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

.. only:: html

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

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

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

.. _sphx_glr_examples_scalable_plot_problem.py:


Scalable problem
================

We want to solve the Aerostructure MDO problem
by means of the :class:`.MDF` formulation
with a higher dimension for the sweep parameter.
For that, we use the :class:`.ScalableProblem` class.

.. GENERATED FROM PYTHON SOURCE LINES 30-44

.. code-block:: default

    from __future__ import annotations

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.problems.aerostructure.aerostructure_design_space import (
        AerostructureDesignSpace,
    )
    from gemseo.problems.scalable.data_driven.problem import ScalableProblem
    from matplotlib import pyplot as plt

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-51

Define the design problem
-------------------------
In a first step, we define the design problem in terms of
objective function (to maximize or minimize),
design variables (local and global)
and constraints (equality and inequality).

.. GENERATED FROM PYTHON SOURCE LINES 51-57

.. code-block:: default

    design_variables = ["thick_airfoils", "thick_panels", "sweep"]
    objective_function = "range"
    eq_constraints = ["c_rf"]
    ineq_constraints = ["c_lift"]
    maximize_objective = True








.. GENERATED FROM PYTHON SOURCE LINES 58-62

Create the disciplinary datasets
--------------------------------
Then, we create the disciplinary :class:`.AbstractFullCache` datasets
based on a :class:`.DiagonalDOE`.

.. GENERATED FROM PYTHON SOURCE LINES 62-80

.. code-block:: default

    disciplines = create_discipline(["Aerodynamics", "Structure", "Mission"])
    datasets = []
    for discipline in disciplines:
        design_space = AerostructureDesignSpace()
        design_space.filter(discipline.get_input_data_names())
        output_names = iter(discipline.get_output_data_names())
        scenario = create_scenario(
            discipline,
            "DisciplinaryOpt",
            next(output_names),
            design_space,
            scenario_type="DOE",
        )
        for output_name in output_names:
            scenario.add_observable(output_name)
        scenario.execute({"algo": "DiagonalDOE", "n_samples": 10})
        datasets.append(scenario.export_to_dataset(name=discipline.name, opt_naming=False))





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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.1.0/lib/python3.9/site-packages/gemseo/algos/design_space.py:459: ComplexWarning: Casting complex values to real discards the imaginary part
      self.__current_value[name] = array_value.astype(
        INFO - 14:44:49:  
        INFO - 14:44:49: *** Start DOEScenario execution ***
        INFO - 14:44:49: DOEScenario
        INFO - 14:44:49:    Disciplines: Aerodynamics
        INFO - 14:44:49:    MDO formulation: DisciplinaryOpt
        INFO - 14:44:49: Optimization problem:
        INFO - 14:44:49:    minimize drag(thick_airfoils, sweep, displ)
        INFO - 14:44:49:    with respect to displ, sweep, thick_airfoils
        INFO - 14:44:49:    over the design space:
        INFO - 14:44:49:    +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 14:44:49:    +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:    | thick_airfoils |      5      |   15  |      25     | float |
        INFO - 14:44:49:    | sweep          |      10     |   25  |      35     | float |
        INFO - 14:44:49:    | displ          |    -1000    |  -700 |     1000    | float |
        INFO - 14:44:49:    +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:49: Solving optimization problem with algorithm DiagonalDOE:
        INFO - 14:44:49: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:44:49: ... 100%|██████████| 10/10 [00:00<00:00, 855.06 it/sec, obj=-320]
        INFO - 14:44:49: Optimization result:
        INFO - 14:44:49:    Optimizer info:
        INFO - 14:44:49:       Status: None
        INFO - 14:44:49:       Message: None
        INFO - 14:44:49:       Number of calls to the objective function by the optimizer: 10
        INFO - 14:44:49:    Solution:
        INFO - 14:44:49:       Objective: -319.99905478395067
        INFO - 14:44:49:       Design space: 
        INFO - 14:44:49:       +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:       | name           | lower_bound | value | upper_bound | type  |
        INFO - 14:44:49:       +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:       | thick_airfoils |      5      |   25  |      25     | float |
        INFO - 14:44:49:       | sweep          |      10     |   35  |      35     | float |
        INFO - 14:44:49:       | displ          |    -1000    |  1000 |     1000    | float |
        INFO - 14:44:49:       +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:49: *** End DOEScenario execution (time: 0:00:00.021171) ***
        INFO - 14:44:49:  
        INFO - 14:44:49: *** Start DOEScenario execution ***
        INFO - 14:44:49: DOEScenario
        INFO - 14:44:49:    Disciplines: Structure
        INFO - 14:44:49:    MDO formulation: DisciplinaryOpt
        INFO - 14:44:49: Optimization problem:
        INFO - 14:44:49:    minimize mass(thick_panels, sweep, forces)
        INFO - 14:44:49:    with respect to forces, sweep, thick_panels
        INFO - 14:44:49:    over the design space:
        INFO - 14:44:49:    +--------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:    | name         | lower_bound | value | upper_bound | type  |
        INFO - 14:44:49:    +--------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:    | thick_panels |      1      |   3   |      20     | float |
        INFO - 14:44:49:    | sweep        |      10     |   25  |      35     | float |
        INFO - 14:44:49:    | forces       |    -1000    |  400  |     1000    | float |
        INFO - 14:44:49:    +--------------+-------------+-------+-------------+-------+
        INFO - 14:44:49: Solving optimization problem with algorithm DiagonalDOE:
        INFO - 14:44:49: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:44:49: ... 100%|██████████| 10/10 [00:00<00:00, 863.91 it/sec, obj=4.02e+5]
        INFO - 14:44:49: Optimization result:
        INFO - 14:44:49:    Optimizer info:
        INFO - 14:44:49:       Status: None
        INFO - 14:44:49:       Message: None
        INFO - 14:44:49:       Number of calls to the objective function by the optimizer: 10
        INFO - 14:44:49:    Solution:
        INFO - 14:44:49:       Objective: 100.08573388203513
        INFO - 14:44:49:       Design space: 
        INFO - 14:44:49:       +--------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:       | name         | lower_bound | value | upper_bound | type  |
        INFO - 14:44:49:       +--------------+-------------+-------+-------------+-------+
        INFO - 14:44:49:       | thick_panels |      1      |   1   |      20     | float |
        INFO - 14:44:49:       | sweep        |      10     |   10  |      35     | float |
        INFO - 14:44:49:       | forces       |    -1000    | -1000 |     1000    | float |
        INFO - 14:44:49:       +--------------+-------------+-------+-------------+-------+
        INFO - 14:44:49: *** End DOEScenario execution (time: 0:00:00.020922) ***
        INFO - 14:44:49:  
        INFO - 14:44:49: *** Start DOEScenario execution ***
        INFO - 14:44:49: DOEScenario
        INFO - 14:44:49:    Disciplines: Mission
        INFO - 14:44:49:    MDO formulation: DisciplinaryOpt
        INFO - 14:44:49: Optimization problem:
        INFO - 14:44:49:    minimize range(drag, lift, mass, reserve_fact)
        INFO - 14:44:49:    with respect to drag, lift, mass, reserve_fact
        INFO - 14:44:49:    over the design space:
        INFO - 14:44:49:    +--------------+-------------+--------+-------------+-------+
        INFO - 14:44:49:    | name         | lower_bound | value  | upper_bound | type  |
        INFO - 14:44:49:    +--------------+-------------+--------+-------------+-------+
        INFO - 14:44:49:    | drag         |     100     |  340   |     1000    | float |
        INFO - 14:44:49:    | lift         |     0.1     |  0.5   |      1      | float |
        INFO - 14:44:49:    | mass         |    100000   | 100000 |    500000   | float |
        INFO - 14:44:49:    | reserve_fact |    -1000    |   0    |     1000    | float |
        INFO - 14:44:49:    +--------------+-------------+--------+-------------+-------+
        INFO - 14:44:49: Solving optimization problem with algorithm DiagonalDOE:
        INFO - 14:44:49: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:44:49: ... 100%|██████████| 10/10 [00:00<00:00, 835.80 it/sec, obj=1.6e+3+j]
        INFO - 14:44:49: Optimization result:
        INFO - 14:44:49:    Optimizer info:
        INFO - 14:44:49:       Status: None
        INFO - 14:44:49:       Message: None
        INFO - 14:44:49:       Number of calls to the objective function by the optimizer: 10
        INFO - 14:44:49:    Solution:
        INFO - 14:44:49:       Objective: (1600+0j)
        INFO - 14:44:49:       Design space: 
        INFO - 14:44:49:       +--------------+-------------+--------+-------------+-------+
        INFO - 14:44:49:       | name         | lower_bound | value  | upper_bound | type  |
        INFO - 14:44:49:       +--------------+-------------+--------+-------------+-------+
        INFO - 14:44:49:       | drag         |     100     |  1000  |     1000    | float |
        INFO - 14:44:49:       | lift         |     0.1     |   1    |      1      | float |
        INFO - 14:44:49:       | mass         |    100000   | 500000 |    500000   | float |
        INFO - 14:44:49:       | reserve_fact |    -1000    |  1000  |     1000    | float |
        INFO - 14:44:49:       +--------------+-------------+--------+-------------+-------+
        INFO - 14:44:49: *** End DOEScenario execution (time: 0:00:00.022038) ***




.. GENERATED FROM PYTHON SOURCE LINES 81-86

Instantiate a scalable problem
------------------------------
In a third stage, we instantiate a :class:`.ScalableProblem`
from these disciplinary datasets and from the definition of the MDO problem.
We also increase the dimension of the sweep parameter.

.. GENERATED FROM PYTHON SOURCE LINES 86-97

.. code-block:: default

    problem = ScalableProblem(
        datasets,
        design_variables,
        objective_function,
        eq_constraints,
        ineq_constraints,
        maximize_objective,
        sizes={"sweep": 2},
    )
    print(problem)





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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.1.0/lib/python3.9/site-packages/gemseo/problems/scalable/data_driven/model.py:147: ComplexWarning: Casting complex values to real discards the imaginary part
      data[:, indices] = (value - lower_bound) / (upper_bound - lower_bound)
    MDO problem
       Disciplines: Aerodynamics, Structure, Mission
       Design variables: thick_airfoils, thick_panels, sweep
       Objective function: range (to maximize)
       Inequality constraints: c_lift
       Equality constraints: c_rf
       Sizes: displ (1), sweep (2), thick_airfoils (1), drag (1), forces (1), lift (1), thick_panels (1), mass (1), reserve_fact (1), c_lift (1), c_rf (1), range (1)




.. GENERATED FROM PYTHON SOURCE LINES 98-104

.. note::

   We could also provide options to the :class:`.ScalableModel` objects
   by means of the constructor of :class:`.ScalableProblem`,
   e.g. :code:`fill_factor` in the frame of the :class:`.ScalableDiagonalModel`.
   In this example, we use the standard ones.

.. GENERATED FROM PYTHON SOURCE LINES 106-109

Visualize the N2 chart
----------------------
We can see the coupling between disciplines through this N2 chart:

.. GENERATED FROM PYTHON SOURCE LINES 109-111

.. code-block:: default

    problem.plot_n2_chart(save=False, show=True)




.. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_001.png
   :alt: plot problem
   :srcset: /examples/scalable/images/sphx_glr_plot_problem_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 112-117

Create an MDO scenario
----------------------
Lastly, we create a :class:`.MDOScenario` with the :class:`.MDF` formulation
and start the optimization at equilibrium,
thus ensuring the feasibility of the first iterate.

.. GENERATED FROM PYTHON SOURCE LINES 117-119

.. code-block:: default

    scenario = problem.create_scenario("MDF", start_at_equilibrium=True)





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

 .. code-block:: none

        INFO - 14:44:49: Build a preliminary MDA to start at equilibrium




.. GENERATED FROM PYTHON SOURCE LINES 120-126

.. note::

   We could also provide options for the scalable models to the constructor
   of :class:`.ScalableProblem`, e.g. :code:`fill_factor` in the frame of
   the :class:`.ScalableDiagonalModel`.
   In this example, we use the standard ones.

.. GENERATED FROM PYTHON SOURCE LINES 128-131

Once the scenario is created, we can execute it as any scenario.
Here, we use the :code:`NLOPT_SLSQP` optimization algorithm
with no more than 100 iterations.

.. GENERATED FROM PYTHON SOURCE LINES 131-133

.. code-block:: default

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





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

 .. code-block:: none

        INFO - 14:44:50:  
        INFO - 14:44:50: *** Start MDOScenario execution ***
        INFO - 14:44:50: MDOScenario
        INFO - 14:44:50:    Disciplines: sdm_Aerodynamics sdm_Mission sdm_Structure
        INFO - 14:44:50:    MDO formulation: MDF
        INFO - 14:44:50: Optimization problem:
        INFO - 14:44:50:    minimize -range(thick_airfoils, thick_panels, sweep)
        INFO - 14:44:50:    with respect to sweep, thick_airfoils, thick_panels
        INFO - 14:44:50:    subject to constraints:
        INFO - 14:44:50:       c_lift(thick_airfoils, thick_panels, sweep) <= [0.74804822]
        INFO - 14:44:50:       c_rf(thick_airfoils, thick_panels, sweep) == 0.4974338463722027
        INFO - 14:44:50:    over the design space:
        INFO - 14:44:50:    +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:50:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 14:44:50:    +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:50:    | thick_airfoils |      0      |  0.5  |      1      | float |
        INFO - 14:44:50:    | thick_panels   |      0      |  0.5  |      1      | float |
        INFO - 14:44:50:    | sweep[0]       |      0      |  0.5  |      1      | float |
        INFO - 14:44:50:    | sweep[1]       |      0      |  0.5  |      1      | float |
        INFO - 14:44:50:    +----------------+-------------+-------+-------------+-------+
        INFO - 14:44:50: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 14:44:50: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 14:44:50: ...   3%|▎         | 3/100 [00:00<00:00, 728.88 it/sec, obj=-.168]
        INFO - 14:44:50: ...   6%|▌         | 6/100 [00:00<00:00, 368.58 it/sec, obj=-.168]
        INFO - 14:44:50: ...   8%|▊         | 8/100 [00:00<00:00, 278.27 it/sec, obj=-.168]
        INFO - 14:44:50: Optimization result:
        INFO - 14:44:50:    Optimizer info:
        INFO - 14:44:50:       Status: None
        INFO - 14:44:50:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 14:44:50:       Number of calls to the objective function by the optimizer: 8
        INFO - 14:44:50:    Solution:
        INFO - 14:44:50:       The solution is feasible.
        INFO - 14:44:50:       Objective: -0.2985276625156288
        INFO - 14:44:50:       Standardized constraints:
        INFO - 14:44:50:          c_lift + offset = [-0.49234168]
        INFO - 14:44:50:          c_rf - 0.4974338463722027 = 0.0
        INFO - 14:44:50:       Design space: 
        INFO - 14:44:50:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 14:44:50:       | name           | lower_bound |       value        | upper_bound | type  |
        INFO - 14:44:50:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 14:44:50:       | thick_airfoils |      0      | 0.9999999999999978 |      1      | float |
        INFO - 14:44:50:       | thick_panels   |      0      | 0.5155052311585148 |      1      | float |
        INFO - 14:44:50:       | sweep[0]       |      0      | 0.9999999999999969 |      1      | float |
        INFO - 14:44:50:       | sweep[1]       |      0      | 0.9999999999999923 |      1      | float |
        INFO - 14:44:50:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 14:44:50: *** End MDOScenario execution (time: 0:00:00.373551) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 134-136

We can post-process the results.
Here, we use the standard :class:`.OptHistoryView`.

.. GENERATED FROM PYTHON SOURCE LINES 136-139

.. code-block:: default

    scenario.post_process("OptHistoryView", save=False, show=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



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


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/scalable/images/sphx_glr_plot_problem_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/scalable/images/sphx_glr_plot_problem_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_004.png
         :alt: Distance to the optimum
         :srcset: /examples/scalable/images/sphx_glr_plot_problem_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_005.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/scalable/images/sphx_glr_plot_problem_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_006.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/scalable/images/sphx_glr_plot_problem_006.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_plot_problem_007.png
         :alt: Evolution of the equality constraints
         :srcset: /examples/scalable/images/sphx_glr_plot_problem_007.png
         :class: sphx-glr-multi-img






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

   **Total running time of the script:** ( 0 minutes  2.006 seconds)


.. _sphx_glr_download_examples_scalable_plot_problem.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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