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

.. only:: html

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

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

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

.. _sphx_glr_examples_scalable_scalable_study.py:


Scalable study
==============

We want to compare :class:`.IDF` and :class:`.MDF` formulations
with respect to the problem dimension for the aerostructure problem.
For that,
we use the :class:`.ScalabilityStudy` and :class:`.PostScalabilityStudy` classes.

.. GENERATED FROM PYTHON SOURCE LINES 30-42

.. code-block:: default

    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.api import create_scalability_study
    from gemseo.problems.scalable.data_driven.api import plot_scalability_results

    configure_logger()






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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 43-47

Create the disciplinary datasets
--------------------------------
First of all, we create the disciplinary :class:`.Dataset` datasets
based on a :class:`.DiagonalDOE`.

.. GENERATED FROM PYTHON SOURCE LINES 47-67

.. code-block:: default

    datasets = {}
    disciplines = create_discipline(["Aerodynamics", "Structure", "Mission"])
    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[discipline.name] = scenario.export_to_dataset(
            name=discipline.name, opt_naming=False
        )





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

 Out:

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/lib/python3.9/site-packages/gemseo/algos/design_space.py:448: ComplexWarning: Casting complex values to real discards the imaginary part
      self.__current_value[name] = array_value.astype(
        INFO - 10:04:37:  
        INFO - 10:04:37: *** Start DOEScenario execution ***
        INFO - 10:04:37: DOEScenario
        INFO - 10:04:37:    Disciplines: Aerodynamics
        INFO - 10:04:37:    MDO formulation: DisciplinaryOpt
        INFO - 10:04:37: Optimization problem:
        INFO - 10:04:37:    minimize drag(thick_airfoils, sweep, displ)
        INFO - 10:04:37:    with respect to displ, sweep, thick_airfoils
        INFO - 10:04:37:    over the design space:
        INFO - 10:04:37:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 10:04:37:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:    | thick_airfoils |      5      |   15  |      25     | float |
        INFO - 10:04:37:    | sweep          |      10     |   25  |      35     | float |
        INFO - 10:04:37:    | displ          |    -1000    |  -700 |     1000    | float |
        INFO - 10:04:37:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:37: Solving optimization problem with algorithm DiagonalDOE:
        INFO - 10:04:37: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 10:04:37: ... 100%|██████████| 10/10 [00:00<00:00, 780.48 it/sec, obj=-320]
        INFO - 10:04:37: Optimization result:
        INFO - 10:04:37:    Optimizer info:
        INFO - 10:04:37:       Status: None
        INFO - 10:04:37:       Message: None
        INFO - 10:04:37:       Number of calls to the objective function by the optimizer: 10
        INFO - 10:04:37:    Solution:
        INFO - 10:04:37:       Objective: -319.99905478395067
        INFO - 10:04:37:       Design space:
        INFO - 10:04:37:       +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:       | name           | lower_bound | value | upper_bound | type  |
        INFO - 10:04:37:       +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:       | thick_airfoils |      5      |   25  |      25     | float |
        INFO - 10:04:37:       | sweep          |      10     |   35  |      35     | float |
        INFO - 10:04:37:       | displ          |    -1000    |  1000 |     1000    | float |
        INFO - 10:04:37:       +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:37: *** End DOEScenario execution (time: 0:00:00.021679) ***
        INFO - 10:04:37:  
        INFO - 10:04:37: *** Start DOEScenario execution ***
        INFO - 10:04:37: DOEScenario
        INFO - 10:04:37:    Disciplines: Structure
        INFO - 10:04:37:    MDO formulation: DisciplinaryOpt
        INFO - 10:04:37: Optimization problem:
        INFO - 10:04:37:    minimize mass(thick_panels, sweep, forces)
        INFO - 10:04:37:    with respect to forces, sweep, thick_panels
        INFO - 10:04:37:    over the design space:
        INFO - 10:04:37:    +--------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:    | name         | lower_bound | value | upper_bound | type  |
        INFO - 10:04:37:    +--------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:    | thick_panels |      1      |   3   |      20     | float |
        INFO - 10:04:37:    | sweep        |      10     |   25  |      35     | float |
        INFO - 10:04:37:    | forces       |    -1000    |  400  |     1000    | float |
        INFO - 10:04:37:    +--------------+-------------+-------+-------------+-------+
        INFO - 10:04:37: Solving optimization problem with algorithm DiagonalDOE:
        INFO - 10:04:37: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 10:04:37: ... 100%|██████████| 10/10 [00:00<00:00, 793.89 it/sec, obj=4.02e+5]
        INFO - 10:04:37: Optimization result:
        INFO - 10:04:37:    Optimizer info:
        INFO - 10:04:37:       Status: None
        INFO - 10:04:37:       Message: None
        INFO - 10:04:37:       Number of calls to the objective function by the optimizer: 10
        INFO - 10:04:37:    Solution:
        INFO - 10:04:37:       Objective: 100.08573388203513
        INFO - 10:04:37:       Design space:
        INFO - 10:04:37:       +--------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:       | name         | lower_bound | value | upper_bound | type  |
        INFO - 10:04:37:       +--------------+-------------+-------+-------------+-------+
        INFO - 10:04:37:       | thick_panels |      1      |   1   |      20     | float |
        INFO - 10:04:37:       | sweep        |      10     |   10  |      35     | float |
        INFO - 10:04:37:       | forces       |    -1000    | -1000 |     1000    | float |
        INFO - 10:04:37:       +--------------+-------------+-------+-------------+-------+
        INFO - 10:04:37: *** End DOEScenario execution (time: 0:00:00.021486) ***
        INFO - 10:04:37:  
        INFO - 10:04:37: *** Start DOEScenario execution ***
        INFO - 10:04:37: DOEScenario
        INFO - 10:04:37:    Disciplines: Mission
        INFO - 10:04:37:    MDO formulation: DisciplinaryOpt
        INFO - 10:04:37: Optimization problem:
        INFO - 10:04:37:    minimize range(drag, lift, mass, reserve_fact)
        INFO - 10:04:37:    with respect to drag, lift, mass, reserve_fact
        INFO - 10:04:37:    over the design space:
        INFO - 10:04:37:    +--------------+-------------+--------+-------------+-------+
        INFO - 10:04:37:    | name         | lower_bound | value  | upper_bound | type  |
        INFO - 10:04:37:    +--------------+-------------+--------+-------------+-------+
        INFO - 10:04:37:    | drag         |     100     |  340   |     1000    | float |
        INFO - 10:04:37:    | lift         |     0.1     |  0.5   |      1      | float |
        INFO - 10:04:37:    | mass         |    100000   | 100000 |    500000   | float |
        INFO - 10:04:37:    | reserve_fact |    -1000    |   0    |     1000    | float |
        INFO - 10:04:37:    +--------------+-------------+--------+-------------+-------+
        INFO - 10:04:37: Solving optimization problem with algorithm DiagonalDOE:
        INFO - 10:04:37: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 10:04:37: ... 100%|██████████| 10/10 [00:00<00:00, 754.86 it/sec, obj=1.6e+3+j]
        INFO - 10:04:37: Optimization result:
        INFO - 10:04:37:    Optimizer info:
        INFO - 10:04:37:       Status: None
        INFO - 10:04:37:       Message: None
        INFO - 10:04:37:       Number of calls to the objective function by the optimizer: 10
        INFO - 10:04:37:    Solution:
        INFO - 10:04:37:       Objective: (1600+0j)
        INFO - 10:04:37:       Design space:
        INFO - 10:04:37:       +--------------+-------------+--------+-------------+-------+
        INFO - 10:04:37:       | name         | lower_bound | value  | upper_bound | type  |
        INFO - 10:04:37:       +--------------+-------------+--------+-------------+-------+
        INFO - 10:04:37:       | drag         |     100     |  1000  |     1000    | float |
        INFO - 10:04:37:       | lift         |     0.1     |   1    |      1      | float |
        INFO - 10:04:37:       | mass         |    100000   | 500000 |    500000   | float |
        INFO - 10:04:37:       | reserve_fact |    -1000    |  1000  |     1000    | float |
        INFO - 10:04:37:       +--------------+-------------+--------+-------------+-------+
        INFO - 10:04:37: *** End DOEScenario execution (time: 0:00:00.022460) ***




.. GENERATED FROM PYTHON SOURCE LINES 68-82

Define the design problem
-------------------------
Then, we instantiate a :class:`.ScalabilityStudy`
from the definition of the design problem, expressed in terms of
objective function (to maximize or minimize),
design variables (local and global)
and constraints (equality and inequality).
We can also specify the coupling variables that we could scale.
Note that this information is only required by the scaling stage.
Indeed, MDO formulations know perfectly
how to automatically recognize the coupling variables.
Lastly, we can specify some properties of the scalable methodology
such as the fill factor
describing the level of dependence between inputs and outputs.

.. GENERATED FROM PYTHON SOURCE LINES 82-93

.. code-block:: default


    study = create_scalability_study(
        objective="range",
        design_variables=["thick_airfoils", "thick_panels", "sweep"],
        eq_constraints=["c_rf"],
        ineq_constraints=["c_lift"],
        maximize_objective=True,
        coupling_variables=["forces", "displ"],
        fill_factor=-1,
    )





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

 Out:

 .. code-block:: none

        INFO - 10:04:37: Initialize the scalability study
        INFO - 10:04:37:    Create directories
        INFO - 10:04:37:       Working directory: study
        INFO - 10:04:37:       Post-processing: study/visualization
        INFO - 10:04:37:       Optimization history view: study/visualization/optimization_history
        INFO - 10:04:37:       Scalability views: study/visualization/scalability_study
        INFO - 10:04:37:       Dependency matrices: study/visualization/dependency_matrix
        INFO - 10:04:37:       Results: study/results
        INFO - 10:04:37:    Optimization problem
        INFO - 10:04:37:       Objective: maximize range
        INFO - 10:04:37:       Design variables: ['thick_airfoils', 'thick_panels', 'sweep']
        INFO - 10:04:37:       Equality constraints: ['c_rf']
        INFO - 10:04:37:       Inequality constraints: ['c_lift']
        INFO - 10:04:37:    Study properties
        INFO - 10:04:37:       Default fill factor: -1
        INFO - 10:04:37:       Active probability: 0.1
        INFO - 10:04:37:       Feasibility level: 0.8
        INFO - 10:04:37:       Start at equilibrium: True
        INFO - 10:04:37:       Early stopping: True




.. GENERATED FROM PYTHON SOURCE LINES 94-96

Add the disciplinary datasets
-----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 96-100

.. code-block:: default

    study.add_discipline(datasets["Aerodynamics"])
    study.add_discipline(datasets["Structure"])
    study.add_discipline(datasets["Mission"])





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

 Out:

 .. code-block:: none

        INFO - 10:04:37: Add scalable discipline # 1
        INFO - 10:04:37:    Name: Aerodynamics
        INFO - 10:04:37:    Inputs: displ(1), sweep(1), thick_airfoils(1)
        INFO - 10:04:37:    Outputs: drag(1), forces(1), lift(1)
        INFO - 10:04:37:    Built from 10
        INFO - 10:04:37: Add scalable discipline # 2
        INFO - 10:04:37:    Name: Structure
        INFO - 10:04:37:    Inputs: forces(1), sweep(1), thick_panels(1)
        INFO - 10:04:37:    Outputs: displ(1), mass(1), reserve_fact(1)
        INFO - 10:04:37:    Built from 10
        INFO - 10:04:37: Add scalable discipline # 3
        INFO - 10:04:37:    Name: Mission
        INFO - 10:04:37:    Inputs: drag(1), lift(1), mass(1), reserve_fact(1)
        INFO - 10:04:37:    Outputs: c_lift(1), c_rf(1), range(1)
        INFO - 10:04:37:    Built from 10




.. GENERATED FROM PYTHON SOURCE LINES 101-113

Add the optimization strategies
-------------------------------
Then, we define the different optimization strategies we want to compare:
In this case, the strategies are:

- :class:`.MDF` formulation with the :code:`"NLOPT_SLSQP"` optimization algorithm
  and no more than 100 iterations,
- :class:`.IDF` formulation with the :code:`"NLOPT_SLSQP"` optimization algorithm
  and no more than 100 iterations,

Note that in this case, we compare MDO formulations
but we could easily compare optimization algorithms.

.. GENERATED FROM PYTHON SOURCE LINES 113-116

.. code-block:: default

    study.add_optimization_strategy("NLOPT_SLSQP", 100, "MDF")
    study.add_optimization_strategy("NLOPT_SLSQP", 100, "IDF")





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

 Out:

 .. code-block:: none

        INFO - 10:04:37: Add optimization strategy # 1
        INFO - 10:04:37:    Algorithm: NLOPT_SLSQP
        INFO - 10:04:37:    Algorithm options: max_iter(100)
        INFO - 10:04:37:    Formulation: MDF
        INFO - 10:04:37:    Formulation options: None
        INFO - 10:04:37: Add optimization strategy # 2
        INFO - 10:04:37:    Algorithm: NLOPT_SLSQP
        INFO - 10:04:37:    Algorithm options: max_iter(100)
        INFO - 10:04:37:    Formulation: IDF
        INFO - 10:04:37:    Formulation options: None




.. GENERATED FROM PYTHON SOURCE LINES 117-145

Add the scaling strategy
------------------------
After that, we define the different scaling strategies
for which we want to compare the optimization strategies.
In this case, the strategies are:

1. All design parameters have a size equal to 1,
2. All design parameters have a size equal to 20.

To do that, we pass :code:`design_size=[1, 20]`
to the :meth:`.ScalabilityStudy.add_scaling_strategies` method.
:code:`design_size` expects either:

- a list of integer where the ith component is the size for the ith scaling strategy,
- an integer changing the fixed size (if :code:`None`, use the original size).

Note that we could also compare the optimization strategies while

- varying the size of the different coupling variables (use :code:`coupling_size`),
- varying the size of the different equality constraints (use :code:`eq_size`),
- varying the size of the different inequality constraints (use :code:`ineq_size`),
- varying the size of any variable (use :code:`variables`),

where the corresponding arguments works in the same way as :code:`design_size`,
except for :code:`variables` which expects a list of dictionary
whose keys are variables names and values are variables sizes.
In this way, we can use this argument to fine-tune a scaling strategy
to very specific variables, e.g. local variables.

.. GENERATED FROM PYTHON SOURCE LINES 145-147

.. code-block:: default

    study.add_scaling_strategies(design_size=[1, 20])





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

 Out:

 .. code-block:: none

        INFO - 10:04:37: Add scaling strategies
        INFO - 10:04:37:    Number of strategies: 2
        INFO - 10:04:37:    Strategy # 1
        INFO - 10:04:37:       Design variables: 1
        INFO - 10:04:37:       Coupling variables: None
        INFO - 10:04:37:       Equality constraints: None
        INFO - 10:04:37:       Inequality constraints: None
        INFO - 10:04:37:       Variables: None
        INFO - 10:04:37:    Strategy # 2
        INFO - 10:04:37:       Design variables: 20
        INFO - 10:04:37:       Coupling variables: None
        INFO - 10:04:37:       Equality constraints: None
        INFO - 10:04:37:       Inequality constraints: None
        INFO - 10:04:37:       Variables: None




.. GENERATED FROM PYTHON SOURCE LINES 148-155

Execute the scalable study
--------------------------
Then, we execute the scalability study,
i.e. to build and execute a :class:`.ScalableProblem`
for each optimization strategy and each scaling strategy,
and repeat it 2 times in order to get statistics on the results
(because the :class:`.ScalableDiagonalModel` relies on stochastic features.

.. GENERATED FROM PYTHON SOURCE LINES 155-157

.. code-block:: default

    study.execute(n_replicates=2)





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

 Out:

 .. code-block:: none

        INFO - 10:04:37: Execute scalability study 2 times
        INFO - 10:04:37:    Formulation: MDF - Algo: NLOPT_SLSQP - Scaling: 1/2 - Replicate: 1/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:04:37: Build a preliminary MDA to start at equilibrium
        INFO - 10:04:38:  
        INFO - 10:04:38: *** Start MDOScenario execution ***
        INFO - 10:04:38: MDOScenario
        INFO - 10:04:38:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:04:38:    MDO formulation: MDF
        INFO - 10:04:38: Optimization problem:
        INFO - 10:04:38:    minimize -range(thick_airfoils, thick_panels, sweep)
        INFO - 10:04:38:    with respect to sweep, thick_airfoils, thick_panels
        INFO - 10:04:38:    subject to constraints:
        INFO - 10:04:38:       c_lift(thick_airfoils, thick_panels, sweep) <= [0.89921929]
        INFO - 10:04:38:       c_rf(thick_airfoils, thick_panels, sweep) == 0.4974338463722028
        INFO - 10:04:38:    over the design space:
        INFO - 10:04:38:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:38:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 10:04:38:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:38:    | thick_airfoils |      0      |  0.5  |      1      | float |
        INFO - 10:04:38:    | thick_panels   |      0      |  0.5  |      1      | float |
        INFO - 10:04:38:    | sweep          |      0      |  0.5  |      1      | float |
        INFO - 10:04:38:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:38: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:38: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:38: ...   3%|▎         | 3/100 [00:00<00:00, 836.89 it/sec]
        INFO - 10:04:38: ...   6%|▌         | 6/100 [00:00<00:00, 411.09 it/sec]
     WARNING - 10:04:38: MDAJacobi has reached its maximum number of iterations but the normed residual 0.5590169943749475 is still above the tolerance 1e-06.
        INFO - 10:04:38: ...   9%|▉         | 9/100 [00:00<00:00, 249.41 it/sec]
        INFO - 10:04:38: ...   9%|▉         | 9/100 [00:00<00:00, 248.82 it/sec]
        INFO - 10:04:38: Optimization result:
        INFO - 10:04:38:    Optimizer info:
        INFO - 10:04:38:       Status: None
        INFO - 10:04:38:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:38:       Number of calls to the objective function by the optimizer: 9
        INFO - 10:04:38:    Solution:
        INFO - 10:04:38:       The solution is feasible.
        INFO - 10:04:38:       Objective: -0.2601666720067595
        INFO - 10:04:38:       Standardized constraints:
        INFO - 10:04:38:          c_lift + offset = [-0.60364682]
        INFO - 10:04:38:          c_rf - 0.4974338463722028 = -5.551115123125783e-17
        INFO - 10:04:38:       Design space:
        INFO - 10:04:38:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 10:04:38:       | name           | lower_bound |       value        | upper_bound | type  |
        INFO - 10:04:38:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 10:04:38:       | thick_airfoils |      0      | 0.9999999999996533 |      1      | float |
        INFO - 10:04:38:       | thick_panels   |      0      | 0.3912634521674405 |      1      | float |
        INFO - 10:04:38:       | sweep          |      0      | 0.9999999999980954 |      1      | float |
        INFO - 10:04:38:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 10:04:38: *** End MDOScenario execution (time: 0:00:00.412528) ***
        INFO - 10:04:40:    Formulation: MDF - Algo: NLOPT_SLSQP - Scaling: 1/2 - Replicate: 2/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:04:41: Build a preliminary MDA to start at equilibrium
        INFO - 10:04:41:  
        INFO - 10:04:41: *** Start MDOScenario execution ***
        INFO - 10:04:41: MDOScenario
        INFO - 10:04:41:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:04:41:    MDO formulation: MDF
        INFO - 10:04:41: Optimization problem:
        INFO - 10:04:41:    minimize -range(thick_airfoils, thick_panels, sweep)
        INFO - 10:04:41:    with respect to sweep, thick_airfoils, thick_panels
        INFO - 10:04:41:    subject to constraints:
        INFO - 10:04:41:       c_lift(thick_airfoils, thick_panels, sweep) <= [0.89918761]
        INFO - 10:04:41:       c_rf(thick_airfoils, thick_panels, sweep) == 0.49640175939595016
        INFO - 10:04:41:    over the design space:
        INFO - 10:04:41:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:41:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 10:04:41:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:41:    | thick_airfoils |      0      |  0.5  |      1      | float |
        INFO - 10:04:41:    | thick_panels   |      0      |  0.5  |      1      | float |
        INFO - 10:04:41:    | sweep          |      0      |  0.5  |      1      | float |
        INFO - 10:04:41:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:41: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:41: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:41: ...   3%|▎         | 3/100 [00:00<00:00, 882.01 it/sec]
        INFO - 10:04:41: ...   6%|▌         | 6/100 [00:00<00:00, 451.78 it/sec]
        INFO - 10:04:41: ...   8%|▊         | 8/100 [00:00<00:00, 339.81 it/sec]
        INFO - 10:04:41: Optimization result:
        INFO - 10:04:41:    Optimizer info:
        INFO - 10:04:41:       Status: None
        INFO - 10:04:41:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:41:       Number of calls to the objective function by the optimizer: 8
        INFO - 10:04:41:    Solution:
        INFO - 10:04:41:       The solution is feasible.
        INFO - 10:04:41:       Objective: -0.2696970985756206
        INFO - 10:04:41:       Standardized constraints:
        INFO - 10:04:41:          c_lift + offset = [-0.48406661]
        INFO - 10:04:41:          c_rf - 0.49640175939595016 = 2.7755575615628914e-16
        INFO - 10:04:41:       Design space:
        INFO - 10:04:41:       +----------------+-------------+-----------------------+-------------+-------+
        INFO - 10:04:41:       | name           | lower_bound |         value         | upper_bound | type  |
        INFO - 10:04:41:       +----------------+-------------+-----------------------+-------------+-------+
        INFO - 10:04:41:       | thick_airfoils |      0      | 7.858468983373231e-17 |      1      | float |
        INFO - 10:04:41:       | thick_panels   |      0      |   0.1305332770797188  |      1      | float |
        INFO - 10:04:41:       | sweep          |      0      | 3.077348745177621e-17 |      1      | float |
        INFO - 10:04:41:       +----------------+-------------+-----------------------+-------------+-------+
        INFO - 10:04:41: *** End MDOScenario execution (time: 0:00:00.304753) ***
        INFO - 10:04:43:    Formulation: MDF - Algo: NLOPT_SLSQP - Scaling: 2/2 - Replicate: 1/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:04:44: Build a preliminary MDA to start at equilibrium
        INFO - 10:04:44:  
        INFO - 10:04:44: *** Start MDOScenario execution ***
        INFO - 10:04:44: MDOScenario
        INFO - 10:04:44:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:04:44:    MDO formulation: MDF
        INFO - 10:04:44: Optimization problem:
        INFO - 10:04:44:    minimize -range(thick_airfoils, thick_panels, sweep)
        INFO - 10:04:44:    with respect to sweep, thick_airfoils, thick_panels
        INFO - 10:04:44:    subject to constraints:
        INFO - 10:04:44:       c_lift(thick_airfoils, thick_panels, sweep) <= [0.89921929]
        INFO - 10:04:44:       c_rf(thick_airfoils, thick_panels, sweep) == 0.4974338463722027
        INFO - 10:04:44: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:44: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:44: ...   2%|▏         | 2/100 [00:00<00:00, 974.79 it/sec]
        INFO - 10:04:45: ...   5%|▌         | 5/100 [00:00<00:00, 395.23 it/sec]
        INFO - 10:04:45: ...   7%|▋         | 7/100 [00:00<00:00, 281.44 it/sec]
        INFO - 10:04:45: ...   9%|▉         | 9/100 [00:00<00:00, 215.70 it/sec]
        INFO - 10:04:45: ...  11%|█         | 11/100 [00:00<00:00, 175.57 it/sec]
        INFO - 10:04:45: ...  13%|█▎        | 13/100 [00:00<00:00, 147.92 it/sec]
        INFO - 10:04:45: ...  15%|█▌        | 15/100 [00:00<00:00, 127.82 it/sec]
        INFO - 10:04:45: ...  17%|█▋        | 17/100 [00:00<00:00, 112.29 it/sec]
        INFO - 10:04:45: ...  19%|█▉        | 19/100 [00:01<00:00, 99.99 it/sec]
        INFO - 10:04:45: ...  21%|██        | 21/100 [00:01<00:00, 90.85 it/sec]
        INFO - 10:04:46: ...  23%|██▎       | 23/100 [00:01<00:00, 82.63 it/sec]
        INFO - 10:04:46: ...  25%|██▌       | 25/100 [00:01<00:00, 75.73 it/sec]
        INFO - 10:04:46: ...  27%|██▋       | 27/100 [00:01<00:01, 69.69 it/sec]
        INFO - 10:04:46: ...  29%|██▉       | 29/100 [00:01<00:01, 64.78 it/sec]
        INFO - 10:04:46: ...  31%|███       | 31/100 [00:01<00:01, 60.09 it/sec]
        INFO - 10:04:46: ...  33%|███▎      | 33/100 [00:01<00:01, 55.99 it/sec]
        INFO - 10:04:46: ...  35%|███▌      | 35/100 [00:01<00:01, 52.95 it/sec]
        INFO - 10:04:46: ...  37%|███▋      | 37/100 [00:01<00:01, 50.06 it/sec]
        INFO - 10:04:46: ...  39%|███▉      | 39/100 [00:02<00:01, 47.42 it/sec]
        INFO - 10:04:47: ...  41%|████      | 41/100 [00:02<00:01, 45.10 it/sec]
        INFO - 10:04:47: ...  43%|████▎     | 43/100 [00:02<00:01, 42.99 it/sec]
        INFO - 10:04:47: ...  45%|████▌     | 45/100 [00:02<00:01, 41.03 it/sec]
        INFO - 10:04:47: ...  47%|████▋     | 47/100 [00:02<00:01, 39.28 it/sec]
        INFO - 10:04:47: ...  49%|████▉     | 49/100 [00:02<00:01, 37.68 it/sec]
        INFO - 10:04:47: ...  51%|█████     | 51/100 [00:02<00:01, 36.23 it/sec]
        INFO - 10:04:47: ...  53%|█████▎    | 53/100 [00:02<00:01, 34.83 it/sec]
        INFO - 10:04:47: ...  55%|█████▌    | 55/100 [00:02<00:01, 33.49 it/sec]
        INFO - 10:04:47: ...  57%|█████▋    | 57/100 [00:03<00:01, 32.34 it/sec]
        INFO - 10:04:48: ...  59%|█████▉    | 59/100 [00:03<00:01, 31.27 it/sec]
        INFO - 10:04:48: ...  61%|██████    | 61/100 [00:03<00:01, 30.24 it/sec]
        INFO - 10:04:48: ...  63%|██████▎   | 63/100 [00:03<00:01, 29.27 it/sec]
        INFO - 10:04:48: ...  65%|██████▌   | 65/100 [00:03<00:01, 28.36 it/sec]
        INFO - 10:04:48: ...  67%|██████▋   | 67/100 [00:03<00:01, 27.50 it/sec]
        INFO - 10:04:48: ...  69%|██████▉   | 69/100 [00:03<00:01, 26.66 it/sec]
        INFO - 10:04:48: ...  71%|███████   | 71/100 [00:03<00:01, 25.92 it/sec]
        INFO - 10:04:48: ...  73%|███████▎  | 73/100 [00:03<00:01, 25.19 it/sec]
        INFO - 10:04:48: ...  75%|███████▌  | 75/100 [00:04<00:01, 24.50 it/sec]
        INFO - 10:04:49: ...  77%|███████▋  | 77/100 [00:04<00:00, 23.87 it/sec]
        INFO - 10:04:49: ...  77%|███████▋  | 77/100 [00:04<00:00, 23.85 it/sec]
        INFO - 10:04:49: Optimization result:
        INFO - 10:04:49:    Optimizer info:
        INFO - 10:04:49:       Status: None
        INFO - 10:04:49:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:49:       Number of calls to the objective function by the optimizer: 77
        INFO - 10:04:49:    Solution:
        INFO - 10:04:49:       The solution is feasible.
        INFO - 10:04:49:       Objective: -0.47216032578366923
        INFO - 10:04:49:       Standardized constraints:
        INFO - 10:04:49:          c_lift + offset = [-0.72037473]
        INFO - 10:04:49:          c_rf - 0.4974338463722027 = 4.84604467665406e-10
        INFO - 10:04:49: *** End MDOScenario execution (time: 0:00:04.200570) ***
        INFO - 10:04:51:    Formulation: MDF - Algo: NLOPT_SLSQP - Scaling: 2/2 - Replicate: 2/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:04:53: Build a preliminary MDA to start at equilibrium
        INFO - 10:04:53:  
        INFO - 10:04:53: *** Start MDOScenario execution ***
        INFO - 10:04:53: MDOScenario
        INFO - 10:04:53:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:04:53:    MDO formulation: MDF
        INFO - 10:04:53: Optimization problem:
        INFO - 10:04:53:    minimize -range(thick_airfoils, thick_panels, sweep)
        INFO - 10:04:53:    with respect to sweep, thick_airfoils, thick_panels
        INFO - 10:04:53:    subject to constraints:
        INFO - 10:04:53:       c_lift(thick_airfoils, thick_panels, sweep) <= [0.89918761]
        INFO - 10:04:53:       c_rf(thick_airfoils, thick_panels, sweep) == 0.49640175939595016
        INFO - 10:04:53: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:53: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:53: ...   3%|▎         | 3/100 [00:00<00:00, 668.50 it/sec]
        INFO - 10:04:53: ...   6%|▌         | 6/100 [00:00<00:00, 331.43 it/sec]
        INFO - 10:04:53: ...   8%|▊         | 8/100 [00:00<00:00, 247.90 it/sec]
        INFO - 10:04:53: ...  11%|█         | 11/100 [00:00<00:00, 180.95 it/sec]
        INFO - 10:04:53: ...  13%|█▎        | 13/100 [00:00<00:00, 152.53 it/sec]
        INFO - 10:04:54: ...  15%|█▌        | 15/100 [00:00<00:00, 131.07 it/sec]
        INFO - 10:04:54: ...  17%|█▋        | 17/100 [00:00<00:00, 114.90 it/sec]
        INFO - 10:04:54: ...  19%|█▉        | 19/100 [00:00<00:00, 102.28 it/sec]
        INFO - 10:04:54: ...  21%|██        | 21/100 [00:01<00:00, 92.25 it/sec]
        INFO - 10:04:54: ...  23%|██▎       | 23/100 [00:01<00:00, 83.83 it/sec]
        INFO - 10:04:54: ...  25%|██▌       | 25/100 [00:01<00:00, 76.77 it/sec]
        INFO - 10:04:54: ...  27%|██▋       | 27/100 [00:01<00:01, 71.09 it/sec]
        INFO - 10:04:54: ...  29%|██▉       | 29/100 [00:01<00:01, 66.12 it/sec]
        INFO - 10:04:54: ...  31%|███       | 31/100 [00:01<00:01, 61.75 it/sec]
        INFO - 10:04:55: ...  33%|███▎      | 33/100 [00:01<00:01, 57.84 it/sec]
        INFO - 10:04:55: ...  35%|███▌      | 35/100 [00:01<00:01, 54.25 it/sec]
        INFO - 10:04:55: ...  37%|███▋      | 37/100 [00:01<00:01, 51.14 it/sec]
        INFO - 10:04:55: ...  39%|███▉      | 39/100 [00:02<00:01, 48.39 it/sec]
        INFO - 10:04:55: ...  39%|███▉      | 39/100 [00:02<00:01, 48.34 it/sec]
        INFO - 10:04:55: Optimization result:
        INFO - 10:04:55:    Optimizer info:
        INFO - 10:04:55:       Status: None
        INFO - 10:04:55:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:55:       Number of calls to the objective function by the optimizer: 39
        INFO - 10:04:55:    Solution:
        INFO - 10:04:55:       The solution is feasible.
        INFO - 10:04:55:       Objective: -0.5465979730661812
        INFO - 10:04:55:       Standardized constraints:
        INFO - 10:04:55:          c_lift + offset = [-0.55583389]
        INFO - 10:04:55:          c_rf - 0.49640175939595016 = -3.4138469828803863e-10
        INFO - 10:04:55: *** End MDOScenario execution (time: 0:00:02.076949) ***
        INFO - 10:04:58:    Formulation: IDF - Algo: NLOPT_SLSQP - Scaling: 1/2 - Replicate: 1/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:04:58: Build a preliminary MDA to start at equilibrium
        INFO - 10:04:59:  
        INFO - 10:04:59: *** Start MDOScenario execution ***
        INFO - 10:04:59: MDOScenario
        INFO - 10:04:59:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:04:59:    MDO formulation: IDF
        INFO - 10:04:59: Optimization problem:
        INFO - 10:04:59:    minimize -range(lift, mass, reserve_fact, drag)
        INFO - 10:04:59:    with respect to displ, drag, forces, lift, mass, reserve_fact, sweep, thick_airfoils, thick_panels
        INFO - 10:04:59:    subject to constraints:
        INFO - 10:04:59:       c_lift(lift, mass, reserve_fact, drag) <= [0.89921929]
        INFO - 10:04:59:       drag_forces_lift: drag#forces#lift(thick_airfoils, sweep, displ): drag(thick_airfoils, sweep, displ) - drag == 0.0
        INFO - 10:04:59:                                                       forces(thick_airfoils, sweep, displ) - forces == 0.0
        INFO - 10:04:59:                                                       lift(thick_airfoils, sweep, displ) - lift == 0.0
        INFO - 10:04:59:       displ_mass_reserve_fact: displ#mass#reserve_fact(thick_panels, sweep, forces): displ(thick_panels, sweep, forces) - displ == 0.0
        INFO - 10:04:59:                                                             mass(thick_panels, sweep, forces) - mass == 0.0
        INFO - 10:04:59:                                                             reserve_fact(thick_panels, sweep, forces) - reserve_fact == 0.0
        INFO - 10:04:59:       c_rf(lift, mass, reserve_fact, drag) == 0.4974338463722028
        INFO - 10:04:59:    over the design space:
        INFO - 10:04:59:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:59:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 10:04:59:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:59:    | thick_airfoils |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | thick_panels   |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | sweep          |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | lift           |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | displ          |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | mass           |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | reserve_fact   |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | drag           |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    | forces         |      0      |  0.5  |      1      | float |
        INFO - 10:04:59:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:04:59: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:04:59: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:04:59: ...   9%|▉         | 9/100 [00:00<00:00, 1623.56 it/sec]
        INFO - 10:04:59: Optimization result:
        INFO - 10:04:59:    Optimizer info:
        INFO - 10:04:59:       Status: None
        INFO - 10:04:59:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:04:59:       Number of calls to the objective function by the optimizer: 9
        INFO - 10:04:59:    Solution:
        INFO - 10:04:59:       The solution is feasible.
        INFO - 10:04:59:       Objective: -0.2602798816865293
        INFO - 10:04:59:       Standardized constraints:
        INFO - 10:04:59:          c_lift + offset = [-0.60380946]
        INFO - 10:04:59:          c_rf - 0.4974338463722028 = 1.1102230246251565e-16
        INFO - 10:04:59:          displ_mass_reserve_fact = [1.11022302e-16 7.49533020e-08 0.00000000e+00]
        INFO - 10:04:59:          drag_forces_lift = [7.52224839e-04 9.43689571e-16 1.85962357e-15]
        INFO - 10:04:59:       Design space:
        INFO - 10:04:59:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 10:04:59:       | name           | lower_bound |       value        | upper_bound | type  |
        INFO - 10:04:59:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 10:04:59:       | thick_airfoils |      0      |         1          |      1      | float |
        INFO - 10:04:59:       | thick_panels   |      0      | 0.3918787447278465 |      1      | float |
        INFO - 10:04:59:       | sweep          |      0      |         1          |      1      | float |
        INFO - 10:04:59:       | lift           |      0      | 0.1597339997710884 |      1      | float |
        INFO - 10:04:59:       | displ          |      0      | 0.2036563246825801 |      1      | float |
        INFO - 10:04:59:       | mass           |      0      | 0.586193716821707  |      1      | float |
        INFO - 10:04:59:       | reserve_fact   |      0      | 0.6287729345538414 |      1      | float |
        INFO - 10:04:59:       | drag           |      0      | 0.2880021596911273 |      1      | float |
        INFO - 10:04:59:       | forces         |      0      | 0.4446778719377943 |      1      | float |
        INFO - 10:04:59:       +----------------+-------------+--------------------+-------------+-------+
        INFO - 10:04:59: *** End MDOScenario execution (time: 0:00:00.076080) ***
        INFO - 10:05:01:    Formulation: IDF - Algo: NLOPT_SLSQP - Scaling: 1/2 - Replicate: 2/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:05:01: Build a preliminary MDA to start at equilibrium
        INFO - 10:05:01:  
        INFO - 10:05:01: *** Start MDOScenario execution ***
        INFO - 10:05:01: MDOScenario
        INFO - 10:05:01:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:05:01:    MDO formulation: IDF
        INFO - 10:05:01: Optimization problem:
        INFO - 10:05:01:    minimize -range(lift, mass, reserve_fact, drag)
        INFO - 10:05:01:    with respect to displ, drag, forces, lift, mass, reserve_fact, sweep, thick_airfoils, thick_panels
        INFO - 10:05:01:    subject to constraints:
        INFO - 10:05:01:       c_lift(lift, mass, reserve_fact, drag) <= [0.89918761]
        INFO - 10:05:01:       drag_forces_lift: drag#forces#lift(thick_airfoils, sweep, displ): drag(thick_airfoils, sweep, displ) - drag == 0.0
        INFO - 10:05:01:                                                       forces(thick_airfoils, sweep, displ) - forces == 0.0
        INFO - 10:05:01:                                                       lift(thick_airfoils, sweep, displ) - lift == 0.0
        INFO - 10:05:01:       displ_mass_reserve_fact: displ#mass#reserve_fact(thick_panels, sweep, forces): displ(thick_panels, sweep, forces) - displ == 0.0
        INFO - 10:05:01:                                                             mass(thick_panels, sweep, forces) - mass == 0.0
        INFO - 10:05:01:                                                             reserve_fact(thick_panels, sweep, forces) - reserve_fact == 0.0
        INFO - 10:05:01:       c_rf(lift, mass, reserve_fact, drag) == 0.49640175939595016
        INFO - 10:05:02:    over the design space:
        INFO - 10:05:02:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:05:02:    | name           | lower_bound | value | upper_bound | type  |
        INFO - 10:05:02:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:05:02:    | thick_airfoils |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | thick_panels   |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | sweep          |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | lift           |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | displ          |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | mass           |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | reserve_fact   |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | drag           |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    | forces         |      0      |  0.5  |      1      | float |
        INFO - 10:05:02:    +----------------+-------------+-------+-------------+-------+
        INFO - 10:05:02: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:05:02: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:05:02: ...   8%|▊         | 8/100 [00:00<00:00, 1846.10 it/sec]
        INFO - 10:05:02: Optimization result:
        INFO - 10:05:02:    Optimizer info:
        INFO - 10:05:02:       Status: None
        INFO - 10:05:02:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:05:02:       Number of calls to the objective function by the optimizer: 8
        INFO - 10:05:02:    Solution:
        INFO - 10:05:02:       The solution is feasible.
        INFO - 10:05:02:       Objective: -0.2696970985756207
        INFO - 10:05:02:       Standardized constraints:
        INFO - 10:05:02:          c_lift + offset = [-0.48406661]
        INFO - 10:05:02:          c_rf - 0.49640175939595016 = 0.0
        INFO - 10:05:02:          displ_mass_reserve_fact = [ 0.00000000e+00  0.00000000e+00 -2.77555756e-17]
        INFO - 10:05:02:          drag_forces_lift = [-1.11022302e-16  0.00000000e+00  1.11022302e-16]
        INFO - 10:05:02:       Design space:
        INFO - 10:05:02:       +----------------+-------------+-----------------------+-------------+-------+
        INFO - 10:05:02:       | name           | lower_bound |         value         | upper_bound | type  |
        INFO - 10:05:02:       +----------------+-------------+-----------------------+-------------+-------+
        INFO - 10:05:02:       | thick_airfoils |      0      | 1.600564755384918e-16 |      1      | float |
        INFO - 10:05:02:       | thick_panels   |      0      |   0.1305332770797183  |      1      | float |
        INFO - 10:05:02:       | sweep          |      0      |           0           |      1      | float |
        INFO - 10:05:02:       | lift           |      0      |   0.8922327706542336  |      1      | float |
        INFO - 10:05:02:       | displ          |      0      |   0.5916701425799068  |      1      | float |
        INFO - 10:05:02:       | mass           |      0      |   0.3236885735428515  |      1      | float |
        INFO - 10:05:02:       | reserve_fact   |      0      |   0.1773984242002992  |      1      | float |
        INFO - 10:05:02:       | drag           |      0      |   0.7393753041390633  |      1      | float |
        INFO - 10:05:02:       | forces         |      0      |   0.7828315097092865  |      1      | float |
        INFO - 10:05:02:       +----------------+-------------+-----------------------+-------------+-------+
        INFO - 10:05:02: *** End MDOScenario execution (time: 0:00:00.068797) ***
        INFO - 10:05:04:    Formulation: IDF - Algo: NLOPT_SLSQP - Scaling: 2/2 - Replicate: 1/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:05:05: Build a preliminary MDA to start at equilibrium
        INFO - 10:05:05:  
        INFO - 10:05:05: *** Start MDOScenario execution ***
        INFO - 10:05:05: MDOScenario
        INFO - 10:05:05:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:05:05:    MDO formulation: IDF
        INFO - 10:05:05: Optimization problem:
        INFO - 10:05:05:    minimize -range(lift, mass, reserve_fact, drag)
        INFO - 10:05:05:    with respect to displ, drag, forces, lift, mass, reserve_fact, sweep, thick_airfoils, thick_panels
        INFO - 10:05:05:    subject to constraints:
        INFO - 10:05:05:       c_lift(lift, mass, reserve_fact, drag) <= [0.89921929]
        INFO - 10:05:05:       drag_forces_lift: drag#forces#lift(thick_airfoils, sweep, displ): drag(thick_airfoils, sweep, displ) - drag == 0.0
        INFO - 10:05:05:                                                       forces(thick_airfoils, sweep, displ) - forces == 0.0
        INFO - 10:05:05:                                                       lift(thick_airfoils, sweep, displ) - lift == 0.0
        INFO - 10:05:05:       displ_mass_reserve_fact: displ#mass#reserve_fact(thick_panels, sweep, forces): displ(thick_panels, sweep, forces) - displ == 0.0
        INFO - 10:05:05:                                                             mass(thick_panels, sweep, forces) - mass == 0.0
        INFO - 10:05:05:                                                             reserve_fact(thick_panels, sweep, forces) - reserve_fact == 0.0
        INFO - 10:05:05:       c_rf(lift, mass, reserve_fact, drag) == 0.4974338463722027
        INFO - 10:05:05: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:05:05: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:05:05: ...   9%|▉         | 9/100 [00:00<00:00, 869.06 it/sec]
        INFO - 10:05:05: ...  17%|█▋        | 17/100 [00:00<00:00, 414.85 it/sec]
        INFO - 10:05:05: ...  24%|██▍       | 24/100 [00:00<00:00, 282.74 it/sec]
        INFO - 10:05:06: ...  31%|███       | 31/100 [00:00<00:00, 214.38 it/sec]
        INFO - 10:05:06: ...  38%|███▊      | 38/100 [00:00<00:00, 172.47 it/sec]
        INFO - 10:05:06: ...  45%|████▌     | 45/100 [00:00<00:00, 144.16 it/sec]
        INFO - 10:05:06: ...  52%|█████▏    | 52/100 [00:00<00:00, 123.94 it/sec]
        INFO - 10:05:06: ...  59%|█████▉    | 59/100 [00:00<00:00, 108.53 it/sec]
        INFO - 10:05:06: ...  66%|██████▌   | 66/100 [00:01<00:00, 96.53 it/sec]
        INFO - 10:05:06: ...  73%|███████▎  | 73/100 [00:01<00:00, 86.89 it/sec]
        INFO - 10:05:06: ...  78%|███████▊  | 78/100 [00:01<00:00, 80.91 it/sec]
        INFO - 10:05:06: Optimization result:
        INFO - 10:05:06:    Optimizer info:
        INFO - 10:05:06:       Status: None
        INFO - 10:05:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:05:06:       Number of calls to the objective function by the optimizer: 78
        INFO - 10:05:06:    Solution:
        INFO - 10:05:06:       The solution is feasible.
        INFO - 10:05:06:       Objective: -0.4721603268164957
        INFO - 10:05:06:       Standardized constraints:
        INFO - 10:05:06:          c_lift + offset = [-0.72037473]
        INFO - 10:05:06:          c_rf - 0.4974338463722027 = 5.551115123125783e-17
        INFO - 10:05:06:          displ_mass_reserve_fact = [-2.15885904e-09  1.64748681e-09 -9.69851754e-10]
        INFO - 10:05:06:          drag_forces_lift = [5.64415060e-10 9.02571455e-10 2.11442742e-10]
        INFO - 10:05:06: *** End MDOScenario execution (time: 0:00:01.246025) ***
        INFO - 10:05:09:    Formulation: IDF - Algo: NLOPT_SLSQP - Scaling: 2/2 - Replicate: 2/2
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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)
        INFO - 10:05:11: Build a preliminary MDA to start at equilibrium
        INFO - 10:05:11:  
        INFO - 10:05:11: *** Start MDOScenario execution ***
        INFO - 10:05:11: MDOScenario
        INFO - 10:05:11:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 10:05:11:    MDO formulation: IDF
        INFO - 10:05:11: Optimization problem:
        INFO - 10:05:11:    minimize -range(lift, mass, reserve_fact, drag)
        INFO - 10:05:11:    with respect to displ, drag, forces, lift, mass, reserve_fact, sweep, thick_airfoils, thick_panels
        INFO - 10:05:11:    subject to constraints:
        INFO - 10:05:11:       c_lift(lift, mass, reserve_fact, drag) <= [0.89918761]
        INFO - 10:05:11:       drag_forces_lift: drag#forces#lift(thick_airfoils, sweep, displ): drag(thick_airfoils, sweep, displ) - drag == 0.0
        INFO - 10:05:11:                                                       forces(thick_airfoils, sweep, displ) - forces == 0.0
        INFO - 10:05:11:                                                       lift(thick_airfoils, sweep, displ) - lift == 0.0
        INFO - 10:05:11:       displ_mass_reserve_fact: displ#mass#reserve_fact(thick_panels, sweep, forces): displ(thick_panels, sweep, forces) - displ == 0.0
        INFO - 10:05:11:                                                             mass(thick_panels, sweep, forces) - mass == 0.0
        INFO - 10:05:11:                                                             reserve_fact(thick_panels, sweep, forces) - reserve_fact == 0.0
        INFO - 10:05:11:       c_rf(lift, mass, reserve_fact, drag) == 0.49640175939595016
        INFO - 10:05:11: Solving optimization problem with algorithm NLOPT_SLSQP:
        INFO - 10:05:11: ...   0%|          | 0/100 [00:00<?, ?it]
        INFO - 10:05:11: ...   9%|▉         | 9/100 [00:00<00:00, 872.91 it/sec]
        INFO - 10:05:11: ...  17%|█▋        | 17/100 [00:00<00:00, 414.37 it/sec]
        INFO - 10:05:11: ...  24%|██▍       | 24/100 [00:00<00:00, 281.34 it/sec]
        INFO - 10:05:11: ...  31%|███       | 31/100 [00:00<00:00, 212.76 it/sec]
        INFO - 10:05:11: ...  38%|███▊      | 38/100 [00:00<00:00, 170.76 it/sec]
        INFO - 10:05:11: ...  39%|███▉      | 39/100 [00:00<00:00, 165.42 it/sec]
        INFO - 10:05:11: Optimization result:
        INFO - 10:05:11:    Optimizer info:
        INFO - 10:05:11:       Status: None
        INFO - 10:05:11:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:05:11:       Number of calls to the objective function by the optimizer: 39
        INFO - 10:05:11:    Solution:
        INFO - 10:05:11:       The solution is feasible.
        INFO - 10:05:11:       Objective: -0.5465979624197809
        INFO - 10:05:11:       Standardized constraints:
        INFO - 10:05:11:          c_lift + offset = [-0.55583389]
        INFO - 10:05:11:          c_rf - 0.49640175939595016 = 0.0
        INFO - 10:05:11:          displ_mass_reserve_fact = [ 1.11022302e-16 -1.04083409e-17  1.38777878e-17]
        INFO - 10:05:11:          drag_forces_lift = [0.0000000e+00 4.4408921e-16 0.0000000e+00]
        INFO - 10:05:11: *** End MDOScenario execution (time: 0:00:00.614326) ***

    [<gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbf857cbb0>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbf81192e0>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbf84a45b0>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbfa5a3b20>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbfb368be0>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbfa7c9e50>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbf81220d0>, <gemseo.problems.scalable.data_driven.study.result.ScalabilityResult object at 0x7fdbe15ccc40>]



.. GENERATED FROM PYTHON SOURCE LINES 158-174

Look at the dependency matrices
-------------------------------
Here are the dependency matrices obtained with the 1st replicate when
:code:`design_size=10`.

Aerodynamics
~~~~~~~~~~~~
.. image:: /_images/scalable_example/2_1_sdm_Aerodynamics_dependency-1.png

Structure
~~~~~~~~~~~~
.. image:: /_images/scalable_example/2_1_sdm_Structure_dependency-1.png

Mission
~~~~~~~
.. image:: /_images/scalable_example/2_1_sdm_Mission_dependency-1.png

.. GENERATED FROM PYTHON SOURCE LINES 176-213

Look at optimization histories
------------------------------
Here are the optimization histories obtained with the 1st replicate when
:code:`design_size=10`, where the left side represents the :class:`.MDF` formulation
while the right one represents the :class:`.IDF` formulation.

Objective function
~~~~~~~~~~~~~~~~~~
.. image:: /_images/scalable_example/MDF_2_1_obj_history-1.png
   :width: 45%

.. image:: /_images/scalable_example/IDF_2_1_obj_history-1.png
   :width: 45%

Design variables
~~~~~~~~~~~~~~~~
.. image:: /_images/scalable_example/MDF_2_1_variables_history-1.png
   :width: 45%

.. image:: /_images/scalable_example/IDF_2_1_variables_history-1.png
   :width: 45%

Equality constraints
~~~~~~~~~~~~~~~~~~~~
.. image:: /_images/scalable_example/MDF_2_1_eq_constraints_history-1.png
   :width: 45%

.. image:: /_images/scalable_example/IDF_2_1_eq_constraints_history-1.png
   :width: 45%

Inequality constraints
~~~~~~~~~~~~~~~~~~~~~~
.. image:: /_images/scalable_example/MDF_2_1_ineq_constraints_history-1.png
   :width: 45%

.. image:: /_images/scalable_example/IDF_2_1_ineq_constraints_history-1.png
   :width: 45%

.. GENERATED FROM PYTHON SOURCE LINES 215-227

Post-process the results
------------------------
Lastly, we plot the results.
Because of the replicates,
the latter are not displayed as one line per optimization strategy
w.r.t. scaling strategy,
but as one series of boxplots per optimization strategy w.r.t. scaling strategy,
where the boxplots represents the variability due to the 10 replicates.
In this case, it seems that
the :class:`.MDF` formulation is more expensive than the :class:`.IDF` one
when the design space dimension increases
while they seems to be the same when each design parameter has a size equal to 1.

.. GENERATED FROM PYTHON SOURCE LINES 227-231

.. code-block:: default

    post = plot_scalability_results("study")
    post.labelize_scaling_strategy("Number of design parameters per type.")
    post.plot(xmargin=3.0, xticks=[1.0, 20.0], xticks_labels=["1", "20"], widths=1.0)




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


    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_study_001.png
         :alt: scalable study
         :srcset: /examples/scalable/images/sphx_glr_scalable_study_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_study_002.png
         :alt: scalable study
         :srcset: /examples/scalable/images/sphx_glr_scalable_study_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_study_003.png
         :alt: scalable study
         :srcset: /examples/scalable/images/sphx_glr_scalable_study_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_study_004.png
         :alt: scalable study
         :srcset: /examples/scalable/images/sphx_glr_scalable_study_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/scalable/images/sphx_glr_scalable_study_005.png
         :alt: scalable study
         :srcset: /examples/scalable/images/sphx_glr_scalable_study_005.png
         :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none

        INFO - 10:05:14: Post-process for scalability study
        INFO - 10:05:14:    Working directory: study
        INFO - 10:05:14:    Save exec_time plot in study/visualization/scalability_study/exec_time.png
        INFO - 10:05:14:    Save n_calls plot in study/visualization/scalability_study/n_calls.png
        INFO - 10:05:15:    Save n_calls_linearize plot in study/visualization/scalability_study/n_calls_linearize.png
        INFO - 10:05:15:    Save total_calls plot in study/visualization/scalability_study/total_calls.png
        INFO - 10:05:15:    Save is_feasible plot in study/visualization/scalability_study/is_feasible.png
        INFO - 10:05:15: Execute post-processing
        INFO - 10:05:15:    Type: replicate




.. GENERATED FROM PYTHON SOURCE LINES 232-234

.. image:: /_images/scalable_example/exec_time-1.png



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

   **Total running time of the script:** ( 0 minutes  38.518 seconds)


.. _sphx_glr_download_examples_scalable_scalable_study.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_study.py <scalable_study.py>`



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

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


.. only:: html

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

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