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.. only:: html

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        :ref:`Go to the end <sphx_glr_download_examples_post_process_algorithms_plot_para_coord.py>`
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.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_post_process_algorithms_plot_para_coord.py:


Parallel coordinates
====================

In this example, we illustrate the use of the
:class:`.ParallelCoordinates` plot on the Sobieski's SSBJ
problem.

.. GENERATED FROM PYTHON SOURCE LINES 29-36

.. code-block:: default

    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo.problems.sobieski.core.problem import SobieskiProblem








.. GENERATED FROM PYTHON SOURCE LINES 37-41

Import
------
The first step is to import some high-level functions
and a method to get the design space.

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: default


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-59

Description
-----------

The :class:`.ParallelCoordinates` post-processing
builds parallel coordinates plots among design
variables, outputs functions and constraints.

The :class:`.ParallelCoordinates` portrays the design
variables history during the scenario execution. Each vertical coordinate is
dedicated to a design variable, normalized by its bounds.

A polyline joins all components of a given design vector and is colored
by objective function values. This highlights the correlations between
the values of the design variables and the values of the objective function.

.. GENERATED FROM PYTHON SOURCE LINES 61-65

Create disciplines
------------------
At this point, we instantiate the disciplines of Sobieski's SSBJ problem:
Propulsion, Aerodynamics, Structure and Mission

.. GENERATED FROM PYTHON SOURCE LINES 65-74

.. code-block:: default

    disciplines = create_discipline(
        [
            "SobieskiPropulsion",
            "SobieskiAerodynamics",
            "SobieskiStructure",
            "SobieskiMission",
        ]
    )








.. GENERATED FROM PYTHON SOURCE LINES 75-78

Create design space
-------------------
We also read the design space from the :class:`.SobieskiProblem`.

.. GENERATED FROM PYTHON SOURCE LINES 78-80

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 81-88

Create and execute scenario
---------------------------
The next step is to build an MDO scenario in order to maximize the range,
encoded 'y_4', with respect to the design parameters, while satisfying the
inequality constraints 'g_1', 'g_2' and 'g_3'. We can use the MDF formulation,
the SLSQP optimization algorithm
and a maximum number of iterations equal to 100.

.. GENERATED FROM PYTHON SOURCE LINES 88-100

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="MDF",
        objective_name="y_4",
        maximize_objective=True,
        design_space=design_space,
    )
    scenario.set_differentiation_method()
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, "ineq")
    scenario.execute({"algo": "SLSQP", "max_iter": 10})





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

 .. code-block:: none

        INFO - 16:24:57:  
        INFO - 16:24:57: *** Start MDOScenario execution ***
        INFO - 16:24:57: MDOScenario
        INFO - 16:24:57:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 16:24:57:    MDO formulation: MDF
        INFO - 16:24:57: Optimization problem:
        INFO - 16:24:57:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 16:24:57:    with respect to x_1, x_2, x_3, x_shared
        INFO - 16:24:57:    subject to constraints:
        INFO - 16:24:57:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:24:57:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:24:57:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:24:57:    over the design space:
        INFO - 16:24:57:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:57:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 16:24:57:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:57:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:24:57:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:24:57:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:24:57:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:24:57:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:24:57:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:24:57:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 16:24:57:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 16:24:57:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 16:24:57:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 16:24:57:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:57: Solving optimization problem with algorithm SLSQP:
        INFO - 16:24:57: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 16:24:57: ...  10%|█         | 1/10 [00:00<00:00, 10.19 it/sec, obj=-536]
        INFO - 16:24:57: ...  20%|██        | 2/10 [00:00<00:01,  7.39 it/sec, obj=-2.12e+3]
     WARNING - 16:24:57: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
        INFO - 16:24:57: ...  30%|███       | 3/10 [00:00<00:01,  6.42 it/sec, obj=-3.75e+3]
        INFO - 16:24:58: ...  40%|████      | 4/10 [00:00<00:00,  6.22 it/sec, obj=-4.01e+3]
     WARNING - 16:24:58: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
        INFO - 16:24:58: ...  50%|█████     | 5/10 [00:00<00:00,  5.92 it/sec, obj=-4.49e+3]
        INFO - 16:24:58: ...  60%|██████    | 6/10 [00:01<00:00,  5.96 it/sec, obj=-3.4e+3]
        INFO - 16:24:58: ...  70%|███████   | 7/10 [00:01<00:00,  6.55 it/sec, obj=-4.93e+3]
        INFO - 16:24:58: ...  80%|████████  | 8/10 [00:01<00:00,  6.91 it/sec, obj=-4.76e+3]
        INFO - 16:24:58: ...  90%|█████████ | 9/10 [00:01<00:00,  7.27 it/sec, obj=-4.62e+3]
        INFO - 16:24:58: ... 100%|██████████| 10/10 [00:01<00:00,  7.65 it/sec, obj=-4.56e+3]
        INFO - 16:24:58: Optimization result:
        INFO - 16:24:58:    Optimizer info:
        INFO - 16:24:58:       Status: None
        INFO - 16:24:58:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 16:24:58:       Number of calls to the objective function by the optimizer: 12
        INFO - 16:24:58:    Solution:
        INFO - 16:24:58:       The solution is feasible.
        INFO - 16:24:58:       Objective: -3749.8868975554387
        INFO - 16:24:58:       Standardized constraints:
        INFO - 16:24:58:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
        INFO - 16:24:58:  -0.10219342]
        INFO - 16:24:58:          g_2 = -0.0004062839430756249
        INFO - 16:24:58:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
        INFO - 16:24:58:       Design space: 
        INFO - 16:24:58:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:58:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 16:24:58:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:58:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
        INFO - 16:24:58:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
        INFO - 16:24:58:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 16:24:58:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
        INFO - 16:24:58:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
        INFO - 16:24:58:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
        INFO - 16:24:58:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 16:24:58:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
        INFO - 16:24:58:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
        INFO - 16:24:58:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
        INFO - 16:24:58:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:58: *** End MDOScenario execution (time: 0:00:01.328415) ***

    {'max_iter': 10, 'algo': 'SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 101-106

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the
:class:`.ParallelCoordinates` plot which parallel
coordinates plots among design variables, objective function and constraints.

.. GENERATED FROM PYTHON SOURCE LINES 108-116

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the high-level function
   :func:`.get_post_processing_options_schema` to print a table with
   the options for any post-processing algorithm.
   Or refer to our dedicated page:
   :ref:`gen_post_algos`.

.. GENERATED FROM PYTHON SOURCE LINES 116-117

.. code-block:: default

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



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


    *

      .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_para_coord_001.png
         :alt: Design variables history colored by '-y_4' value
         :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_para_coord_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_para_coord_002.png
         :alt: Objective function and constraints history colored by '-y_4' value.
         :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_para_coord_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.0/lib/python3.9/site-packages/genson/schema/strategies/base.py:42: UserWarning: Schema incompatible. Keyword 'description' has conflicting values ('The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.' vs. 'The width and height of the figure in inches, e.g. `(w, h)`.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'). Using 'The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'
      warn(('Schema incompatible. Keyword {0!r} has conflicting '

    <gemseo.post.para_coord.ParallelCoordinates object at 0x7fea4fe8ae20>




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

   **Total running time of the script:** ( 0 minutes  2.019 seconds)


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