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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_scenario_plot_doe_scenario.py>`
        to download the full example code

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

.. _sphx_glr_examples_scenario_plot_doe_scenario.py:


Create a DOE Scenario
=====================

.. GENERATED FROM PYTHON SOURCE LINES 26-39

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import get_available_doe_algorithms
    from gemseo import get_available_post_processings

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 40-61

Let :math:`(P)` be a simple optimization problem:

.. math::

   (P) = \left\{
   \begin{aligned}
     & \underset{x\in\mathbb{N}^2}{\text{minimize}}
     & & f(x) = x_1 + x_2 \\
     & \text{subject to}
     & & -5 \leq x \leq 5
   \end{aligned}
   \right.

In this example, we will see how to use |g|
to solve this problem :math:`(P)` by means of a Design Of Experiments (DOE)

Define the discipline
---------------------
Firstly, by means of the :func:`.create_discipline` API function,
we create an :class:`.MDODiscipline` of :class:`.AnalyticDiscipline` type
from a Python function:

.. GENERATED FROM PYTHON SOURCE LINES 62-66

.. code-block:: Python


    expressions = {"y": "x1+x2"}
    discipline = create_discipline("AnalyticDiscipline", expressions=expressions)








.. GENERATED FROM PYTHON SOURCE LINES 67-75

Now, we want to minimize this :class:`.MDODiscipline`
over a design of experiments (DOE).

Define the design space
-----------------------
For that, by means of the :func:`.create_design_space` API function,
we define the :class:`.DesignSpace` :math:`[-5, 5]\times[-5, 5]`
by using its :meth:`.DesignSpace.add_variable` method.

.. GENERATED FROM PYTHON SOURCE LINES 75-80

.. code-block:: Python


    design_space = create_design_space()
    design_space.add_variable("x1", l_b=-5, u_b=5, var_type="integer")
    design_space.add_variable("x2", l_b=-5, u_b=5, var_type="integer")








.. GENERATED FROM PYTHON SOURCE LINES 81-86

Define the DOE scenario
-----------------------
Then, by means of the :func:`.create_scenario` API function,
we define a :class:`.DOEScenario` from the :class:`.MDODiscipline`
and the :class:`.DesignSpace` defined above:

.. GENERATED FROM PYTHON SOURCE LINES 86-91

.. code-block:: Python


    scenario = create_scenario(
        discipline, "DisciplinaryOpt", "y", design_space, scenario_type="DOE"
    )








.. GENERATED FROM PYTHON SOURCE LINES 92-99

Execute the DOE scenario
------------------------
Lastly, we solve the :class:`.OptimizationProblem` included in the
:class:`.DOEScenario` defined above by minimizing the objective function
over a design of experiments included in the :class:`.DesignSpace`.
Precisely, we choose a `full factorial design
<https://en.wikipedia.org/wiki/Factorial_experiment>`_ of size :math:`11^2`:

.. GENERATED FROM PYTHON SOURCE LINES 99-102

.. code-block:: Python


    scenario.execute({"algo": "fullfact", "n_samples": 11**2})





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

 .. code-block:: none

        INFO - 13:54:39:  
        INFO - 13:54:39: *** Start DOEScenario execution ***
        INFO - 13:54:39: DOEScenario
        INFO - 13:54:39:    Disciplines: AnalyticDiscipline
        INFO - 13:54:39:    MDO formulation: DisciplinaryOpt
        INFO - 13:54:39: Optimization problem:
        INFO - 13:54:39:    minimize y(x1, x2)
        INFO - 13:54:39:    with respect to x1, x2
        INFO - 13:54:39:    over the design space:
        INFO - 13:54:39:       +------+-------------+-------+-------------+---------+
        INFO - 13:54:39:       | Name | Lower bound | Value | Upper bound | Type    |
        INFO - 13:54:39:       +------+-------------+-------+-------------+---------+
        INFO - 13:54:39:       | x1   |      -5     |  None |      5      | integer |
        INFO - 13:54:39:       | x2   |      -5     |  None |      5      | integer |
        INFO - 13:54:39:       +------+-------------+-------+-------------+---------+
        INFO - 13:54:39: Solving optimization problem with algorithm fullfact:
        INFO - 13:54:39:      1%|          | 1/121 [00:00<00:00, 403.45 it/sec, obj=-10]
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        INFO - 13:54:39:    100%|██████████| 121/121 [00:00<00:00, 1608.63 it/sec, obj=10]
        INFO - 13:54:39: Optimization result:
        INFO - 13:54:39:    Optimizer info:
        INFO - 13:54:39:       Status: None
        INFO - 13:54:39:       Message: None
        INFO - 13:54:39:       Number of calls to the objective function by the optimizer: 121
        INFO - 13:54:39:    Solution:
        INFO - 13:54:39:       Objective: -10.0
        INFO - 13:54:39:       Design space:
        INFO - 13:54:39:          +------+-------------+-------+-------------+---------+
        INFO - 13:54:39:          | Name | Lower bound | Value | Upper bound | Type    |
        INFO - 13:54:39:          +------+-------------+-------+-------------+---------+
        INFO - 13:54:39:          | x1   |      -5     |   -5  |      5      | integer |
        INFO - 13:54:39:          | x2   |      -5     |   -5  |      5      | integer |
        INFO - 13:54:39:          +------+-------------+-------+-------------+---------+
        INFO - 13:54:39: *** End DOEScenario execution (time: 0:00:00.087691) ***

    {'eval_jac': False, 'n_samples': 121, 'algo': 'fullfact'}



.. GENERATED FROM PYTHON SOURCE LINES 103-105

The optimum results can be found in the execution log. It is also possible to
access them with :attr:`.Scenario.optimization_result`:

.. GENERATED FROM PYTHON SOURCE LINES 105-109

.. code-block:: Python


    optimization_result = scenario.optimization_result
    f"The solution of P is (x*, f(x*)) = ({optimization_result.x_opt}, {optimization_result.f_opt})"





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

 .. code-block:: none


    'The solution of P is (x*, f(x*)) = ([-5. -5.], -10.0)'



.. GENERATED FROM PYTHON SOURCE LINES 110-113

Available DOE algorithms
------------------------
In order to get the list of available DOE algorithms, use:

.. GENERATED FROM PYTHON SOURCE LINES 113-115

.. code-block:: Python

    get_available_doe_algorithms()





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

 .. code-block:: none


    ['CustomDOE', 'DiagonalDOE', 'OT_SOBOL', 'OT_RANDOM', 'OT_HASELGROVE', 'OT_REVERSE_HALTON', 'OT_HALTON', 'OT_FAURE', 'OT_MONTE_CARLO', 'OT_FACTORIAL', 'OT_COMPOSITE', 'OT_AXIAL', 'OT_OPT_LHS', 'OT_LHS', 'OT_LHSC', 'OT_FULLFACT', 'OT_SOBOL_INDICES', 'fullfact', 'ff2n', 'pbdesign', 'bbdesign', 'ccdesign', 'lhs', 'Halton', 'LHS', 'MC', 'PoissonDisk', 'Sobol']



.. GENERATED FROM PYTHON SOURCE LINES 116-119

Available post-processing
-------------------------
In order to get the list of available post-processing algorithms, use:

.. GENERATED FROM PYTHON SOURCE LINES 119-121

.. code-block:: Python

    get_available_post_processings()





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

 .. code-block:: none


    ['Animation', 'BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', 'DataVersusModel', 'GradientSensitivity', 'HighTradeOff', 'MultiObjectiveDiagram', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'Petal', 'QuadApprox', 'Radar', 'RadarChart', 'Robustness', 'SOM', 'ScatterPareto', 'ScatterPlotMatrix', 'TopologyView', 'VariableInfluence']



.. GENERATED FROM PYTHON SOURCE LINES 122-128

You can also look at the examples:

.. raw:: html

   <div style="text-align: center;"><a class="btn gemseo-btn mb-1"
   href="../post_process/index.html" role="button">Examples</a></div>


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

   **Total running time of the script:** (0 minutes 0.101 seconds)


.. _sphx_glr_download_examples_scenario_plot_doe_scenario.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_doe_scenario.py <plot_doe_scenario.py>`


.. only:: html

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

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