.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/optimization_problem/plot_simple_opt_2.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_optimization_problem_plot_simple_opt_2.py>`
        to download the full example code

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

.. _sphx_glr_examples_optimization_problem_plot_simple_opt_2.py:


Analytical test case # 2
========================

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In this example, we consider a simple optimization problem to illustrate
algorithms interfaces and optimization libraries integration.

Imports
-------

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.. code-block:: Python

    from __future__ import annotations

    from numpy import cos
    from numpy import exp
    from numpy import ones
    from numpy import sin

    from gemseo import configure_logger
    from gemseo import execute_post
    from gemseo.algos.design_space import DesignSpace
    from gemseo.algos.doe.doe_factory import DOEFactory
    from gemseo.algos.opt.opt_factory import OptimizersFactory
    from gemseo.algos.opt_problem import OptimizationProblem
    from gemseo.core.mdofunctions.mdo_function import MDOFunction

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



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Define the objective function
-----------------------------
We define the objective function :math:`f(x)=\sin(x)-\exp(x)`
using an :class:`.MDOFunction` defined by the sum of :class:`.MDOFunction` objects.

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.. code-block:: Python

    f_1 = MDOFunction(sin, name="f_1", jac=cos, expr="sin(x)")
    f_2 = MDOFunction(exp, name="f_2", jac=exp, expr="exp(x)")
    objective = f_1 - f_2








.. GENERATED FROM PYTHON SOURCE LINES 57-65

.. seealso::

   The following operators are implemented: addition, subtraction and multiplication.
   The minus operator is also defined.

Define the design space
-----------------------
Then, we define the :class:`.DesignSpace` with |g|.

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.. code-block:: Python

    design_space = DesignSpace()
    design_space.add_variable("x", l_b=-2.0, u_b=2.0, value=-0.5 * ones(1))








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Define the optimization problem
-------------------------------
Then, we define the :class:`.OptimizationProblem` with |g|.

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.. code-block:: Python

    problem = OptimizationProblem(design_space)
    problem.objective = objective








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Solve the optimization problem using an optimization algorithm
--------------------------------------------------------------
Finally, we solve the optimization problems with |g| interface.

Solve the problem
^^^^^^^^^^^^^^^^^

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.. code-block:: Python

    opt = OptimizersFactory().execute(problem, "L-BFGS-B", normalize_design_space=True)
    opt





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

 .. code-block:: none

        INFO - 13:52:44: Optimization problem:
        INFO - 13:52:44:    minimize [f_1-f_2] = sin(x)-exp(x)
        INFO - 13:52:44:    with respect to x
        INFO - 13:52:44:    over the design space:
        INFO - 13:52:44:       +------+-------------+-------+-------------+-------+
        INFO - 13:52:44:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:52:44:       +------+-------------+-------+-------------+-------+
        INFO - 13:52:44:       | x    |      -2     |  -0.5 |      2      | float |
        INFO - 13:52:44:       +------+-------------+-------+-------------+-------+
        INFO - 13:52:44: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 13:52:44:      1%|          | 5/999 [00:00<00:00, 1312.28 it/sec, obj=-1.24]
        INFO - 13:52:44:      1%|          | 6/999 [00:00<00:00, 1218.15 it/sec, obj=-1.24]
        INFO - 13:52:44:      1%|          | 7/999 [00:00<00:00, 1173.84 it/sec, obj=-1.24]
        INFO - 13:52:44: Optimization result:
        INFO - 13:52:44:    Optimizer info:
        INFO - 13:52:44:       Status: 0
        INFO - 13:52:44:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
        INFO - 13:52:44:       Number of calls to the objective function by the optimizer: 8
        INFO - 13:52:44:    Solution:
        INFO - 13:52:44:       Objective: -1.2361083418592416
        INFO - 13:52:44:       Design space:
        INFO - 13:52:44:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:52:44:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 13:52:44:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:52:44:          | x    |      -2     | -1.292695718944152 |      2      | float |
        INFO - 13:52:44:          +------+-------------+--------------------+-------------+-------+


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>Optimization result:<br/><ul><li>Design variables: [-1.29269572]</li><li>Objective function: -1.2361083418592416</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />

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Note that you can get all the optimization algorithms names:

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.. code-block:: Python

    OptimizersFactory().algorithms





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

 .. code-block:: none


    ['Augmented_Lagrangian_order_0', 'Augmented_Lagrangian_order_1', 'MMA', 'MNBI', 'NLOPT_MMA', 'NLOPT_COBYLA', 'NLOPT_SLSQP', 'NLOPT_BOBYQA', 'NLOPT_BFGS', 'NLOPT_NEWUOA', 'PDFO_COBYLA', 'PDFO_BOBYQA', 'PDFO_NEWUOA', 'PSEVEN', 'PSEVEN_FD', 'PSEVEN_MOM', 'PSEVEN_NCG', 'PSEVEN_NLS', 'PSEVEN_POWELL', 'PSEVEN_QP', 'PSEVEN_SQP', 'PSEVEN_SQ2P', 'PYMOO_GA', 'PYMOO_NSGA2', 'PYMOO_NSGA3', 'PYMOO_UNSGA3', 'PYMOO_RNSGA3', 'DUAL_ANNEALING', 'SHGO', 'DIFFERENTIAL_EVOLUTION', 'LINEAR_INTERIOR_POINT', 'REVISED_SIMPLEX', 'SIMPLEX', 'HIGHS_INTERIOR_POINT', 'HIGHS_DUAL_SIMPLEX', 'HIGHS', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'NELDER-MEAD']



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Save the optimization results
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
We can serialize the results for further exploitation.

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.. code-block:: Python

    problem.to_hdf("my_optim.hdf5")





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

 .. code-block:: none

        INFO - 13:52:44: Exporting the optimization problem to the file my_optim.hdf5 at node 




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Post-process the results
^^^^^^^^^^^^^^^^^^^^^^^^

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.. code-block:: Python

    execute_post(problem, "OptHistoryView", show=True, save=False)




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


    *

      .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_001.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_002.png
         :alt: Evolution of the objective value
         :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_003.png
         :alt: Distance to the optimum
         :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_004.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_004.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f2d62bb0ac0>



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.. note::

   We can also save this plot using the arguments ``save=False``
   and ``file_path='file_path'``.

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Solve the optimization problem using a DOE algorithm
----------------------------------------------------
We can also see this optimization problem as a trade-off
and solve it by means of a design of experiments (DOE).

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.. code-block:: Python

    opt = DOEFactory().execute(problem, "lhs", n_samples=10, normalize_design_space=True)
    opt




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

 .. code-block:: none

        INFO - 13:52:45: Optimization problem:
        INFO - 13:52:45:    minimize [f_1-f_2] = sin(x)-exp(x)
        INFO - 13:52:45:    with respect to x
        INFO - 13:52:45:    over the design space:
        INFO - 13:52:45:       +------+-------------+--------------------+-------------+-------+
        INFO - 13:52:45:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 13:52:45:       +------+-------------+--------------------+-------------+-------+
        INFO - 13:52:45:       | x    |      -2     | -1.292695718944152 |      2      | float |
        INFO - 13:52:45:       +------+-------------+--------------------+-------------+-------+
        INFO - 13:52:45: Solving optimization problem with algorithm lhs:
        INFO - 13:52:45:     10%|█         | 1/10 [00:00<00:00, 2718.28 it/sec, obj=-5.17]
        INFO - 13:52:45:     20%|██        | 2/10 [00:00<00:00, 2427.26 it/sec, obj=-1.15]
        INFO - 13:52:45:     30%|███       | 3/10 [00:00<00:00, 2495.62 it/sec, obj=-1.24]
        INFO - 13:52:45:     40%|████      | 4/10 [00:00<00:00, 2547.41 it/sec, obj=-1.13]
        INFO - 13:52:45:     50%|█████     | 5/10 [00:00<00:00, 2585.25 it/sec, obj=-2.91]
        INFO - 13:52:45:     60%|██████    | 6/10 [00:00<00:00, 2615.72 it/sec, obj=-1.75]
        INFO - 13:52:45:     70%|███████   | 7/10 [00:00<00:00, 2597.32 it/sec, obj=-1.14]
        INFO - 13:52:45:     80%|████████  | 8/10 [00:00<00:00, 2600.31 it/sec, obj=-1.05]
        INFO - 13:52:45:     90%|█████████ | 9/10 [00:00<00:00, 2616.90 it/sec, obj=-1.23]
        INFO - 13:52:45:    100%|██████████| 10/10 [00:00<00:00, 2632.13 it/sec, obj=-1]
        INFO - 13:52:45: Optimization result:
        INFO - 13:52:45:    Optimizer info:
        INFO - 13:52:45:       Status: None
        INFO - 13:52:45:       Message: None
        INFO - 13:52:45:       Number of calls to the objective function by the optimizer: 18
        INFO - 13:52:45:    Solution:
        INFO - 13:52:45:       Objective: -5.174108803965849
        INFO - 13:52:45:       Design space:
        INFO - 13:52:45:          +------+-------------+-------------------+-------------+-------+
        INFO - 13:52:45:          | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 13:52:45:          +------+-------------+-------------------+-------------+-------+
        INFO - 13:52:45:          | x    |      -2     | 1.815526693601343 |      2      | float |
        INFO - 13:52:45:          +------+-------------+-------------------+-------------+-------+


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>Optimization result:<br/><ul><li>Design variables: [1.81552669]</li><li>Objective function: -5.174108803965849</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />


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   **Total running time of the script:** (0 minutes 1.041 seconds)


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