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

.. only:: html

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

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

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

.. _sphx_glr_auto_numerical_methods_optimization_plot_optimization_bonmin.py:


Optimization using bonmin
=========================

.. GENERATED FROM PYTHON SOURCE LINES 8-12

In this example we are going to explore mixed-integer non linear problems
optimization using the `bonmin <https://www.coin-or.org/Bonmin/index.html>`_
interface.
%%

.. GENERATED FROM PYTHON SOURCE LINES 12-16

.. code-block:: Python

    import openturns as ot

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 17-18

List available algorithms

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.. code-block:: Python

    for algo in ot.Bonmin.GetAlgorithmNames():
        print(algo)





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

 .. code-block:: none

    B-BB
    B-OA
    B-QG
    B-Hyb
    B-Ecp
    B-iFP




.. GENERATED FROM PYTHON SOURCE LINES 22-24

Details and references on bonmin algorithms are available
`here <https://projects.coin-or.org/Bonmin>`_ .

.. GENERATED FROM PYTHON SOURCE LINES 26-60

Setting up and solving a simple problem
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The following example will demonstrate the use of bonmin "BB" algorithm to
solve the following problem:

.. math::
   \min - x_0 - x_1 - x_2

such that:

.. math::
   \begin{array}{l}
   (x_1 - \frac{1}{2})^2 + (x_2 - \frac{1}{2})^2 \leq \frac{1}{4} \\
   x_0 - x_1 \leq 0 \\
   x_0 + x_2 + x_3 \leq 2\\
   x_0 \in \{0,1\}^n\\
   (x_1, x_2) \in \mathbb{R}^2\\
   x_3 \in \mathbb{N}
   \end{array}

The theoretical minimum is reached for :math:`x = [1,1,0.5,0]`.
At this point, the objective function value is :math:`-2.5`

N.B.: OpenTURNS requires equality and inequality constraints to be stated as
:math:`g(x) = 0` and :math:`h(x) \geq 0`, respectively. Thus the inequalities
above will have to be restated to match this requirement:

.. math::
   \begin{array}{l}
   -(x_1 - \frac{1}{2})^2 - (x_2 - \frac{1}{2})^2 + \frac{1}{4} \geq 0\\
   -x_0 + x_1 \geq 0 \\
   -x_0 - x_2 - x_3 + 2 \geq 0\\
   \end{array}

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Definition of objective function

.. GENERATED FROM PYTHON SOURCE LINES 63-102

.. code-block:: Python

    objectiveFunction = ot.SymbolicFunction(["x0", "x1", "x2", "x3"], ["-x0 -x1 -x2"])

    # Definition of variables bounds
    bounds = ot.Interval(
        [0, 0, 0, 0],
        [1, 1e99, 1e99, 5],
        [True, True, True, True],
        [True, False, False, True],
    )

    # Definition of constraints
    # Constraints in OpenTURNS are defined as g(x) = 0 and h(x) >= 0
    #    No equality constraint -> nothing to do
    #    Inequality constraints:
    h = ot.SymbolicFunction(
        ["x0", "x1", "x2", "x3"],
        ["-(x1-0.5)^2 - (x2-0.5)^2 + 0.25", "x1 - x0", "-x0 - x2 - x3 + 2"],
    )

    # Definition of variables types
    CONTINUOUS = ot.OptimizationProblemImplementation.CONTINUOUS
    BINARY = ot.OptimizationProblemImplementation.BINARY
    INTEGER = ot.OptimizationProblemImplementation.INTEGER
    variablesType = [BINARY, CONTINUOUS, CONTINUOUS, INTEGER]

    # Setting up Bonmin problem
    problem = ot.OptimizationProblem(objectiveFunction)
    problem.setBounds(bounds)
    problem.setVariablesType(variablesType)
    problem.setInequalityConstraint(h)

    bonminAlgorithm = ot.Bonmin(problem, "B-BB")
    bonminAlgorithm.setMaximumEvaluationNumber(10000)
    bonminAlgorithm.setMaximumIterationNumber(1000)
    bonminAlgorithm.setStartingPoint([0, 0, 0, 0])

    ot.ResourceMap.AddAsString("Bonmin-mu_oracle", "loqo")
    ot.ResourceMap.AddAsScalar("Bonmin-bonmin.time_limit", 5)








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Running the solver

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.. code-block:: Python

    bonminAlgorithm.run()

    # Retrieving the results
    result = bonminAlgorithm.getResult()
    print(" -- Optimal point = " + str(result.getOptimalPoint()))
    print(" -- Optimal value = " + str(result.getOptimalValue()))
    print(" -- Evaluation number = " + str(result.getInputSample().getSize()))




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

 .. code-block:: none

     -- Optimal point = [1,1,0.502856,0]
     -- Optimal value = [-2.50286]
     -- Evaluation number = 147





.. _sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_bonmin.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_optimization_bonmin.ipynb <plot_optimization_bonmin.ipynb>`

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

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