.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/scenario/plot_mdo_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_mdo_scenario.py>`
        to download the full example code.

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

.. _sphx_glr_examples_scenario_plot_mdo_scenario.py:


Create an MDO Scenario
======================

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.. code-block:: Python


    from __future__ import annotations

    from numpy import ones

    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_opt_algorithms
    from gemseo 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}{\text{minimize}}
    & & f(x) = \sin(x) - \exp(x) \\
    & \text{subject to}
    & & -2 \leq x \leq 2
  \end{aligned}
  \right.

In this subsection, we will see how to use |g| to solve this problem
:math:`(P)` by means of an optimization algorithm.

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

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.. code-block:: Python


    expressions = {"y": "sin(x)-exp(x)"}
    discipline = create_discipline("AnalyticDiscipline", expressions=expressions)








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We can quickly access the most relevant information of any discipline (name, inputs,
and outputs) with their string representations. Moreover, we can get the default
input values of a discipline with the attribute :attr:`.Discipline.default_input_data`

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.. code-block:: Python

    discipline, discipline.default_input_data





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 .. code-block:: none


    (AnalyticDiscipline
       Inputs: x
       Outputs: y, {'x': array([0.])})



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Now, we can minimize an output of this :class:`.Discipline` over a design space,
by means of a quasi-Newton method from the initial point :math:`0.5`.

Define the design space
-----------------------
For that, by means of the high-level function :func:`.create_design_space`,
we define the :class:`.DesignSpace` :math:`[-2, 2]` with initial value :math:`0.5`
by using its :meth:`.DesignSpace.add_variable` method.

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.. code-block:: Python


    design_space = create_design_space()
    design_space.add_variable("x", lower_bound=-2.0, upper_bound=2.0, value=-0.5 * ones(1))








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Define the MDO scenario
-----------------------
Then, by means of the :func:`.create_scenario` API function,
we define an :class:`.MDOScenario` from the :class:`.Discipline`
and the :class:`.DesignSpace` defined above:

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.. code-block:: Python


    scenario = create_scenario(
        discipline, "y", design_space, formulation_name="DisciplinaryOpt"
    )








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What about the differentiation method?
--------------------------------------
The :class:`.AnalyticDiscipline` automatically differentiates the
expressions to obtain the Jacobian matrices. Therefore, there is no need to
define a differentiation method in this case. Keep in mind that for a
generic discipline with no defined Jacobian function, you can use the
:meth:`.Scenario.set_differentiation_method` method to define a numerical
approximation of the gradients.

.. code::

   scenario.set_differentiation_method("finite_differences")

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Execute the MDO scenario
------------------------
Lastly, we solve the :class:`.OptimizationProblem` included in the
:class:`.MDOScenario` defined above by minimizing the objective function over
the :class:`.DesignSpace`. Precisely, we choose the `L-BFGS-B algorithm
<https://en.wikipedia.org/wiki/Limited-memory_BFGS>`_ implemented in the
function ``scipy.optimize.fmin_l_bfgs_b``.

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.. code-block:: Python


    scenario.execute(algo_name="L-BFGS-B", max_iter=100)





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 .. code-block:: none

        INFO - 08:36:18:  
        INFO - 08:36:18: *** Start MDOScenario execution ***
        INFO - 08:36:18: MDOScenario
        INFO - 08:36:18:    Disciplines: AnalyticDiscipline
        INFO - 08:36:18:    MDO formulation: DisciplinaryOpt
        INFO - 08:36:18: Optimization problem:
        INFO - 08:36:18:    minimize y(x)
        INFO - 08:36:18:    with respect to x
        INFO - 08:36:18:    over the design space:
        INFO - 08:36:18:       +------+-------------+-------+-------------+-------+
        INFO - 08:36:18:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:36:18:       +------+-------------+-------+-------------+-------+
        INFO - 08:36:18:       | x    |      -2     |  -0.5 |      2      | float |
        INFO - 08:36:18:       +------+-------------+-------+-------------+-------+
        INFO - 08:36:18: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 08:36:18:      1%|          | 1/100 [00:00<00:00, 388.94 it/sec, obj=-1.09]
        INFO - 08:36:18:      2%|▏         | 2/100 [00:00<00:00, 477.00 it/sec, obj=-1.04]
        INFO - 08:36:18:      3%|▎         | 3/100 [00:00<00:00, 573.31 it/sec, obj=-1.24]
        INFO - 08:36:18:      4%|▍         | 4/100 [00:00<00:00, 597.59 it/sec, obj=-1.23]
        INFO - 08:36:18:      5%|▌         | 5/100 [00:00<00:00, 617.01 it/sec, obj=-1.24]
        INFO - 08:36:18:      6%|▌         | 6/100 [00:00<00:00, 609.90 it/sec, obj=-1.24]
        INFO - 08:36:18:      7%|▋         | 7/100 [00:00<00:00, 621.67 it/sec, obj=-1.24]
        INFO - 08:36:18: Optimization result:
        INFO - 08:36:18:    Optimizer info:
        INFO - 08:36:18:       Status: 0
        INFO - 08:36:18:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
        INFO - 08:36:18:       Number of calls to the objective function by the optimizer: 8
        INFO - 08:36:18:    Solution:
        INFO - 08:36:18:       Objective: -1.2361083418592416
        INFO - 08:36:18:       Design space:
        INFO - 08:36:18:          +------+-------------+--------------------+-------------+-------+
        INFO - 08:36:18:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 08:36:18:          +------+-------------+--------------------+-------------+-------+
        INFO - 08:36:18:          | x    |      -2     | -1.292695718944152 |      2      | float |
        INFO - 08:36:18:          +------+-------------+--------------------+-------------+-------+
        INFO - 08:36:18: *** End MDOScenario execution (time: 0:00:00.015763) ***




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

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.. 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})"





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 .. code-block:: none


    'The solution of P is (x*, f(x*)) = ([-1.29269572], -1.2361083418592416)'



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.. seealso::

   You can find the `SciPy <https://scipy.org/>`_ implementation of the
   `L-BFGS-B algorithm <https://en.wikipedia.org/wiki/Limited-memory_BFGS>`_
   algorithm `by clicking here
   <https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.fmin_l_bfgs_b.html>`_.

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

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.. code-block:: Python

    get_available_opt_algorithms()





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 .. code-block:: none


    ['Augmented_Lagrangian_order_0', 'Augmented_Lagrangian_order_1', 'MNBI', 'MultiStart', 'NLOPT_MMA', 'NLOPT_COBYLA', 'NLOPT_SLSQP', 'NLOPT_BOBYQA', 'NLOPT_BFGS', 'NLOPT_NEWUOA', 'DUAL_ANNEALING', 'SHGO', 'DIFFERENTIAL_EVOLUTION', 'INTERIOR_POINT', 'DUAL_SIMPLEX', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'NELDER-MEAD']



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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:: Python

    get_available_post_processings()





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

 .. code-block:: none


    ['Animation', 'BasicHistory', 'ConstraintsHistory', 'Correlations', 'GradientSensitivity', 'HessianHistory', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'QuadApprox', 'RadarChart', 'Robustness', 'SOM', 'ScatterPlotMatrix', 'TopologyView', 'VariableInfluence']



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Exporting the problem data.
---------------------------
After the execution of the scenario, you may want to export your data to use it
elsewhere. The :meth:`.Scenario.to_dataset` will allow you to export your
results to a :class:`.Dataset`, the basic |g| class to store data.

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.. code-block:: Python

    dataset = scenario.to_dataset("a_name_for_my_dataset")








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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>


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

   **Total running time of the script:** (0 minutes 0.038 seconds)


.. _sphx_glr_download_examples_scenario_plot_mdo_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_mdo_scenario.ipynb <plot_mdo_scenario.ipynb>`

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_mdo_scenario.zip <plot_mdo_scenario.zip>`


.. only:: html

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