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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/scenario/plot_doe_scenario.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
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        Click :ref:`here <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
=====================

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.. code-block:: default

    from __future__ import annotations

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

    configure_logger()






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 .. code-block:: none


    <RootLogger root (INFO)>



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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 :meth:`~gemseo.api.create_discipline` API function,
we create an :class:`.MDODiscipline` of :class:`.AnalyticDiscipline` type
from a Python function:

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.. code-block:: default


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








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

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

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.. code-block:: default


    design_space = create_design_space()
    design_space.add_variable("x1", 1, l_b=-5, u_b=5, var_type="integer")
    design_space.add_variable("x2", 1, l_b=-5, u_b=5, var_type="integer")








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

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.. code-block:: default


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








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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`:

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.. code-block:: default


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





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 .. code-block:: none

        INFO - 14:46:11:  
        INFO - 14:46:11: *** Start DOEScenario execution ***
        INFO - 14:46:11: DOEScenario
        INFO - 14:46:11:    Disciplines: AnalyticDiscipline
        INFO - 14:46:11:    MDO formulation: DisciplinaryOpt
        INFO - 14:46:11: Optimization problem:
        INFO - 14:46:11:    minimize y(x1, x2)
        INFO - 14:46:11:    with respect to x1, x2
        INFO - 14:46:11:    over the design space:
        INFO - 14:46:11:    +------+-------------+-------+-------------+---------+
        INFO - 14:46:11:    | name | lower_bound | value | upper_bound | type    |
        INFO - 14:46:11:    +------+-------------+-------+-------------+---------+
        INFO - 14:46:11:    | x1   |      -5     |  None |      5      | integer |
        INFO - 14:46:11:    | x2   |      -5     |  None |      5      | integer |
        INFO - 14:46:11:    +------+-------------+-------+-------------+---------+
        INFO - 14:46:11: Solving optimization problem with algorithm fullfact:
        INFO - 14:46:11: ...   0%|          | 0/121 [00:00<?, ?it]
        INFO - 14:46:11: ... 100%|██████████| 121/121 [00:00<00:00, 3063.90 it/sec, obj=10]
        INFO - 14:46:11: Optimization result:
        INFO - 14:46:11:    Optimizer info:
        INFO - 14:46:11:       Status: None
        INFO - 14:46:11:       Message: None
        INFO - 14:46:11:       Number of calls to the objective function by the optimizer: 121
        INFO - 14:46:11:    Solution:
        INFO - 14:46:11:       Objective: -10.0
        INFO - 14:46:11:       Design space: 
        INFO - 14:46:11:       +------+-------------+-------+-------------+---------+
        INFO - 14:46:11:       | name | lower_bound | value | upper_bound | type    |
        INFO - 14:46:11:       +------+-------------+-------+-------------+---------+
        INFO - 14:46:11:       | x1   |      -5     |   -5  |      5      | integer |
        INFO - 14:46:11:       | x2   |      -5     |   -5  |      5      | integer |
        INFO - 14:46:11:       +------+-------------+-------+-------------+---------+
        INFO - 14:46:11: *** End DOEScenario execution (time: 0:00:00.048401) ***

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



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The optimum results can be found in the execution log. It is also possible to
extract them by invoking the :meth:`.Scenario.get_optimum` method. It
returns a dictionary containing the optimum results for the
scenario under consideration:

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.. code-block:: default


    opt_results = scenario.get_optimum()
    print(
        "The solution of P is (x*,f(x*)) = ({}, {})".format(
            opt_results.x_opt, opt_results.f_opt
        ),
    )





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

 .. code-block:: none

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




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

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.. code-block:: default


    algo_list = get_available_doe_algorithms()
    print(f"Available algorithms: {algo_list}")





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 .. code-block:: none

    Available algorithms: ['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']




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

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.. code-block:: default


    post_list = get_available_post_processings()
    print(f"Available algorithms: {post_list}")





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

 .. code-block:: none

    Available algorithms: ['BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', 'GradientSensitivity', 'HighTradeOff', 'KMeans', 'MultiObjectiveDiagram', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'Petal', 'QuadApprox', 'Radar', 'RadarChart', 'Robustness', 'SOM', 'ScatterPareto', 'ScatterPlotMatrix', 'VariableInfluence']




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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>


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   **Total running time of the script:** ( 0 minutes  0.065 seconds)


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

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