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.. "examples/optimization_problem/plot_simple_opt_3.py"
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.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_optimization_problem_plot_simple_opt_3.py>`
        to download the full example code

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

.. _sphx_glr_examples_optimization_problem_plot_simple_opt_3.py:


Analytical test case # 3
========================

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In this example, we consider a simple optimization problem to illustrate
algorithms interfaces and DOE libraries integration.
Integer variables are used

Imports
-------

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.. code-block:: default

    from gemseo.algos.design_space import DesignSpace
    from gemseo.algos.doe.doe_factory import DOEFactory
    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 sum as np_sum

    LOGGER = configure_logger()









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Define the objective function
-----------------------------
We define the objective function :math:`f(x)=\sum_{i=1}^dx_i`
using a :class:`.MDOFunction`.

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.. code-block:: default

    objective = MDOFunction(np_sum, name="f", expr="sum(x)")








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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", 2, l_b=-5, u_b=5, var_type="integer")








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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 a DOE algorithm
----------------------------------------------------
We can see this optimization problem as a trade-off
and solve it by means of a design of experiments (DOE),
e.g. full factorial design

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.. code-block:: default

    DOEFactory().execute(problem, "fullfact", n_samples=11**2)





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

 Out:

 .. code-block:: none

        INFO - 10:06:11: Optimization problem:
        INFO - 10:06:11:    minimize f = sum(x)
        INFO - 10:06:11:    with respect to x
        INFO - 10:06:11:    over the design space:
        INFO - 10:06:11:    +------+-------------+-------+-------------+---------+
        INFO - 10:06:11:    | name | lower_bound | value | upper_bound | type    |
        INFO - 10:06:11:    +------+-------------+-------+-------------+---------+
        INFO - 10:06:11:    | x    |      -5     |  None |      5      | integer |
        INFO - 10:06:11:    | x    |      -5     |  None |      5      | integer |
        INFO - 10:06:11:    +------+-------------+-------+-------------+---------+
        INFO - 10:06:11: Solving optimization problem with algorithm fullfact:
        INFO - 10:06:11: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 121 samples: 11
        INFO - 10:06:11: Final number of samples for DOE = 121 vs 121 requested
        INFO - 10:06:11: ...   0%|          | 0/121 [00:00<?, ?it]
        INFO - 10:06:11: ... 100%|██████████| 121/121 [00:00<00:00, 10772.66 it/sec, obj=10]
        INFO - 10:06:11: Optimization result:
        INFO - 10:06:11:    Optimizer info:
        INFO - 10:06:11:       Status: None
        INFO - 10:06:11:       Message: None
        INFO - 10:06:11:       Number of calls to the objective function by the optimizer: 121
        INFO - 10:06:11:    Solution:
        INFO - 10:06:11:       Objective: -10.0
        INFO - 10:06:11:       Design space:
        INFO - 10:06:11:       +------+-------------+-------+-------------+---------+
        INFO - 10:06:11:       | name | lower_bound | value | upper_bound | type    |
        INFO - 10:06:11:       +------+-------------+-------+-------------+---------+
        INFO - 10:06:11:       | x    |      -5     |   -5  |      5      | integer |
        INFO - 10:06:11:       | x    |      -5     |   -5  |      5      | integer |
        INFO - 10:06:11:       +------+-------------+-------+-------------+---------+

    Optimization result:
       Design variables: [-5. -5.]
       Objective function: -10.0
       Feasible solution: True



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

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.. code-block:: default

    execute_post(
        problem, "ScatterPlotMatrix", variable_names=["x", "f"], save=False, show=False
    )
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()




.. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_3_001.png
   :alt: plot simple opt 3
   :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_3_001.png
   :class: sphx-glr-single-img





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Note that you can get all the optimization algorithms names:

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.. code-block:: default

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




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

 Out:

 .. 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']





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

   **Total running time of the script:** ( 0 minutes  0.597 seconds)


.. _sphx_glr_download_examples_optimization_problem_plot_simple_opt_3.py:


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