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

.. _sphx_glr_examples_post_process_plot_opt_hist_view.py:


Optimization History View
=========================

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

.. GENERATED FROM PYTHON SOURCE LINES 28-36

.. 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.sobieski.core.problem import SobieskiProblem
    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 37-41

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

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: default


    configure_logger()




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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 44-67

Description
-----------
The **OptHistoryView** post-processing
creates a series of plots:

- The design variables history - This graph shows the normalized values of the
  design variables, the :math:`y` axis is the index of the inputs in the vector;
  and the :math:`x` axis represents the iterations.
- The objective function history - It shows the evolution of the objective
  value during the optimization.
- The distance to the best design variables - Plots the vector
  :math:`log( ||x-x^*|| )` in log scale.
- The history of the Hessian approximation of the objective - Plots an approximation
  of the second order derivatives of the objective function
  :math:`\frac{\partial^2 f(x)}{\partial x^2}`, which is a measure of
  the sensitivity of the function with respect to the design variables,
  and of the anisotropy of the problem (differences of curvatures in the
  design space).
- The inequality constraint history - Portrays the evolution of the values of the
  :term:`constraints`. The inequality constraints must be non-positive, that is why
  the plot must be green or white for satisfied constraints (white = active,
  red = violated). For an :ref:`IDF formulation <idf_formulation>`, an additional
  plot is created to track the equality constraint history.

.. GENERATED FROM PYTHON SOURCE LINES 69-73

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

.. GENERATED FROM PYTHON SOURCE LINES 73-82

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 83-86

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

.. GENERATED FROM PYTHON SOURCE LINES 86-88

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 89-96

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 96-108

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="MDF",
        objective_name="y_4",
        maximize_objective=True,
        design_space=design_space,
    )
    scenario.set_differentiation_method("user")
    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 - 14:43:34:  
        INFO - 14:43:34: *** Start MDOScenario execution ***
        INFO - 14:43:34: MDOScenario
        INFO - 14:43:34:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 14:43:34:    MDO formulation: MDF
        INFO - 14:43:34: Optimization problem:
        INFO - 14:43:34:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 14:43:34:    with respect to x_1, x_2, x_3, x_shared
        INFO - 14:43:34:    subject to constraints:
        INFO - 14:43:34:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:34:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:34:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:34:    over the design space:
        INFO - 14:43:34:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:34:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 14:43:34:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:34:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 14:43:34:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 14:43:34:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 14:43:34:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 14:43:34:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 14:43:34:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 14:43:34:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 14:43:34:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:34:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:34:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 14:43:34:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:34: Solving optimization problem with algorithm SLSQP:
        INFO - 14:43:34: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:43:34: ...  20%|██        | 2/10 [00:00<00:00, 40.93 it/sec, obj=-2.12e+3]
     WARNING - 14:43:34: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
        INFO - 14:43:34: ...  30%|███       | 3/10 [00:00<00:00, 23.58 it/sec, obj=-3.75e+3]
        INFO - 14:43:34: ...  40%|████      | 4/10 [00:00<00:00, 17.20 it/sec, obj=-4.01e+3]
     WARNING - 14:43:35: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
        INFO - 14:43:35: ...  50%|█████     | 5/10 [00:00<00:00, 13.09 it/sec, obj=-4.49e+3]
        INFO - 14:43:35: ...  60%|██████    | 6/10 [00:00<00:00, 11.10 it/sec, obj=-3.4e+3]
        INFO - 14:43:35: ...  80%|████████  | 8/10 [00:01<00:00,  9.45 it/sec, obj=-4.76e+3]
        INFO - 14:43:35: ... 100%|██████████| 10/10 [00:01<00:00,  8.23 it/sec, obj=-4.56e+3]
        INFO - 14:43:35: ... 100%|██████████| 10/10 [00:01<00:00,  8.21 it/sec, obj=-4.56e+3]
        INFO - 14:43:35: Optimization result:
        INFO - 14:43:35:    Optimizer info:
        INFO - 14:43:35:       Status: None
        INFO - 14:43:35:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 14:43:35:       Number of calls to the objective function by the optimizer: 12
        INFO - 14:43:35:    Solution:
        INFO - 14:43:35:       The solution is feasible.
        INFO - 14:43:35:       Objective: -3749.8868975554387
        INFO - 14:43:35:       Standardized constraints:
        INFO - 14:43:35:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
        INFO - 14:43:35:  -0.10219342]
        INFO - 14:43:35:          g_2 = -0.0004062839430756249
        INFO - 14:43:35:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
        INFO - 14:43:35:       Design space: 
        INFO - 14:43:35:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:35:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 14:43:35:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:35:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
        INFO - 14:43:35:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
        INFO - 14:43:35:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 14:43:35:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
        INFO - 14:43:35:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
        INFO - 14:43:35:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
        INFO - 14:43:35:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 14:43:35:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
        INFO - 14:43:35:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
        INFO - 14:43:35:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
        INFO - 14:43:35:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:35: *** End MDOScenario execution (time: 0:00:01.234570) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 109-114

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.OptHistoryView`
plot which plots the history of optimization for both objective function,
constraints, design parameters and distance to the optimum.

.. GENERATED FROM PYTHON SOURCE LINES 116-124

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the API function
   :meth:`~gemseo.api.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 124-127

.. 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/post_process/images/sphx_glr_plot_opt_hist_view_001.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/post_process/images/sphx_glr_plot_opt_hist_view_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/images/sphx_glr_plot_opt_hist_view_002.png
         :alt: Evolution of the objective value
         :srcset: /examples/post_process/images/sphx_glr_plot_opt_hist_view_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/images/sphx_glr_plot_opt_hist_view_003.png
         :alt: Distance to the optimum
         :srcset: /examples/post_process/images/sphx_glr_plot_opt_hist_view_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/images/sphx_glr_plot_opt_hist_view_004.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/post_process/images/sphx_glr_plot_opt_hist_view_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/images/sphx_glr_plot_opt_hist_view_005.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/post_process/images/sphx_glr_plot_opt_hist_view_005.png
         :class: sphx-glr-multi-img






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