.. 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 32-43

.. code-block:: default

    from __future__ import division, unicode_literals

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

    configure_logger()






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

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 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 44-50

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 50-56

.. 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 57-61

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

.. GENERATED FROM PYTHON SOURCE LINES 61-72

.. code-block:: default

    disciplines = create_discipline(["Aerodynamics", "Structure", "Mission"])
    for discipline in disciplines:
        discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)
        design_space = AerostructureDesignSpace()
        design_space.filter(discipline.get_input_data_names())
        output = next(iter(discipline.get_output_data_names()))
        scenario = create_scenario(
            discipline, "DisciplinaryOpt", output, design_space, scenario_type="DOE"
        )
        scenario.execute({"algo": "DiagonalDOE", "n_samples": 10})





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

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 .. code-block:: none

        INFO - 09:23:45:  
        INFO - 09:23:45: *** Start DOE Scenario execution ***
        INFO - 09:23:45: DOEScenario
        INFO - 09:23:45:    Disciplines: Aerodynamics
        INFO - 09:23:45:    MDOFormulation: DisciplinaryOpt
        INFO - 09:23:45:    Algorithm: DiagonalDOE
        INFO - 09:23:45: Optimization problem:
        INFO - 09:23:45:    Minimize: drag(thick_airfoils, sweep, displ)
        INFO - 09:23:45:    With respect to: thick_airfoils, sweep, displ
        INFO - 09:23:45: DOE sampling:   0%|          | 0/10 [00:00<?, ?it]
        INFO - 09:23:45: DOE sampling: 100%|██████████| 10/10 [00:00<00:00, 451.19 it/sec, obj=-320]
        INFO - 09:23:45: Optimization result:
        INFO - 09:23:45: Objective value = -319.99905478395067
        INFO - 09:23:45: The result is feasible.
        INFO - 09:23:45: Status: None
        INFO - 09:23:45: Optimizer message: None
        INFO - 09:23:45: Number of calls to the objective function by the optimizer: 10
        INFO - 09:23:45: Design Space:
        INFO - 09:23:45: +----------------+-------------+-------+-------------+-------+
        INFO - 09:23:45: | name           | lower_bound | value | upper_bound | type  |
        INFO - 09:23:45: +----------------+-------------+-------+-------------+-------+
        INFO - 09:23:45: | thick_airfoils |      5      |   25  |      25     | float |
        INFO - 09:23:45: | sweep          |      10     |   35  |      35     | float |
        INFO - 09:23:45: | displ          |    -1000    |  1000 |     1000    | float |
        INFO - 09:23:45: +----------------+-------------+-------+-------------+-------+
        INFO - 09:23:45: *** DOE Scenario run terminated ***
        INFO - 09:23:45:  
        INFO - 09:23:45: *** Start DOE Scenario execution ***
        INFO - 09:23:45: DOEScenario
        INFO - 09:23:45:    Disciplines: Structure
        INFO - 09:23:45:    MDOFormulation: DisciplinaryOpt
        INFO - 09:23:45:    Algorithm: DiagonalDOE
        INFO - 09:23:45: Optimization problem:
        INFO - 09:23:45:    Minimize: mass(thick_panels, sweep, forces)
        INFO - 09:23:45:    With respect to: thick_panels, sweep, forces
        INFO - 09:23:45: DOE sampling:   0%|          | 0/10 [00:00<?, ?it]
        INFO - 09:23:45: DOE sampling: 100%|██████████| 10/10 [00:00<00:00, 382.36 it/sec, obj=4.02e+5]
        INFO - 09:23:45: Optimization result:
        INFO - 09:23:45: Objective value = 100.08573388203513
        INFO - 09:23:45: The result is feasible.
        INFO - 09:23:45: Status: None
        INFO - 09:23:45: Optimizer message: None
        INFO - 09:23:45: Number of calls to the objective function by the optimizer: 10
        INFO - 09:23:45: Design Space:
        INFO - 09:23:45: +--------------+-------------+-------+-------------+-------+
        INFO - 09:23:45: | name         | lower_bound | value | upper_bound | type  |
        INFO - 09:23:45: +--------------+-------------+-------+-------------+-------+
        INFO - 09:23:45: | thick_panels |      1      |   1   |      20     | float |
        INFO - 09:23:45: | sweep        |      10     |   10  |      35     | float |
        INFO - 09:23:45: | forces       |    -1000    | -1000 |     1000    | float |
        INFO - 09:23:45: +--------------+-------------+-------+-------------+-------+
        INFO - 09:23:45: *** DOE Scenario run terminated ***
        INFO - 09:23:45:  
        INFO - 09:23:45: *** Start DOE Scenario execution ***
        INFO - 09:23:45: DOEScenario
        INFO - 09:23:45:    Disciplines: Mission
        INFO - 09:23:45:    MDOFormulation: DisciplinaryOpt
        INFO - 09:23:45:    Algorithm: DiagonalDOE
        INFO - 09:23:45: Optimization problem:
        INFO - 09:23:45:    Minimize: range(drag, lift, mass, reserve_fact)
        INFO - 09:23:45:    With respect to: drag, lift, mass, reserve_fact
        INFO - 09:23:45: DOE sampling:   0%|          | 0/10 [00:00<?, ?it]
        INFO - 09:23:45: DOE sampling: 100%|██████████| 10/10 [00:00<00:00, 453.12 it/sec, obj=1600.0]
        INFO - 09:23:45: Optimization result:
        INFO - 09:23:45: Objective value = 1600.0
        INFO - 09:23:45: The result is feasible.
        INFO - 09:23:45: Status: None
        INFO - 09:23:45: Optimizer message: None
        INFO - 09:23:45: Number of calls to the objective function by the optimizer: 10
        INFO - 09:23:45: Design Space:
        INFO - 09:23:45: +--------------+-------------+--------+-------------+-------+
        INFO - 09:23:45: | name         | lower_bound | value  | upper_bound | type  |
        INFO - 09:23:45: +--------------+-------------+--------+-------------+-------+
        INFO - 09:23:45: | drag         |     100     |  1000  |     1000    | float |
        INFO - 09:23:45: | lift         |     0.1     |   1    |      1      | float |
        INFO - 09:23:45: | mass         |    100000   | 500000 |    500000   | float |
        INFO - 09:23:45: | reserve_fact |    -1000    |  1000  |     1000    | float |
        INFO - 09:23:45: +--------------+-------------+--------+-------------+-------+
        INFO - 09:23:45: *** DOE Scenario run terminated ***




.. GENERATED FROM PYTHON SOURCE LINES 73-78

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 78-90

.. code-block:: default

    datasets = [discipline.cache.export_to_dataset() for discipline in disciplines]
    problem = ScalableProblem(
        datasets,
        design_variables,
        objective_function,
        eq_constraints,
        ineq_constraints,
        maximize_objective,
        sizes={"sweep": 2},
    )
    print(problem)





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

 Out:

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.1.0/lib/python3.8/site-packages/gemseo/problems/scalable/data_driven/model.py:150: 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: sweep (2), thick_airfoils (1), displ (1), drag (1), forces (1), lift (1), thick_panels (1), mass (1), reserve_fact (1), range (1), c_lift (1), c_rf (1)




.. GENERATED FROM PYTHON SOURCE LINES 91-97

.. 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 99-102

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

.. GENERATED FROM PYTHON SOURCE LINES 102-104

.. code-block:: default

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




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





.. GENERATED FROM PYTHON SOURCE LINES 105-110

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 110-112

.. code-block:: default

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





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 .. code-block:: none

        INFO - 09:23:46: Build a preliminary MDA to start at equilibrium




.. GENERATED FROM PYTHON SOURCE LINES 113-119

.. 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 121-124

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 124-126

.. code-block:: default

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





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

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 .. code-block:: none

        INFO - 09:23:46:  
        INFO - 09:23:46: *** Start MDO Scenario execution ***
        INFO - 09:23:46: MDOScenario
        INFO - 09:23:46:    Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
        INFO - 09:23:46:    MDOFormulation: MDF
        INFO - 09:23:46:    Algorithm: NLOPT_SLSQP
        INFO - 09:23:46: Optimization problem:
        INFO - 09:23:46:    Minimize: -range(thick_airfoils, thick_panels, sweep)
        INFO - 09:23:46:    With respect to: thick_airfoils, thick_panels, sweep
        INFO - 09:23:46:    Subject to constraints:
        INFO - 09:23:46:       c_lift(thick_airfoils, thick_panels, sweep) <= [0.74804822]
        INFO - 09:23:46:       c_rf(thick_airfoils, thick_panels, sweep) == 0.4974338463722028
        INFO - 09:23:46: Design Space:
        INFO - 09:23:46: +----------------+-------------+-------+-------------+-------+
        INFO - 09:23:46: | name           | lower_bound | value | upper_bound | type  |
        INFO - 09:23:46: +----------------+-------------+-------+-------------+-------+
        INFO - 09:23:46: | thick_airfoils |      0      |  0.5  |      1      | float |
        INFO - 09:23:46: | thick_panels   |      0      |  0.5  |      1      | float |
        INFO - 09:23:46: | sweep          |      0      |  0.5  |      1      | float |
        INFO - 09:23:46: | sweep          |      0      |  0.5  |      1      | float |
        INFO - 09:23:46: +----------------+-------------+-------+-------------+-------+
        INFO - 09:23:46: Optimization:   0%|          | 0/100 [00:00<?, ?it]
        INFO - 09:23:46: Optimization:   4%|▍         | 4/100 [00:00<00:00, 800.81 it/sec, obj=0.197]
       ERROR - 09:23:46: NLOPT run failed : NLopt roundoff-limited, RoundoffLimited
        INFO - 09:23:46: Optimization:   7%|▋         | 7/100 [00:00<00:00, 372.11 it/sec, obj=0.299]
        INFO - 09:23:46: Optimization result:
        INFO - 09:23:46: Objective value = 0.2985276625156317
        INFO - 09:23:46: The result is feasible.
        INFO - 09:23:46: Status: None
        INFO - 09:23:46: Optimizer message:  GEMSEO Stopped the driver
        INFO - 09:23:46: Number of calls to the objective function by the optimizer: 8
        INFO - 09:23:46: Constraints values w.r.t. 0: 
        INFO - 09:23:46:    c_lift = [-0.49234168]
        INFO - 09:23:46:    c_rf = -1.4988010832439613e-15
        INFO - 09:23:46: Design Space:
        INFO - 09:23:46: +----------------+-------------+--------------------+-------------+-------+
        INFO - 09:23:46: | name           | lower_bound |       value        | upper_bound | type  |
        INFO - 09:23:46: +----------------+-------------+--------------------+-------------+-------+
        INFO - 09:23:46: | thick_airfoils |      0      |         1          |      1      | float |
        INFO - 09:23:46: | thick_panels   |      0      | 0.5155052311585078 |      1      | float |
        INFO - 09:23:46: | sweep          |      0      |         1          |      1      | float |
        INFO - 09:23:46: | sweep          |      0      |         1          |      1      | float |
        INFO - 09:23:46: +----------------+-------------+--------------------+-------------+-------+
        INFO - 09:23:46: *** MDO Scenario run terminated in 0:00:00.281022 ***

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



.. GENERATED FROM PYTHON SOURCE LINES 127-129

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

.. GENERATED FROM PYTHON SOURCE LINES 129-130

.. code-block:: default

    scenario.post_process("OptHistoryView", save=False, show=True)




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

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 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f61b8c85040>




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

   **Total running time of the script:** ( 0 minutes  1.261 seconds)


.. _sphx_glr_download_examples_scalable_plot_problem.py:


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