10:04:04: Optimization result:
        INFO - 10:04:04:    Optimizer info:
        INFO - 10:04:04:       Status: None
        INFO - 10:04:04:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:04:       Number of calls to the objective function by the optimizer: 10
        INFO - 10:04:04:    Solution:
        INFO - 10:04:04:       The solution is feasible.
        INFO - 10:04:04:       Objective: 0.2505909523154283
        INFO - 10:04:04:       Standardized constraints:
        INFO - 10:04:04:          cstr_0 + offset = [ -1.27965363  -2.31226949 -19.05735903]
        INFO - 10:04:04:          cstr_1 + offset = [-0.59186125  0.         -1.52367146]
        INFO - 10:04:04:          y_0 = [ 5.55111512e-17  0.00000000e+00 -5.55111512e-17]
        INFO - 10:04:04:          y_1 = [ 1.11022302e-16 -5.55111512e-17 -1.11022302e-16]
        INFO - 10:04:04:       +--------------------------------------------------------------------------------------------+
        INFO - 10:04:04:       |                                      Parameter space                                       |
        INFO - 10:04:04:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:04:       | name      | lower_bound |        value        | upper_bound | type  | Initial distribution |
        INFO - 10:04:04:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:04:       | x_local_0 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:04:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:04:       | x_local_1 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:04:       | x_local_1 |      0      |  0.7594082578802717 |      1      | float |                      |
        INFO - 10:04:04:       | x_shared  |      0      |  0.1558252960698979 |      1      | float |                      |
        INFO - 10:04:04:       | x_shared  |      0      |  0.2044810243675251 |      1      | float |                      |
        INFO - 10:04:04:       | x_shared  |      0      | 0.08695435101337673 |      1      | float |                      |
        INFO - 10:04:04:       | y_0       |      0      |  0.4682527561624886 |      1      | float |                      |
        INFO - 10:04:04:       | y_0       |      0      |   0.40066110028851  |      1      | float |                      |
        INFO - 10:04:04:       | y_0       |      0      |  0.4690830695053916 |      1      | float |                      |
        INFO - 10:04:04:       | y_1       |      0      |  0.5017764477639917 |      1      | float |                      |
        INFO - 10:04:04:       | y_1       |      0      |         0.5         |      1      | float |                      |
        INFO - 10:04:04:       | y_1       |      0      |  0.5046058665567719 |      1      | float |                      |
        INFO - 10:04:04:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:04: *** End MDOScenario execution (time: 0:00:00.086344) ***
        INFO - 10:04:06: Generating HTML XDSM file in : results/coupling/IDF_xdsm.html

    {'x_opt': array([1.        , 1.        , 1.        , 0.75940826, 0.1558253 ,
           0.20448102, 0.08695435, 0.46825276, 0.4006611 , 0.46908307,
           0.50177645, 0.5       , 0.50460587]), 'f_opt': 0.2505909523154283, 'status': None, 'n_iter': 62, 'is_feas': True, 'exec_time': 0.08641172900388483}



.. GENERATED FROM PYTHON SOURCE LINES 272-273

We can look at the result in the console:

.. GENERATED FROM PYTHON SOURCE LINES 273-275

.. code-block:: default

    print(study)





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

 Out:

 .. code-block:: none

    Scalable study
    .... 2 disciplines
    .... 3 shared design parameters
    .... 2 local design parameters per discipline
    .... 3 coupling variables per discipline
    MDO formulations
    .... MDF
    ........ MainModel = 10 calls / 8 linearizations / 0.0021817759989062324 seconds
    ........ SubModel_0 = 147 calls / 8 linearizations / 0.014235965929401573 seconds
    ........ SubModel_1 = 139 calls / 8 linearizations / 0.0128868909960147 seconds
    ........ mda = 8 calls / 8 linearizations / 0.48482988299656427 seconds
    ........ mdo_chain = 8 calls / 0 linearizations / 0.11343992301408434 seconds
    ........ sub_mda = 8 calls / 0 linearizations / 0.10515520201442996 seconds
    ........ scenario = 1 calls / 0 linearizations / 0.5371053260023473 seconds
    .... IDF
    ........ MainModel = 12 calls / 10 linearizations / 0.0025057530001504347 seconds
    ........ SubModel_0 = 11 calls / 9 linearizations / 0.001998121020733379 seconds
    ........ SubModel_1 = 11 calls / 9 linearizations / 0.0019471219784463756 seconds
    ........ mda = 0 calls / 0 linearizations / 0.0 seconds
    ........ mdo_chain = 0 calls / 0 linearizations / 0.0 seconds
    ........ sub_mda = 0 calls / 0 linearizations / 0.0 seconds
    ........ scenario = 1 calls / 0 linearizations / 0.08641172900388483 seconds




.. GENERATED FROM PYTHON SOURCE LINES 276-301

.. code-block:: console

   Scalable study
   > 2 disciplines
   > 3 shared design parameters
   > 2 local design parameters per discipline
   > 3 coupling variables per discipline

   MDO formulations
   > MDF
      >> TM_System = 9 calls / 7 linearizations / 3.29e-03 seconds
      >> TM_Discipline_0 = 132 calls / 7 linearizations / 2.19e-02 seconds
      >> TM_Discipline_1 = 124 calls / 7 linearizations / 2.04e-02 seconds
      >> mda = 7 calls / 7 linearizations / 2.68e-01 seconds
      >> mdo_chain = 7 calls / 0 linearizations / 1.20e-01 seconds
      >> sub_mda = 7 calls / 0 linearizations / 1.16e-01 seconds
      >> scenario = 1 calls / 0 linearizations / 3.35e-01 seconds
   > IDF
      >> TM_System = 12 calls / 9 linearizations / 2.98e-03 seconds
      >> TM_Discipline_0 = 12 calls / 9 linearizations / 2.19e-03 seconds
      >> TM_Discipline_1 = 11 calls / 9 linearizations / 2.01e-03 seconds
      >> mda = 0 calls / 0 linearizations / 0.00e+00 seconds
      >> mdo_chain = 0 calls / 0 linearizations / 0.00e+00 seconds
      >> sub_mda = 0 calls / 0 linearizations / 0.00e+00 seconds
      >> scenario = 1 calls / 0 linearizations / 7.60e-02 seconds

.. GENERATED FROM PYTHON SOURCE LINES 303-304

or plot the execution time:

.. GENERATED FROM PYTHON SOURCE LINES 304-306

.. code-block:: default

    study.plot_exec_time()








.. GENERATED FROM PYTHON SOURCE LINES 307-308

.. image:: /_images/scalable_tm/exec_time.png

.. GENERATED FROM PYTHON SOURCE LINES 310-319

Parametric scalability study
----------------------------
We define a parametric scalability study
based on two strongly coupled disciplines
and a weakly one, with the following properties:

- 3 shared design parameters,
- 2 coupling variables for each strongly coupled discipline,
- 1, 5 or 25 local design parameters for each strongly coupled discipline,

.. GENERATED FROM PYTHON SOURCE LINES 319-322

.. code-block:: default

    study = TMParamSS(n_disciplines=2, n_shared=3, n_local=[1, 5, 25], n_coupling=2)
    print(study)





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

 Out:

 .. code-block:: none

    Parametric scalable study
    > 2 disciplines
    > 3 shared design parameters
    > 1, 5 or 25 local design parameters per discipline
    > 2 coupling variables per discipline





.. GENERATED FROM PYTHON SOURCE LINES 323-330

.. code-block:: console

   Parametric scalable study
   > 2 disciplines
   > 3 shared design parameters
   > 1, 5 or 25 local design parameters per discipline
   > 2 coupling variables per discipline

.. GENERATED FROM PYTHON SOURCE LINES 332-333

Then, we run MDF and IDF formulations:

.. GENERATED FROM PYTHON SOURCE LINES 333-336

.. code-block:: default

    study.run_formulation("MDF")
    study.run_formulation("IDF")




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


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_004.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_005.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_006.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_006.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_007.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_008.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_009.png
         :alt: scalable tm
         :srcset: /examples/scalable/images/sphx_glr_scalable_tm_009.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none

        INFO - 10:04:09: Make the starting point feasible.
        INFO - 10:04:09:  
        INFO - 10:04:09: *** Start MDOScenario execution ***
        INFO - 10:04:09: MDOScenario
        INFO - 10:04:09:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:09:    MDO formulation: MDF
        INFO - 10:04:09: Optimization problem:
        INFO - 10:04:09:    minimize obj(x_local_0, x_local_1, x_shared)
        INFO - 10:04:09:    with respect to x_local_0, x_local_1, x_shared
        INFO - 10:04:09:    subject to constraints:
        INFO - 10:04:09:       cstr_0(x_local_0, x_local_1, x_shared) <= [0.88589544 0.88821903]
        INFO - 10:04:09:       cstr_1(x_local_0, x_local_1, x_shared) <= [-0.17585898 -1.56050583]
        INFO - 10:04:09:    over the design space:
        INFO - 10:04:09:    |                               Parameter space                                |
        INFO - 10:04:09:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:09:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 10:04:09:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:09:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:09:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:09:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:09:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:09:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:09:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:09: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:09: ...   0%|          | 0/100 [00:00<?, ?it]
     WARNING - 10:04:09: MDAGaussSeidel has reached its maximum number of iterations but the normed residual 1.3486125443736518e-14 is still above the tolerance 1e-14.
        INFO - 10:04:09: ...   2%|▏         | 2/100 [00:00<00:00, 961.15 it/sec]
        INFO - 10:04:09: ...   4%|▍         | 4/100 [00:00<00:00, 471.74 it/sec]
     WARNING - 10:04:09: MDAGaussSeidel has reached its maximum number of iterations but the normed residual 1.0303264460093434e-14 is still above the tolerance 1e-14.
     WARNING - 10:04:09: MDAGaussSeidel has reached its maximum number of iterations but the normed residual 1.221308406312274e-14 is still above the tolerance 1e-14.
        INFO - 10:04:09: ...   6%|▌         | 6/100 [00:00<00:00, 311.03 it/sec]
     WARNING - 10:04:09: MDAGaussSeidel has reached its maximum number of iterations but the normed residual 1.0624260076854628e-14 is still above the tolerance 1e-14.
     WARNING - 10:04:09: MDAGaussSeidel has reached its maximum number of iterations but the normed residual 1.1319239632249289e-14 is still above the tolerance 1e-14.
        INFO - 10:04:09: ...   8%|▊         | 8/100 [00:00<00:00, 231.89 it/sec]
        INFO - 10:04:09: ...   8%|▊         | 8/100 [00:00<00:00, 231.42 it/sec]
        INFO - 10:04:09: Optimization result:
        INFO - 10:04:09:    Optimizer info:
        INFO - 10:04:09:       Status: None
        INFO - 10:04:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:09:       Number of calls to the objective function by the optimizer: 8
        INFO - 10:04:09:    Solution:
        INFO - 10:04:09:       The solution is feasible.
        INFO - 10:04:09:       Objective: 0.3805071026441499
        INFO - 10:04:09:       Standardized constraints:
        INFO - 10:04:09:          cstr_0 + offset = [-0.41404086 -0.37054477]
        INFO - 10:04:09:          cstr_1 + offset = [ -4.10330374 -10.67148731]
        INFO - 10:04:09:       +-------------------------------------------------------------------------------------------+
        INFO - 10:04:09:       |                                      Parameter space                                      |
        INFO - 10:04:09:       +-----------+-------------+--------------------+-------------+-------+----------------------+
        INFO - 10:04:09:       | name      | lower_bound |       value        | upper_bound | type  | Initial distribution |
        INFO - 10:04:09:       +-----------+-------------+--------------------+-------------+-------+----------------------+
        INFO - 10:04:09:       | x_local_0 |      0      |         1          |      1      | float |                      |
        INFO - 10:04:09:       | x_local_1 |      0      |         1          |      1      | float |                      |
        INFO - 10:04:09:       | x_shared  |      0      | 0.4316204495066337 |      1      | float |                      |
        INFO - 10:04:09:       | x_shared  |      0      | 0.5112660072459285 |      1      | float |                      |
        INFO - 10:04:09:       | x_shared  |      0      | 0.2050544622846011 |      1      | float |                      |
        INFO - 10:04:09:       +-----------+-------------+--------------------+-------------+-------+----------------------+
        INFO - 10:04:09: *** End MDOScenario execution (time: 0:00:00.455016) ***
        INFO - 10:04:11: Generating HTML XDSM file in : results/coupling/MDF_xdsm.html
        INFO - 10:04:13: Make the starting point feasible.
        INFO - 10:04:13:  
        INFO - 10:04:13: *** Start MDOScenario execution ***
        INFO - 10:04:13: MDOScenario
        INFO - 10:04:13:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:13:    MDO formulation: MDF
        INFO - 10:04:13: Optimization problem:
        INFO - 10:04:13:    minimize obj(x_local_0, x_local_1, x_shared)
        INFO - 10:04:13:    with respect to x_local_0, x_local_1, x_shared
        INFO - 10:04:13:    subject to constraints:
        INFO - 10:04:13:       cstr_0(x_local_0, x_local_1, x_shared) <= [0.89887356 0.86633976]
        INFO - 10:04:13:       cstr_1(x_local_0, x_local_1, x_shared) <= [0.64342256 0.87330214]
        INFO - 10:04:13:    over the design space:
        INFO - 10:04:13:    |                               Parameter space                                |
        INFO - 10:04:13:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:13:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 10:04:13:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:13:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:13:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:13: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:13: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:13: ...   3%|▎         | 3/100 [00:00<00:00, 703.83 it/sec]
        INFO - 10:04:13: ...   6%|▌         | 6/100 [00:00<00:00, 351.26 it/sec]
        INFO - 10:04:13: ...   9%|▉         | 9/100 [00:00<00:00, 232.50 it/sec]
        INFO - 10:04:14: ...  12%|█▏        | 12/100 [00:00<00:00, 174.13 it/sec]
        INFO - 10:04:14: ...  14%|█▍        | 14/100 [00:00<00:00, 149.14 it/sec]
        INFO - 10:04:14: Optimization result:
        INFO - 10:04:14:    Optimizer info:
        INFO - 10:04:14:       Status: None
        INFO - 10:04:14:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:14:       Number of calls to the objective function by the optimizer: 14
        INFO - 10:04:14:    Solution:
        INFO - 10:04:14:       The solution is feasible.
        INFO - 10:04:14:       Objective: 0.1385357381285276
        INFO - 10:04:14:       Standardized constraints:
        INFO - 10:04:14:          cstr_0 + offset = [-0.23668859 -0.10569247]
        INFO - 10:04:14:          cstr_1 + offset = [-1.21308758 -0.34258749]
        INFO - 10:04:14:       +--------------------------------------------------------------------------------------------+
        INFO - 10:04:14:       |                                      Parameter space                                       |
        INFO - 10:04:14:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:14:       | name      | lower_bound |        value        | upper_bound | type  | Initial distribution |
        INFO - 10:04:14:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:14:       | x_local_0 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:14:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:14:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:14:       | x_local_0 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:14:       | x_local_0 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:14:       | x_local_1 |      0      |  0.9999999999999998 |      1      | float |                      |
        INFO - 10:04:14:       | x_local_1 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:14:       | x_local_1 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:14:       | x_local_1 |      0      |  0.9999999999999998 |      1      | float |                      |
        INFO - 10:04:14:       | x_local_1 |      0      |  0.9999999999999998 |      1      | float |                      |
        INFO - 10:04:14:       | x_shared  |      0      |  0.1458505152901145 |      1      | float |                      |
        INFO - 10:04:14:       | x_shared  |      0      |  0.1819162891601797 |      1      | float |                      |
        INFO - 10:04:14:       | x_shared  |      0      | 0.07257747464173495 |      1      | float |                      |
        INFO - 10:04:14:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:14: *** End MDOScenario execution (time: 0:00:00.688485) ***
        INFO - 10:04:16: Generating HTML XDSM file in : results/coupling/MDF_xdsm.html
        INFO - 10:04:17: Make the starting point feasible.
        INFO - 10:04:17:  
        INFO - 10:04:17: *** Start MDOScenario execution ***
        INFO - 10:04:17: MDOScenario
        INFO - 10:04:17:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:17:    MDO formulation: MDF
        INFO - 10:04:17: Optimization problem:
        INFO - 10:04:17:    minimize obj(x_local_0, x_local_1, x_shared)
        INFO - 10:04:17:    with respect to x_local_0, x_local_1, x_shared
        INFO - 10:04:17:    subject to constraints:
        INFO - 10:04:17:       cstr_0(x_local_0, x_local_1, x_shared) <= [ -4.03014722 -18.07597002]
        INFO - 10:04:17:       cstr_1(x_local_0, x_local_1, x_shared) <= [-2.53275899  0.59384442]
        INFO - 10:04:17: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:17: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:18: ...   3%|▎         | 3/100 [00:00<00:00, 714.88 it/sec]
        INFO - 10:04:18: ...   6%|▌         | 6/100 [00:00<00:00, 353.52 it/sec]
        INFO - 10:04:18: ...   9%|▉         | 9/100 [00:00<00:00, 234.76 it/sec]
        INFO - 10:04:18: ...  12%|█▏        | 12/100 [00:00<00:00, 175.27 it/sec]
        INFO - 10:04:18: ...  15%|█▌        | 15/100 [00:00<00:00, 139.76 it/sec]
        INFO - 10:04:18: ...  18%|█▊        | 18/100 [00:00<00:00, 116.32 it/sec]
        INFO - 10:04:18: ...  20%|██        | 20/100 [00:00<00:00, 104.35 it/sec]
        INFO - 10:04:18: Optimization result:
        INFO - 10:04:18:    Optimizer info:
        INFO - 10:04:18:       Status: None
        INFO - 10:04:18:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:18:       Number of calls to the objective function by the optimizer: 20
        INFO - 10:04:18:    Solution:
        INFO - 10:04:18:       The solution is feasible.
        INFO - 10:04:18:       Objective: 0.08650593635886976
        INFO - 10:04:18:       Standardized constraints:
        INFO - 10:04:18:          cstr_0 + offset = [-8.43715914  0.        ]
        INFO - 10:04:18:          cstr_1 + offset = [-6.67439741e-01  4.44089210e-16]
        INFO - 10:04:18: *** End MDOScenario execution (time: 0:00:00.966829) ***
        INFO - 10:04:20: Generating HTML XDSM file in : results/coupling/MDF_xdsm.html
        INFO - 10:04:23: Make the starting point feasible.
        INFO - 10:04:23:  
        INFO - 10:04:23: *** Start MDOScenario execution ***
        INFO - 10:04:23: MDOScenario
        INFO - 10:04:23:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:23:    MDO formulation: IDF
        INFO - 10:04:23: Optimization problem:
        INFO - 10:04:23:    minimize obj(x_shared, y_0, y_1)
        INFO - 10:04:23:    with respect to x_local_0, x_local_1, x_shared, y_0, y_1
        INFO - 10:04:23:    subject to constraints:
        INFO - 10:04:23:       cstr_0(x_shared, y_0, y_1) <= [0.88589544 0.88821903]
        INFO - 10:04:23:       cstr_1(x_shared, y_0, y_1) <= [-0.17585898 -1.56050583]
        INFO - 10:04:23:       y_0: y_0(x_local_0, x_shared, y_1): y_0(x_local_0, x_shared, y_1) - y_0 == 0.0
        INFO - 10:04:23:       y_1: y_1(x_local_1, x_shared, y_0): y_1(x_local_1, x_shared, y_0) - y_1 == 0.0
        INFO - 10:04:23:    over the design space:
        INFO - 10:04:23:    |                               Parameter space                                |
        INFO - 10:04:23:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:23:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 10:04:23:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:23:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:23:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:23: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:23: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:23: ...   8%|▊         | 8/100 [00:00<00:00, 2081.23 it/sec]
        INFO - 10:04:23: Optimization result:
        INFO - 10:04:23:    Optimizer info:
        INFO - 10:04:23:       Status: None
        INFO - 10:04:23:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:23:       Number of calls to the objective function by the optimizer: 8
        INFO - 10:04:23:    Solution:
        INFO - 10:04:23:       The solution is feasible.
        INFO - 10:04:23:       Objective: 0.3805016326090851
        INFO - 10:04:23:       Standardized constraints:
        INFO - 10:04:23:          cstr_0 + offset = [-0.4105685  -0.36790752]
        INFO - 10:04:23:          cstr_1 + offset = [ -4.06820466 -10.60696021]
        INFO - 10:04:23:          y_0 = [-5.55111512e-17  5.55111512e-17]
        INFO - 10:04:23:          y_1 = [-1.66533454e-16  0.00000000e+00]
        INFO - 10:04:23:       +-------------------------------------------------------------------------------------------+
        INFO - 10:04:23:       |                                      Parameter space                                      |
        INFO - 10:04:23:       +-----------+-------------+--------------------+-------------+-------+----------------------+
        INFO - 10:04:23:       | name      | lower_bound |       value        | upper_bound | type  | Initial distribution |
        INFO - 10:04:23:       +-----------+-------------+--------------------+-------------+-------+----------------------+
        INFO - 10:04:23:       | x_local_0 |      0      |         1          |      1      | float |                      |
        INFO - 10:04:23:       | x_local_1 |      0      |         1          |      1      | float |                      |
        INFO - 10:04:23:       | x_shared  |      0      | 0.4349840014945803 |      1      | float |                      |
        INFO - 10:04:23:       | x_shared  |      0      | 0.5153341160240119 |      1      | float |                      |
        INFO - 10:04:23:       | x_shared  |      0      |  0.20620547934211  |      1      | float |                      |
        INFO - 10:04:23:       | y_0       |      0      | 0.4598177788198944 |      1      | float |                      |
        INFO - 10:04:23:       | y_0       |      0      | 0.4291325171427605 |      1      | float |                      |
        INFO - 10:04:23:       | y_1       |      0      | 0.4459772572294342 |      1      | float |                      |
        INFO - 10:04:23:       | y_1       |      0      | 0.5142525316178621 |      1      | float |                      |
        INFO - 10:04:23:       +-----------+-------------+--------------------+-------------+-------+----------------------+
        INFO - 10:04:23: *** End MDOScenario execution (time: 0:00:00.063931) ***
        INFO - 10:04:24: Generating HTML XDSM file in : results/coupling/IDF_xdsm.html
        INFO - 10:04:27: Make the starting point feasible.
        INFO - 10:04:27:  
        INFO - 10:04:27: *** Start MDOScenario execution ***
        INFO - 10:04:27: MDOScenario
        INFO - 10:04:27:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:27:    MDO formulation: IDF
        INFO - 10:04:27: Optimization problem:
        INFO - 10:04:27:    minimize obj(x_shared, y_0, y_1)
        INFO - 10:04:27:    with respect to x_local_0, x_local_1, x_shared, y_0, y_1
        INFO - 10:04:27:    subject to constraints:
        INFO - 10:04:27:       cstr_0(x_shared, y_0, y_1) <= [0.89887356 0.86633976]
        INFO - 10:04:27:       cstr_1(x_shared, y_0, y_1) <= [-0.78288719  0.87330214]
        INFO - 10:04:27:       y_0: y_0(x_local_0, x_shared, y_1): y_0(x_local_0, x_shared, y_1) - y_0 == 0.0
        INFO - 10:04:27:       y_1: y_1(x_local_1, x_shared, y_0): y_1(x_local_1, x_shared, y_0) - y_1 == 0.0
        INFO - 10:04:27:    over the design space:
        INFO - 10:04:27:    |                               Parameter space                                |
        INFO - 10:04:27:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:27:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
        INFO - 10:04:27:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:27:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | x_shared  |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | y_0       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    | y_1       |      0      |  0.5  |      1      | float |                      |
        INFO - 10:04:27:    +-----------+-------------+-------+-------------+-------+----------------------+
        INFO - 10:04:27: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:27: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:27: ...  13%|█▎        | 13/100 [00:00<00:00, 1203.71 it/sec]
        INFO - 10:04:27: Optimization result:
        INFO - 10:04:27:    Optimizer info:
        INFO - 10:04:27:       Status: None
        INFO - 10:04:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:27:       Number of calls to the objective function by the optimizer: 13
        INFO - 10:04:27:    Solution:
        INFO - 10:04:27:       The solution is feasible.
        INFO - 10:04:27:       Objective: 0.15383885100886432
        INFO - 10:04:27:       Standardized constraints:
        INFO - 10:04:27:          cstr_0 + offset = [-0.28367339 -0.13418614]
        INFO - 10:04:27:          cstr_1 + offset = [ 0.         -0.39931711]
        INFO - 10:04:27:          y_0 = [5.55111512e-17 1.66533454e-16]
        INFO - 10:04:27:          y_1 = [1.11022302e-16 1.11022302e-16]
        INFO - 10:04:27:       +--------------------------------------------------------------------------------------------+
        INFO - 10:04:27:       |                                      Parameter space                                       |
        INFO - 10:04:27:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:27:       | name      | lower_bound |        value        | upper_bound | type  | Initial distribution |
        INFO - 10:04:27:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:27:       | x_local_0 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:27:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:27:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:27:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:27:       | x_local_0 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:27:       | x_local_1 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:27:       | x_local_1 |      0      |  0.9999999999999999 |      1      | float |                      |
        INFO - 10:04:27:       | x_local_1 |      0      |          1          |      1      | float |                      |
        INFO - 10:04:27:       | x_local_1 |      0      |  0.9858563292487739 |      1      | float |                      |
        INFO - 10:04:27:       | x_local_1 |      0      |  0.8952030605001723 |      1      | float |                      |
        INFO - 10:04:27:       | x_shared  |      0      | 0.03908896701511936 |      1      | float |                      |
        INFO - 10:04:27:       | x_shared  |      0      | 0.05509382017067609 |      1      | float |                      |
        INFO - 10:04:27:       | x_shared  |      0      | 0.03828687665187131 |      1      | float |                      |
        INFO - 10:04:27:       | y_0       |      0      |  0.3805135756043002 |      1      | float |                      |
        INFO - 10:04:27:       | y_0       |      0      |  0.2003934597112414 |      1      | float |                      |
        INFO - 10:04:27:       | y_1       |      0      |         0.5         |      1      | float |                      |
        INFO - 10:04:27:       | y_1       |      0      |  0.4151727380322101 |      1      | float |                      |
        INFO - 10:04:27:       +-----------+-------------+---------------------+-------------+-------+----------------------+
        INFO - 10:04:27: *** End MDOScenario execution (time: 0:00:00.104657) ***
        INFO - 10:04:29: Generating HTML XDSM file in : results/coupling/IDF_xdsm.html
        INFO - 10:04:31: Make the starting point feasible.
        INFO - 10:04:31:  
        INFO - 10:04:31: *** Start MDOScenario execution ***
        INFO - 10:04:31: MDOScenario
        INFO - 10:04:31:    Disciplines: MainModel SubModel_0 SubModel_1
        INFO - 10:04:31:    MDO formulation: IDF
        INFO - 10:04:31: Optimization problem:
        INFO - 10:04:31:    minimize obj(x_shared, y_0, y_1)
        INFO - 10:04:31:    with respect to x_local_0, x_local_1, x_shared, y_0, y_1
        INFO - 10:04:31:    subject to constraints:
        INFO - 10:04:31:       cstr_0(x_shared, y_0, y_1) <= [-24.15073611  -2.815194  ]
        INFO - 10:04:31:       cstr_1(x_shared, y_0, y_1) <= [-2.53275899  0.59384442]
        INFO - 10:04:31:       y_0: y_0(x_local_0, x_shared, y_1): y_0(x_local_0, x_shared, y_1) - y_0 == 0.0
        INFO - 10:04:31:       y_1: y_1(x_local_1, x_shared, y_0): y_1(x_local_1, x_shared, y_0) - y_1 == 0.0
        INFO - 10:04:31: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:31: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:31: ...  13%|█▎        | 13/100 [00:00<00:00, 918.81 it/sec]
        INFO - 10:04:31: ...  21%|██        | 21/100 [00:00<00:00, 534.99 it/sec]
        INFO - 10:04:31: Optimization result:
        INFO - 10:04:31:    Optimizer info:
        INFO - 10:04:31:       Status: None
        INFO - 10:04:31:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:31:       Number of calls to the objective function by the optimizer: 21
        INFO - 10:04:31:    Solution:
        INFO - 10:04:31:       The solution is feasible.
        INFO - 10:04:31:       Objective: 0.07837467586318368
        INFO - 10:04:31:       Standardized constraints:
        INFO - 10:04:31:          cstr_0 + offset = [ 0.         -3.92093323]
        INFO - 10:04:31:          cstr_1 + offset = [-3.95598136e-01 -1.11022302e-16]
        INFO - 10:04:31:          y_0 = [ 1.66533454e-16 -2.77555756e-17]
        INFO - 10:04:31:          y_1 = [ 0.00000000e+00 -4.16333634e-17]
        INFO - 10:04:31: *** End MDOScenario execution (time: 0:00:00.196499) ***
        INFO - 10:04:33: Generating HTML XDSM file in : results/coupling/IDF_xdsm.html




.. GENERATED FROM PYTHON SOURCE LINES 337-338

and save the results in a pickle file:

.. GENERATED FROM PYTHON SOURCE LINES 338-340

.. code-block:: default

    study.save("results.pkl")








.. GENERATED FROM PYTHON SOURCE LINES 341-343

We can plot these results and compare MDF and IDF formulations in terms
of execution time for different number of local design variables.

.. GENERATED FROM PYTHON SOURCE LINES 343-346

.. code-block:: default

    results = TMParamSSPost("results.pkl")
    results.plot("Comparison of MDF and IDF formulations")




.. image-sg:: /examples/scalable/images/sphx_glr_scalable_tm_010.png
   :alt: Comparison of MDF and IDF formulations
   :srcset: /examples/scalable/images/sphx_glr_scalable_tm_010.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 347-348

.. image:: /_images/scalable_tm/mdf_idf.png


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

   **Total running time of the script:** ( 0 minutes  36.712 seconds)


.. _sphx_glr_download_examples_scalable_scalable_tm.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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