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.. only:: html

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

.. _sphx_glr_examples_post_process_algorithms_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:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo.problems.sobieski.core.design_space import SobieskiDesignSpace








.. 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 41-43

.. code-block:: Python


    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 73-80

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 81-84

Create design space
-------------------
We also create the :class:`.SobieskiDesignSpace`.

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: Python

    design_space = SobieskiDesignSpace()








.. GENERATED FROM PYTHON SOURCE LINES 87-94

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 94-106

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "MDF",
        "y_4",
        design_space,
        maximize_objective=True,
    )
    scenario.set_differentiation_method()
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, constraint_type="ineq")
    scenario.execute({"algo": "SLSQP", "max_iter": 100})





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

 .. code-block:: none

        INFO - 13:57:12:  
        INFO - 13:57:12: *** Start MDOScenario execution ***
        INFO - 13:57:12: MDOScenario
        INFO - 13:57:12:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 13:57:12:    MDO formulation: MDF
        INFO - 13:57:12: Optimization problem:
        INFO - 13:57:12:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 13:57:12:    with respect to x_1, x_2, x_3, x_shared
        INFO - 13:57:12:    subject to constraints:
        INFO - 13:57:12:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 13:57:12:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 13:57:12:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 13:57:12:    over the design space:
        INFO - 13:57:12:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:57:12:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 13:57:12:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:57:12:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 13:57:12:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 13:57:12:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 13:57:12:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 13:57:12:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 13:57:12:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 13:57:12:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 13:57:12:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 13:57:12:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 13:57:12:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 13:57:12:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:57:12: Solving optimization problem with algorithm SLSQP:
        INFO - 13:57:12:      1%|          | 1/100 [00:00<00:09, 10.44 it/sec, obj=-536]
        INFO - 13:57:12:      2%|▏         | 2/100 [00:00<00:13,  7.19 it/sec, obj=-2.12e+3]
     WARNING - 13:57:12: MDAJacobi has reached its maximum number of iterations but the normed residual 1.7130677857005655e-05 is still above the tolerance 1e-06.
        INFO - 13:57:12:      3%|▎         | 3/100 [00:00<00:15,  6.10 it/sec, obj=-3.75e+3]
        INFO - 13:57:12:      4%|▍         | 4/100 [00:00<00:16,  5.86 it/sec, obj=-3.96e+3]
        INFO - 13:57:12:      5%|▌         | 5/100 [00:00<00:16,  5.71 it/sec, obj=-3.96e+3]
        INFO - 13:57:13: Optimization result:
        INFO - 13:57:13:    Optimizer info:
        INFO - 13:57:13:       Status: 8
        INFO - 13:57:13:       Message: Positive directional derivative for linesearch
        INFO - 13:57:13:       Number of calls to the objective function by the optimizer: 6
        INFO - 13:57:13:    Solution:
        INFO - 13:57:13:       The solution is feasible.
        INFO - 13:57:13:       Objective: -3963.408265187933
        INFO - 13:57:13:       Standardized constraints:
        INFO - 13:57:13:          g_1 = [-0.01806104 -0.03334642 -0.04424946 -0.0518346  -0.05732607 -0.13720865
        INFO - 13:57:13:  -0.10279135]
        INFO - 13:57:13:          g_2 = 3.333278582928756e-06
        INFO - 13:57:13:          g_3 = [-7.67181773e-01 -2.32818227e-01  8.30379541e-07 -1.83255000e-01]
        INFO - 13:57:13:       Design space:
        INFO - 13:57:13:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 13:57:13:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:57:13:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 13:57:13:          | x_shared[0] |     0.01    | 0.06000083331964572 |     0.09    | float |
        INFO - 13:57:13:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 13:57:13:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 13:57:13:          | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 13:57:13:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 13:57:13:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 13:57:13:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 13:57:13:          | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
        INFO - 13:57:13:          | x_2         |     0.75    |         0.75        |     1.25    | float |
        INFO - 13:57:13:          | x_3         |     0.1     |  0.1562448753887276 |      1      | float |
        INFO - 13:57:13:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 13:57:13: *** End MDOScenario execution (time: 0:00:01.000171) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 107-112

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 114-122

.. 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 122-125

.. code-block:: Python

    scenario.post_process(
        "OptHistoryView", save=False, show=True, variable_names=["x_2", "x_1"]
    )



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


    *

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

    *

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

    *

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

    *

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

    *

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


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f2d10bb8dc0>




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

   **Total running time of the script:** (0 minutes 2.132 seconds)


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