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

    Click :ref:`here <sphx_glr_download_source_auto_examples_combination_plot_constrained_sum.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_source_auto_examples_combination_plot_constrained_sum.py:


===========================
Constrained sum of elements
===========================

From a shuffled set of integers, find the numbers that minimize the sum of
5 (five) elements, so that the result is also an odd number

In this case, since the objective function is the sum of the elements, the order doesn't matter, so we use the ``Combination`` optimizer.



.. image:: /source/auto_examples/combination/images/sphx_glr_plot_constrained_sum_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    Iteration 0:
       global_best: 17.000   iteration_best: 17.000
    Iteration 1:
       global_best: 15.000   iteration_best: 15.000

    Iteration completed
    ==========================
    Exit code 2: Algorithm has reached the value threshold of 15
    Elapsed time 0.011
    1 iterations
    Best selection: [1, 5, 4, 3, 2]
    Best evaluation: 15.0
    Solution:  [1, 5, 4, 3, 2]





|


.. code-block:: default


    import random
    from psopt import Combination


    def main():
        # define objective function: f([a, b, c, ...]) = a + b + c + ...
        def obj_func(x):
            return sum(x)

        # list of possible candidates
        random.seed(0)
        candidates = random.sample(list(range(1, 12)), 11)

        # constraint: sum of values cannot be even
        def mod(x):
            return sum(x) % 2

        constraint = {"fn": mod, "type": "==", "value": 1}

        # instantiate the optimizer
        opt = Combination(obj_func, candidates, constraints=constraint)

        # define a threshold of acceptance for early convergence
        threshold = 15

        # minimize the obj function
        results = opt.minimize(selection_size=5, threshold=threshold, seed=0, verbose=1)
        print("Solution: ", results.solution)

        results.history.plot(["global_best", "iteration_best"])


    if __name__ == "__main__":
        main()


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

   **Total running time of the script:** ( 0 minutes  0.185 seconds)


.. _sphx_glr_download_source_auto_examples_combination_plot_constrained_sum.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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