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.. 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

        Click :ref:`here <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:: default

    from __future__ import annotations

    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.api import configure_logger
    from gemseo.api import execute_post
    from gemseo.core.mdofunctions.mdo_function import MDOFunction
    from matplotlib import pyplot as plt
    from numpy import cos
    from numpy import exp
    from numpy import ones
    from numpy import sin

    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 a :class:`.MDOFunction` defined by the sum of :class:`.MDOFunction` objects.

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.. code-block:: default

    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 56-64

.. 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:: default

    design_space = DesignSpace()
    design_space.add_variable("x", 1, 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:: default

    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:: default

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

    print("Optimum = ", opt)





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

 .. code-block:: none

        INFO - 14:47:12: Optimization problem:
        INFO - 14:47:12:    minimize f_1-f_2 = sin(x)-exp(x)
        INFO - 14:47:12:    with respect to x
        INFO - 14:47:12:    over the design space:
        INFO - 14:47:12:    +------+-------------+-------+-------------+-------+
        INFO - 14:47:12:    | name | lower_bound | value | upper_bound | type  |
        INFO - 14:47:12:    +------+-------------+-------+-------------+-------+
        INFO - 14:47:12:    | x    |      -2     |  -0.5 |      2      | float |
        INFO - 14:47:12:    +------+-------------+-------+-------------+-------+
        INFO - 14:47:12: Solving optimization problem with algorithm L-BFGS-B:
        INFO - 14:47:12: ...   0%|          | 0/999 [00:00<?, ?it]
        INFO - 14:47:12: ...   1%|          | 7/999 [00:00<00:00, 150853.60 it/sec, obj=[-1.23610834]]
        INFO - 14:47:12: Optimization result:
        INFO - 14:47:12:    Optimizer info:
        INFO - 14:47:12:       Status: 0
        INFO - 14:47:12:       Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
        INFO - 14:47:12:       Number of calls to the objective function by the optimizer: 8
        INFO - 14:47:12:    Solution:
        INFO - 14:47:12:       Objective: [-1.23610834]
        INFO - 14:47:12:       Design space: 
        INFO - 14:47:12:       +------+-------------+--------------------+-------------+-------+
        INFO - 14:47:12:       | name | lower_bound |       value        | upper_bound | type  |
        INFO - 14:47:12:       +------+-------------+--------------------+-------------+-------+
        INFO - 14:47:12:       | x    |      -2     | -1.292695718944152 |      2      | float |
        INFO - 14:47:12:       +------+-------------+--------------------+-------------+-------+
    Optimum =  Optimization result:
       Optimizer info:
          Status: 0
          Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
          Number of calls to the objective function by the optimizer: 8
       Solution:
          Objective: [-1.23610834]




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Note that you can get all the optimization algorithms names:

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.. code-block:: default

    algo_list = OptimizersFactory().algorithms
    print("Available algorithms ", algo_list)





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

 .. code-block:: none

    Available algorithms  ['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', 'SLSQP', 'L-BFGS-B', 'TNC', 'SNOPTB']




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

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.. code-block:: default

    problem.export_hdf("my_optim.hdf5")





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

 .. code-block:: none

        INFO - 14:47:12: Export optimization problem to file: my_optim.hdf5




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

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.. code-block:: default

    execute_post(problem, "OptHistoryView", show=False, save=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()




.. 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


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

 .. code-block:: none

     WARNING - 14:47:12: Failed to create Hessian approximation.
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.1.0/lib/python3.9/site-packages/gemseo/post/opt_history_view.py", line 625, in _create_hessian_approx_plot
        _, diag, _, _ = approximator.build_approximation(
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.1.0/lib/python3.9/site-packages/gemseo/post/core/hessians.py", line 382, in build_approximation
        x_hist, grad_hist, _, _ = self.get_x_grad_history(
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.1.0/lib/python3.9/site-packages/gemseo/post/core/hessians.py", line 185, in get_x_grad_history
        raise ValueError(
    ValueError: Inconsistent gradient and design variables optimization history.




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.. note::

   We can also save this plot using the arguments :code:`save=False`
   and :code:`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:: default

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




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

 .. code-block:: none

     WARNING - 14:47:13: Driver lhs has no option normalize_design_space, option is ignored.
        INFO - 14:47:13: Optimization problem:
        INFO - 14:47:13:    minimize f_1-f_2 = sin(x)-exp(x)
        INFO - 14:47:13:    with respect to x
        INFO - 14:47:13:    over the design space:
        INFO - 14:47:13:    +------+-------------+--------------------+-------------+-------+
        INFO - 14:47:13:    | name | lower_bound |       value        | upper_bound | type  |
        INFO - 14:47:13:    +------+-------------+--------------------+-------------+-------+
        INFO - 14:47:13:    | x    |      -2     | -1.292695718944152 |      2      | float |
        INFO - 14:47:13:    +------+-------------+--------------------+-------------+-------+
        INFO - 14:47:13: Solving optimization problem with algorithm lhs:
        INFO - 14:47:13: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:47:13: ... 100%|██████████| 10/10 [00:00<00:00, 3334.64 it/sec, obj=[-1.00069899]]
        INFO - 14:47:13: Optimization result:
        INFO - 14:47:13:    Optimizer info:
        INFO - 14:47:13:       Status: None
        INFO - 14:47:13:       Message: None
        INFO - 14:47:13:       Number of calls to the objective function by the optimizer: 18
        INFO - 14:47:13:    Solution:
        INFO - 14:47:13:       Objective: [-5.1741088]
        INFO - 14:47:13:       Design space: 
        INFO - 14:47:13:       +------+-------------+-------------------+-------------+-------+
        INFO - 14:47:13:       | name | lower_bound |       value       | upper_bound | type  |
        INFO - 14:47:13:       +------+-------------+-------------------+-------------+-------+
        INFO - 14:47:13:       | x    |      -2     | 1.815526693601343 |      2      | float |
        INFO - 14:47:13:       +------+-------------+-------------------+-------------+-------+
    Optimum =  Optimization result:
       Optimizer info:
          Status: None
          Message: None
          Number of calls to the objective function by the optimizer: 18
       Solution:
          Objective: [-5.1741088]





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   **Total running time of the script:** ( 0 minutes  0.770 seconds)


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