.. 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_highs.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_highs.py>`
        to download the full example code.

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

.. _sphx_glr_auto_numerical_methods_optimization_plot_optimization_highs.py:


Optimization using HiGHS solver
===============================

.. GENERATED FROM PYTHON SOURCE LINES 9-13

In this example we are going to explore mixed-integer non linear problems
optimization using the `HiGHS <https://highs.dev/>`_
interface.
%%

.. GENERATED FROM PYTHON SOURCE LINES 13-16

.. code-block:: Python

    import openturns as ot
    import openturns.experimental as otexp








.. GENERATED FROM PYTHON SOURCE LINES 17-32

The following example will demonstrate the use of HiGHS solver to
solve the following problem:

.. math::
   \max x +   y + 2 z

subject to:

.. math::
   \begin{array}{l}
   x + 2 y + 3 z \leq 4\\
   x + y \ge 1\\
   x, x, z \in \{0,1\}^3\\
   \end{array}


.. GENERATED FROM PYTHON SOURCE LINES 35-36

Definition of objective function as a cost vector

.. GENERATED FROM PYTHON SOURCE LINES 36-38

.. code-block:: Python

    cost = [1, 1, 2]








.. GENERATED FROM PYTHON SOURCE LINES 39-40

Definition of constraints in the form L<=Ax<=U

.. GENERATED FROM PYTHON SOURCE LINES 40-43

.. code-block:: Python

    LU = ot.Interval([-1e30, 1], [4, 1e30])
    A = ot.Matrix([[1, 2, 3], [1, 1, 0]])








.. GENERATED FROM PYTHON SOURCE LINES 44-45

Definition of variables types

.. GENERATED FROM PYTHON SOURCE LINES 45-49

.. code-block:: Python

    BINARY = ot.OptimizationProblemImplementation.BINARY
    variablesType = [BINARY] * 3
    bounds = ot.Interval(3)








.. GENERATED FROM PYTHON SOURCE LINES 50-51

Define the linear problem

.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: Python

    problem = otexp.LinearProblem(cost, bounds, A, LU)
    problem.setVariablesType(variablesType)
    problem.setMinimization(False)








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Run the algorithm

.. GENERATED FROM PYTHON SOURCE LINES 57-60

.. code-block:: Python

    algo = otexp.HiGHS(problem)
    algo.setStartingPoint([0.0] * 3)








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Running the solver

.. GENERATED FROM PYTHON SOURCE LINES 62-69

.. code-block:: Python

    algo.run()

    # Retrieving the results
    result = algo.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 = [1,0,1]
     -- Optimal value = [3]
     -- Evaluation number = 0





.. _sphx_glr_download_auto_numerical_methods_optimization_plot_optimization_highs.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_highs.ipynb <plot_optimization_highs.ipynb>`

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_optimization_highs.zip <plot_optimization_highs.zip>`