.. only:: html

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

        Click :ref:`here <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
=========================

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


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    ot.Log.Show(ot.Log.NONE)








List available algorithms


.. code-block:: default

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





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

 Out:

 .. code-block:: none

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




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

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}

Definition of objective function


.. code-block:: default

    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
    variablesType = [ot.OptimizationProblemImplementation.BINARY,ot.OptimizationProblemImplementation.CONTINUOUS,ot.OptimizationProblemImplementation.CONTINUOUS,ot.OptimizationProblemImplementation.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)








Running the solver


.. code-block:: default

    bonminAlgorithm.run()

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





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

 Out:

 .. code-block:: none

     -- Optimal point = [1,1,0.500141,0]
     -- Optimal value = [-2.50014]
     -- Evaluation number = 147





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

   **Total running time of the script:** ( 0 minutes  0.052 seconds)


.. _sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_bonmin.py:


.. only :: html

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



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

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



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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

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