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

.. only:: html

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

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

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

.. _sphx_glr_examples_mdo_plot_mixed_optimization.py:


Solve a mixed optimization problem.
===================================
.. _mixed_optimization_scenario:

.. GENERATED FROM PYTHON SOURCE LINES 27-42

Introduction
------------
In this example,
we will solve a very simple mixed optimization problem with a full factorial approach.
To do so, we will split the problem into a discrete optimization problem
to enumerate all the combinations
and a continuous one to solve the associated sub-problem.
Thus, we will use the
:class:`.MDOScenarioAdapter` to wrap a :class:`.BaseScenario` and treat it as a
discipline whose inputs are some or all of its design space variables and whose
outputs are some or all of its functions (objective, constraints or observables).
Keep in mind that this approach may be very time-consuming.
It works well when the dimension of the integers to
explore is not too large. Otherwise, a dedicated algorithm may be better suited, such
as the ones available in the ``gemseo-pymoo`` plugin.

.. GENERATED FROM PYTHON SOURCE LINES 44-47

Imports
-------
All the imports needed for the tutorial are performed here.

.. GENERATED FROM PYTHON SOURCE LINES 47-65

.. code-block:: Python

    from __future__ import annotations

    from numpy import ndarray  # noqa: TC002
    from numpy.linalg import norm

    from gemseo import configure_logger
    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo.disciplines.scenario_adapters.mdo_scenario_adapter import MDOScenarioAdapter
    from gemseo.settings.doe import PYDOE_FULLFACT_Settings
    from gemseo.settings.formulations import DisciplinaryOpt_Settings
    from gemseo.settings.opt import NLOPT_COBYLA_Settings
    from gemseo.settings.post import OptHistoryView_Settings

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



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Optimization problem definition.
--------------------------------
We define the following optimization problem:

.. math::

   \begin{aligned}
   \text{minimize the objective function }&\text{f(x,y)}=|x| + |y| \\
   \text{with respect to the design variables }&x,\,y \\
   \text{subject to the general constraint }
   & g(x,y) \geq 2\\
   \text{subject to the bound constraints }
   & 0.0 \leq x \leq 1.0\\
   & 0 \leq y_0 \leq 1\\
   & 0 \leq y_2 \leq 2
   \end{aligned}

and where the general constraint is:

.. math::

   g(x,y) = x + y

Where :math:`y` is an integer vector with two components and :math:`x` is a float
vector with two components.

.. GENERATED FROM PYTHON SOURCE LINES 93-134

Optimization problem reformulation.
-----------------------------------
The problem can be split using the :class:`.MDOScenarioAdapter`. To do this we will
divide the design space in two, a continuous one and a discrete one.
The :class:`.MDOScenarioAdapter` will wrap the continuous inner scenario as a
discipline to be executed taking the inputs from the discrete design space.
These inputs are generated by the outer :class:`.DOEScenario` using a full factorial
method.
It is possible of course to use different DOE algorithms or even generate the samples
first, filter them, and then launch a class:`.CustomDOE` with the filtered samples.

The reformulated optimization problem would read as follows:
For the outer DOE Scenario:

.. math::

   \begin{aligned}
   \text{minimize the objective function }&\text{f(x,y)}=|x| + |y| \\
   \text{with respect to the design variables }&y \\
   \text{subject to the general constraint }
   & g(x,y) \geq 2\\
   \text{subject to the bound constraints }
   & 0 \leq y_0 \leq 1\\
   & 0 \leq y_2 \leq 2
   \end{aligned}

For the inner MDO Scenario:

.. math::

   \begin{aligned}
   \text{minimize the objective function }&\text{f(x,y)}=|x| + |y| \\
   \text{with respect to the design variables }&x \\
   \text{subject to the general constraint }
   & g(x,y) \geq 2\\
   \text{subject to the bound constraints }
   & 0.0 \leq x \leq 1.0
   \end{aligned}

In the next steps, we will build both scenarios and connect them to solve the full
problem.

.. GENERATED FROM PYTHON SOURCE LINES 137-143

Create an :class:`.AutoPyDiscipline` to compute the objective and the constraints.
----------------------------------------------------------------------------------
Since the expressions of our toy problem are very simple, we can use an
:class:`.AutoPyDiscipline` to compute the objective and constraints.
Note that there are no strong couplings in our expressions, which means we could also
compute both the objective and constraints with a single discipline if we wished to.

.. GENERATED FROM PYTHON SOURCE LINES 143-158

.. code-block:: Python

    def obj(x: ndarray, y: ndarray) -> float:
        """A simple Python function to compute f(x,y)."""
        f = norm(x) + norm(y)
        return f  # noqa: RET504


    def const(x: ndarray, y: ndarray) -> ndarray:
        """A simple Python function to compute g(x,y)."""
        g = x + y
        return g  # noqa: RET504


    objective = create_discipline("AutoPyDiscipline", name="f(x,y)", py_func=obj)
    constraint = create_discipline("AutoPyDiscipline", name="g(x,y)", py_func=const)





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

 .. code-block:: none

     WARNING - 20:38:27: The Args section is missing.
     WARNING - 20:38:27: The Args section is missing.




.. GENERATED FROM PYTHON SOURCE LINES 159-163

Create the design space for the entire problem.
-----------------------------------------------
We can define a :class:`.DesignSpace` for the whole problem and then filter
either the continuous variables or the discrete ones.

.. GENERATED FROM PYTHON SOURCE LINES 163-169

.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("x", lower_bound=0, upper_bound=1, value=1.0, size=2)
    design_space.add_variable(
        "y", lower_bound=[0, 0], upper_bound=[1, 2], value=1, size=2, type_="integer"
    )








.. GENERATED FROM PYTHON SOURCE LINES 170-176

Create the design space for the inner scenario.
-----------------------------------------------
The inner scenario is the one that solves the continuous optimization problem, and as
such, it only needs to include the continuous design variables. We use the
:meth:`.DesignSpace.filter` method to keep ``x`` and we set ``copy`` to ``True`` to
keep the original ``design_space`` unchanged, as we will use it later.

.. GENERATED FROM PYTHON SOURCE LINES 176-178

.. code-block:: Python

    design_space_inner_scenario = design_space.filter(keep_variables=["x"], copy=True)








.. GENERATED FROM PYTHON SOURCE LINES 179-181

Create the inner MDO scenario.
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 181-190

.. code-block:: Python

    inner_scenario = create_scenario(
        [objective, constraint],
        "f",
        design_space_inner_scenario,
        formulation_settings_model=DisciplinaryOpt_Settings(),
    )
    inner_scenario.set_algorithm(NLOPT_COBYLA_Settings(max_iter=100))
    inner_scenario.add_constraint("g", constraint_type="ineq", value=2)








.. GENERATED FROM PYTHON SOURCE LINES 191-199

Create the scenario adapter.
----------------------------
An :class:`.MDOScenarioAdapter` wraps an entire :class:`.BaseScenario` as a
:class:`.Discipline`, its inputs are all or
part of the design space variables and its outputs are all or part of the objective
values, constraints or observables.
Here we select the variables of the inner scenario that we wish to set as
inputs/outputs for the adapter.

.. GENERATED FROM PYTHON SOURCE LINES 199-202

.. code-block:: Python

    input_names = ["y"]
    output_names = ["f", "g"]








.. GENERATED FROM PYTHON SOURCE LINES 203-205

The argument ``set_x0_before_opt`` allows us to set the starting point of the adapted
scenario from the outer DOE scenario values.

.. GENERATED FROM PYTHON SOURCE LINES 205-211

.. code-block:: Python

    adapted_inner_scenario = MDOScenarioAdapter(
        inner_scenario,
        input_names,
        output_names,
        set_x0_before_opt=True,
    )







.. GENERATED FROM PYTHON SOURCE LINES 212-227

.. tip::

   You may be interested in keeping the optimization history of the inner scenario for
   each of the executions launched by the outer scenario. To do this, set the argument
   ``keep_opt_history`` to ``True``, this option will store the databases in memory
   and make them accessible via the :attr:`.MDOScenarioAdapter.databases` attribute.
   Keep in mind that depending on the size of the database, storing it in memory may
   lead to a significant increase in memory usage.
   If you prefer to store the databases on disk instead, set the argument
   ``save_opt_history`` to ``True``. An ``hdf5`` file will be saved on the disk at
   each new execution. You may also choose a prefix for the name of these files with
   the argument ``opt_history_file_prefix``. If no prefix is given, the default
   prefix is ``"database"``.
   Both ``keep_opt_history`` and ``save_opt_history`` are independent of
   each-other.

.. GENERATED FROM PYTHON SOURCE LINES 230-237

Create the design space for the outer DOE scenario.
---------------------------------------------------
The outer scenario is the one that solves the discrete optimization problem, and as
such, it only needs to include the integer design variables. Once again, we use the
:meth:`.DesignSpace.filter` method to keep ``y``, the ``copy`` argument ensures that
the original ``design_space`` remains unchanged in case you need it for other
purposes.

.. GENERATED FROM PYTHON SOURCE LINES 237-239

.. code-block:: Python

    design_space_outer_scenario = design_space.filter(keep_variables="y", copy=True)








.. GENERATED FROM PYTHON SOURCE LINES 240-242

Create the outer DOE scenario.
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 242-250

.. code-block:: Python

    outer_scenario = create_scenario(
        adapted_inner_scenario,
        "f",
        design_space_outer_scenario,
        formulation_settings_model=DisciplinaryOpt_Settings(),
        scenario_type="DOE",
    )








.. GENERATED FROM PYTHON SOURCE LINES 251-254

Here, we add the constraints on the outer scenario in order to be able to know if a
given set of integers returns a feasible solution once the inner scenario has been
executed.

.. GENERATED FROM PYTHON SOURCE LINES 254-256

.. code-block:: Python

    outer_scenario.add_constraint("g", constraint_type="ineq", value=2)








.. GENERATED FROM PYTHON SOURCE LINES 257-258

Show an xDSM of the process, including the outer and inner scenarios.

.. GENERATED FROM PYTHON SOURCE LINES 258-260

.. code-block:: Python

    outer_scenario.xdsmize(save_html=False)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

        <script type="text/javascript">
            document.addEventListener('DOMContentLoaded', () => {
              const mdo = {
      "root": {
        "nodes": [
          {
            "id": "Opt",
            "name": "DOE",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "MDOScenario_scn-1-1",
            "type": "mdo",
            "subxdsm": "MDOScenario_scn-1-1",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "y^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "f^*, [g-2]^*"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1"
            ]
          ]
        ],
        "optpb": ""
      },
      "MDOScenario_scn-1-1": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "f(x,y)",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "g(x,y)",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "f^*, [g-2]^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "f"
          },
          {
            "from": "Opt",
            "to": "Dis2",
            "name": "x"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "f"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "g"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2"
            ]
          ]
        ],
        "optpb": ""
      }
    };
              const config = {
                labelizer: {
                    ellipsis: 5,
                    subSupScript: false,
                    showLinkNbOnly: false,
                },
                layout: {
                    origin: { x: 50, y: 20 },
                    cellsize: { w: 150, h: 50 },
                    padding: 10,
                },
                withDefaultDriver: true,
                withTitleTooltip: true,
              };
              xdsmjs.XDSMjs(config).createXdsm(mdo);
            });
        </script>
        <div class='xdsm-toolbar'></div><div class='xdsm2'></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 261-265

Execute the outer scenario (which contains the inner scenario) and solve the whole
problem.
The console will show the progress of the optimization. For each DOE point it will
show the optimization of the continuous problem and its optimal result.

.. GENERATED FROM PYTHON SOURCE LINES 265-267

.. code-block:: Python

    outer_scenario.execute(PYDOE_FULLFACT_Settings(n_samples=9))





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

 .. code-block:: none

        INFO - 20:38:27: *** Start DOEScenario execution ***
        INFO - 20:38:27: DOEScenario
        INFO - 20:38:27:    Disciplines: MDOScenario_adapter
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(y)
        INFO - 20:38:27:    with respect to y
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(y) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+---------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type    |
        INFO - 20:38:27:       +------+-------------+-------+-------------+---------+
        INFO - 20:38:27:       | y[0] |      0      |   1   |      1      | integer |
        INFO - 20:38:27:       | y[1] |      0      |   1   |      2      | integer |
        INFO - 20:38:27:       +------+-------------+-------+-------------+---------+
        INFO - 20:38:27: Solving optimization problem with algorithm PYDOE_FULLFACT:
        INFO - 20:38:27: *** Start MDOScenario execution ***
        INFO - 20:38:27: MDOScenario
        INFO - 20:38:27:    Disciplines: f(x,y) g(x,y)
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(x)
        INFO - 20:38:27:    with respect to x
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(x) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | x[0] |      0      |  None |      1      | float |
        INFO - 20:38:27:       | x[1] |      0      |  None |      1      | float |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 20:38:27:      1%|          | 1/100 [00:00<00:00, 313.12 it/sec, obj=0.707]
        INFO - 20:38:27:      2%|▏         | 2/100 [00:00<00:00, 497.34 it/sec, obj=0.901]
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        INFO - 20:38:27:     58%|█████▊    | 58/100 [00:00<00:00, 1484.97 it/sec, obj=9.78e-12]
        INFO - 20:38:27:     59%|█████▉    | 59/100 [00:00<00:00, 1486.86 it/sec, obj=3.55e-12]
        INFO - 20:38:27:     60%|██████    | 60/100 [00:00<00:00, 1489.07 it/sec, obj=2.06e-13]
        INFO - 20:38:27:     61%|██████    | 61/100 [00:00<00:00, 1490.46 it/sec, obj=1.42e-12]
        INFO - 20:38:27:     62%|██████▏   | 62/100 [00:00<00:00, 1492.75 it/sec, obj=1.19e-13]
        INFO - 20:38:27:     63%|██████▎   | 63/100 [00:00<00:00, 1493.89 it/sec, obj=3e-14]
        INFO - 20:38:27:     64%|██████▍   | 64/100 [00:00<00:00, 1494.93 it/sec, obj=1.85e-13]
        INFO - 20:38:27:     65%|██████▌   | 65/100 [00:00<00:00, 1496.72 it/sec, obj=3.51e-13]
        INFO - 20:38:27:     66%|██████▌   | 66/100 [00:00<00:00, 1497.47 it/sec, obj=2.18e-13]
        INFO - 20:38:27:     67%|██████▋   | 67/100 [00:00<00:00, 1498.29 it/sec, obj=4.71e-15]
        INFO - 20:38:27:     68%|██████▊   | 68/100 [00:00<00:00, 1500.17 it/sec, obj=1.74e-14]
        INFO - 20:38:27:     69%|██████▉   | 69/100 [00:00<00:00, 1501.31 it/sec, obj=2.39e-14]
        INFO - 20:38:27:     70%|███████   | 70/100 [00:00<00:00, 1503.29 it/sec, obj=5.02e-14]
        INFO - 20:38:27:     71%|███████   | 71/100 [00:00<00:00, 1504.41 it/sec, obj=1.61e-14]
        INFO - 20:38:27:     72%|███████▏  | 72/100 [00:00<00:00, 1505.67 it/sec, obj=6.98e-15]
        INFO - 20:38:27:     73%|███████▎  | 73/100 [00:00<00:00, 1507.46 it/sec, obj=2.31e-15]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 1.5700924586837752e-16
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-2. -2.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | Name | Lower bound |         Value         | Upper bound | Type  |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | x[0] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          | x[1] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27: *** End MDOScenario execution ***
        INFO - 20:38:27:     11%|█         | 1/9 [00:00<00:00, 19.38 it/sec, obj=2.31e-15]
        INFO - 20:38:27: *** Start MDOScenario execution ***
        INFO - 20:38:27: MDOScenario
        INFO - 20:38:27:    Disciplines: f(x,y) g(x,y)
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(x)
        INFO - 20:38:27:    with respect to x
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(x) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | x[0] |      0      |  None |      1      | float |
        INFO - 20:38:27:       | x[1] |      0      |  None |      1      | float |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 20:38:27:      1%|          | 1/100 [00:00<00:00, 2766.69 it/sec, obj=1.71]
        INFO - 20:38:27:      2%|▏         | 2/100 [00:00<00:00, 1984.06 it/sec, obj=1.9]
        INFO - 20:38:27:      3%|▎         | 3/100 [00:00<00:00, 2078.45 it/sec, obj=1.9]
        INFO - 20:38:27:      4%|▍         | 4/100 [00:00<00:00, 1866.00 it/sec, obj=1.46]
        INFO - 20:38:27:      5%|▌         | 5/100 [00:00<00:00, 1659.66 it/sec, obj=1.91]
        INFO - 20:38:27:      6%|▌         | 6/100 [00:00<00:00, 1615.68 it/sec, obj=1]
        INFO - 20:38:27:      7%|▋         | 7/100 [00:00<00:00, 1601.84 it/sec, obj=1.25]
        INFO - 20:38:27:      8%|▊         | 8/100 [00:00<00:00, 1590.33 it/sec, obj=1.29]
        INFO - 20:38:27:      9%|▉         | 9/100 [00:00<00:00, 1592.24 it/sec, obj=1.21]
        INFO - 20:38:27:     10%|█         | 10/100 [00:00<00:00, 1587.01 it/sec, obj=1.09]
        INFO - 20:38:27:     11%|█         | 11/100 [00:00<00:00, 1590.28 it/sec, obj=1.19]
        INFO - 20:38:27:     12%|█▏        | 12/100 [00:00<00:00, 1588.85 it/sec, obj=1.29]
        INFO - 20:38:27:     13%|█▎        | 13/100 [00:00<00:00, 1587.78 it/sec, obj=1.12]
        INFO - 20:38:27:     14%|█▍        | 14/100 [00:00<00:00, 1590.90 it/sec, obj=1.3]
        INFO - 20:38:27:     15%|█▌        | 15/100 [00:00<00:00, 1589.51 it/sec, obj=1.27]
        INFO - 20:38:27:     16%|█▌        | 16/100 [00:00<00:00, 1590.79 it/sec, obj=1.4]
        INFO - 20:38:27:     17%|█▋        | 17/100 [00:00<00:00, 1592.02 it/sec, obj=1.03]
        INFO - 20:38:27:     18%|█▊        | 18/100 [00:00<00:00, 1591.26 it/sec, obj=1.09]
        INFO - 20:38:27:     19%|█▉        | 19/100 [00:00<00:00, 1594.31 it/sec, obj=1.06]
        INFO - 20:38:27:     20%|██        | 20/100 [00:00<00:00, 1594.52 it/sec, obj=1.01]
        INFO - 20:38:27:     21%|██        | 21/100 [00:00<00:00, 1588.04 it/sec, obj=1.01]
        INFO - 20:38:27:     22%|██▏       | 22/100 [00:00<00:00, 1590.64 it/sec, obj=1]
        INFO - 20:38:27:     23%|██▎       | 23/100 [00:00<00:00, 1588.52 it/sec, obj=1]
        INFO - 20:38:27:     24%|██▍       | 24/100 [00:00<00:00, 1589.53 it/sec, obj=1]
        INFO - 20:38:27:     25%|██▌       | 25/100 [00:00<00:00, 1591.69 it/sec, obj=1]
        INFO - 20:38:27:     26%|██▌       | 26/100 [00:00<00:00, 1591.12 it/sec, obj=1]
        INFO - 20:38:27:     27%|██▋       | 27/100 [00:00<00:00, 1592.46 it/sec, obj=1]
        INFO - 20:38:27:     28%|██▊       | 28/100 [00:00<00:00, 1590.84 it/sec, obj=1]
        INFO - 20:38:27:     29%|██▉       | 29/100 [00:00<00:00, 1589.27 it/sec, obj=1]
        INFO - 20:38:27:     30%|███       | 30/100 [00:00<00:00, 1589.69 it/sec, obj=1]
        INFO - 20:38:27:     31%|███       | 31/100 [00:00<00:00, 1588.79 it/sec, obj=1]
        INFO - 20:38:27:     32%|███▏      | 32/100 [00:00<00:00, 1588.56 it/sec, obj=1]
        INFO - 20:38:27:     33%|███▎      | 33/100 [00:00<00:00, 1589.10 it/sec, obj=1]
        INFO - 20:38:27:     34%|███▍      | 34/100 [00:00<00:00, 1583.56 it/sec, obj=1]
        INFO - 20:38:27:     35%|███▌      | 35/100 [00:00<00:00, 1582.72 it/sec, obj=1]
        INFO - 20:38:27:     36%|███▌      | 36/100 [00:00<00:00, 1584.07 it/sec, obj=1]
        INFO - 20:38:27:     37%|███▋      | 37/100 [00:00<00:00, 1584.00 it/sec, obj=1]
        INFO - 20:38:27:     38%|███▊      | 38/100 [00:00<00:00, 1585.72 it/sec, obj=1]
        INFO - 20:38:27:     39%|███▉      | 39/100 [00:00<00:00, 1585.66 it/sec, obj=1]
        INFO - 20:38:27:     40%|████      | 40/100 [00:00<00:00, 1585.28 it/sec, obj=1]
        INFO - 20:38:27:     41%|████      | 41/100 [00:00<00:00, 1586.45 it/sec, obj=1]
        INFO - 20:38:27:     42%|████▏     | 42/100 [00:00<00:00, 1586.75 it/sec, obj=1]
        INFO - 20:38:27:     43%|████▎     | 43/100 [00:00<00:00, 1586.99 it/sec, obj=1]
        INFO - 20:38:27:     44%|████▍     | 44/100 [00:00<00:00, 1588.23 it/sec, obj=1]
        INFO - 20:38:27:     45%|████▌     | 45/100 [00:00<00:00, 1587.86 it/sec, obj=1]
        INFO - 20:38:27:     46%|████▌     | 46/100 [00:00<00:00, 1589.14 it/sec, obj=1]
        INFO - 20:38:27:     47%|████▋     | 47/100 [00:00<00:00, 1586.18 it/sec, obj=1]
        INFO - 20:38:27:     48%|████▊     | 48/100 [00:00<00:00, 1586.17 it/sec, obj=1]
        INFO - 20:38:27:     49%|████▉     | 49/100 [00:00<00:00, 1587.56 it/sec, obj=1]
        INFO - 20:38:27:     50%|█████     | 50/100 [00:00<00:00, 1588.16 it/sec, obj=1]
        INFO - 20:38:27:     51%|█████     | 51/100 [00:00<00:00, 1588.14 it/sec, obj=1]
        INFO - 20:38:27:     52%|█████▏    | 52/100 [00:00<00:00, 1589.45 it/sec, obj=1]
        INFO - 20:38:27:     53%|█████▎    | 53/100 [00:00<00:00, 1589.43 it/sec, obj=1]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 1.0000000000000002
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-1. -2.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | Name | Lower bound |         Value         | Upper bound | Type  |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | x[0] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          | x[1] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27: *** End MDOScenario execution ***
        INFO - 20:38:27:     22%|██▏       | 2/9 [00:00<00:00, 22.69 it/sec, obj=1]
        INFO - 20:38:27: *** Start MDOScenario execution ***
        INFO - 20:38:27: MDOScenario
        INFO - 20:38:27:    Disciplines: f(x,y) g(x,y)
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(x)
        INFO - 20:38:27:    with respect to x
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(x) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | x[0] |      0      |  None |      1      | float |
        INFO - 20:38:27:       | x[1] |      0      |  None |      1      | float |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 20:38:27:      1%|          | 1/100 [00:00<00:00, 2894.62 it/sec, obj=1.71]
        INFO - 20:38:27:      2%|▏         | 2/100 [00:00<00:00, 2009.25 it/sec, obj=1.9]
        INFO - 20:38:27:      3%|▎         | 3/100 [00:00<00:00, 2133.42 it/sec, obj=1.9]
        INFO - 20:38:27:      4%|▍         | 4/100 [00:00<00:00, 1914.11 it/sec, obj=1.46]
        INFO - 20:38:27:      5%|▌         | 5/100 [00:00<00:00, 1789.84 it/sec, obj=1.91]
        INFO - 20:38:27:      6%|▌         | 6/100 [00:00<00:00, 1756.16 it/sec, obj=1]
        INFO - 20:38:27:      7%|▋         | 7/100 [00:00<00:00, 1728.49 it/sec, obj=1.25]
        INFO - 20:38:27:      8%|▊         | 8/100 [00:00<00:00, 1700.51 it/sec, obj=1.29]
        INFO - 20:38:27:      9%|▉         | 9/100 [00:00<00:00, 1690.49 it/sec, obj=1.21]
        INFO - 20:38:27:     10%|█         | 10/100 [00:00<00:00, 1678.26 it/sec, obj=1.09]
        INFO - 20:38:27:     11%|█         | 11/100 [00:00<00:00, 1667.41 it/sec, obj=1.19]
        INFO - 20:38:27:     12%|█▏        | 12/100 [00:00<00:00, 1664.52 it/sec, obj=1.29]
        INFO - 20:38:27:     13%|█▎        | 13/100 [00:00<00:00, 1656.52 it/sec, obj=1.12]
        INFO - 20:38:27:     14%|█▍        | 14/100 [00:00<00:00, 1655.82 it/sec, obj=1.3]
        INFO - 20:38:27:     15%|█▌        | 15/100 [00:00<00:00, 1649.27 it/sec, obj=1.27]
        INFO - 20:38:27:     16%|█▌        | 16/100 [00:00<00:00, 1645.07 it/sec, obj=1.4]
        INFO - 20:38:27:     17%|█▋        | 17/100 [00:00<00:00, 1643.54 it/sec, obj=1.03]
        INFO - 20:38:27:     18%|█▊        | 18/100 [00:00<00:00, 1639.65 it/sec, obj=1.09]
        INFO - 20:38:27:     19%|█▉        | 19/100 [00:00<00:00, 1634.43 it/sec, obj=1.06]
        INFO - 20:38:27:     20%|██        | 20/100 [00:00<00:00, 1634.89 it/sec, obj=1.01]
        INFO - 20:38:27:     21%|██        | 21/100 [00:00<00:00, 1631.75 it/sec, obj=1.01]
        INFO - 20:38:27:     22%|██▏       | 22/100 [00:00<00:00, 1632.40 it/sec, obj=1]
        INFO - 20:38:27:     23%|██▎       | 23/100 [00:00<00:00, 1629.43 it/sec, obj=1]
        INFO - 20:38:27:     24%|██▍       | 24/100 [00:00<00:00, 1627.72 it/sec, obj=1]
        INFO - 20:38:27:     25%|██▌       | 25/100 [00:00<00:00, 1622.48 it/sec, obj=1]
        INFO - 20:38:27:     26%|██▌       | 26/100 [00:00<00:00, 1620.29 it/sec, obj=1]
        INFO - 20:38:27:     27%|██▋       | 27/100 [00:00<00:00, 1617.41 it/sec, obj=1]
        INFO - 20:38:27:     28%|██▊       | 28/100 [00:00<00:00, 1613.86 it/sec, obj=1]
        INFO - 20:38:27:     29%|██▉       | 29/100 [00:00<00:00, 1612.40 it/sec, obj=1]
        INFO - 20:38:27:     30%|███       | 30/100 [00:00<00:00, 1610.53 it/sec, obj=1]
        INFO - 20:38:27:     31%|███       | 31/100 [00:00<00:00, 1609.98 it/sec, obj=1]
        INFO - 20:38:27:     32%|███▏      | 32/100 [00:00<00:00, 1608.96 it/sec, obj=1]
        INFO - 20:38:27:     33%|███▎      | 33/100 [00:00<00:00, 1607.55 it/sec, obj=1]
        INFO - 20:38:27:     34%|███▍      | 34/100 [00:00<00:00, 1606.14 it/sec, obj=1]
        INFO - 20:38:27:     35%|███▌      | 35/100 [00:00<00:00, 1601.26 it/sec, obj=1]
        INFO - 20:38:27:     36%|███▌      | 36/100 [00:00<00:00, 1601.73 it/sec, obj=1]
        INFO - 20:38:27:     37%|███▋      | 37/100 [00:00<00:00, 1600.73 it/sec, obj=1]
        INFO - 20:38:27:     38%|███▊      | 38/100 [00:00<00:00, 1600.27 it/sec, obj=1]
        INFO - 20:38:27:     39%|███▉      | 39/100 [00:00<00:00, 1601.08 it/sec, obj=1]
        INFO - 20:38:27:     40%|████      | 40/100 [00:00<00:00, 1600.07 it/sec, obj=1]
        INFO - 20:38:27:     41%|████      | 41/100 [00:00<00:00, 1586.48 it/sec, obj=1]
        INFO - 20:38:27:     42%|████▏     | 42/100 [00:00<00:00, 1586.65 it/sec, obj=1]
        INFO - 20:38:27:     43%|████▎     | 43/100 [00:00<00:00, 1585.93 it/sec, obj=1]
        INFO - 20:38:27:     44%|████▍     | 44/100 [00:00<00:00, 1586.47 it/sec, obj=1]
        INFO - 20:38:27:     45%|████▌     | 45/100 [00:00<00:00, 1588.06 it/sec, obj=1]
        INFO - 20:38:27:     46%|████▌     | 46/100 [00:00<00:00, 1587.90 it/sec, obj=1]
        INFO - 20:38:27:     47%|████▋     | 47/100 [00:00<00:00, 1587.92 it/sec, obj=1]
        INFO - 20:38:27:     48%|████▊     | 48/100 [00:00<00:00, 1589.03 it/sec, obj=1]
        INFO - 20:38:27:     49%|████▉     | 49/100 [00:00<00:00, 1588.87 it/sec, obj=1]
        INFO - 20:38:27:     50%|█████     | 50/100 [00:00<00:00, 1589.32 it/sec, obj=1]
        INFO - 20:38:27:     51%|█████     | 51/100 [00:00<00:00, 1588.75 it/sec, obj=1]
        INFO - 20:38:27:     52%|█████▏    | 52/100 [00:00<00:00, 1587.99 it/sec, obj=1]
        INFO - 20:38:27:     53%|█████▎    | 53/100 [00:00<00:00, 1588.54 it/sec, obj=1]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 1.0000000000000002
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-2. -1.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | Name | Lower bound |         Value         | Upper bound | Type  |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | x[0] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          | x[1] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27: *** End MDOScenario execution ***
        INFO - 20:38:27:     33%|███▎      | 3/9 [00:00<00:00, 24.07 it/sec, obj=1]
        INFO - 20:38:27: *** Start MDOScenario execution ***
        INFO - 20:38:27: MDOScenario
        INFO - 20:38:27:    Disciplines: f(x,y) g(x,y)
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(x)
        INFO - 20:38:27:    with respect to x
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(x) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | x[0] |      0      |  None |      1      | float |
        INFO - 20:38:27:       | x[1] |      0      |  None |      1      | float |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 20:38:27:      1%|          | 1/100 [00:00<00:00, 2721.81 it/sec, obj=2.12]
        INFO - 20:38:27:      2%|▏         | 2/100 [00:00<00:00, 2042.02 it/sec, obj=2.32]
        INFO - 20:38:27:      3%|▎         | 3/100 [00:00<00:00, 2118.34 it/sec, obj=2.32]
        INFO - 20:38:27:      4%|▍         | 4/100 [00:00<00:00, 1912.37 it/sec, obj=1.87]
        INFO - 20:38:27:      5%|▌         | 5/100 [00:00<00:00, 1832.37 it/sec, obj=2.33]
        INFO - 20:38:27:      6%|▌         | 6/100 [00:00<00:00, 1773.37 it/sec, obj=1.41]
        INFO - 20:38:27:      7%|▋         | 7/100 [00:00<00:00, 1749.50 it/sec, obj=1.67]
        INFO - 20:38:27:      8%|▊         | 8/100 [00:00<00:00, 1723.83 it/sec, obj=1.7]
        INFO - 20:38:27:      9%|▉         | 9/100 [00:00<00:00, 1707.47 it/sec, obj=1.62]
        INFO - 20:38:27:     10%|█         | 10/100 [00:00<00:00, 1699.20 it/sec, obj=1.51]
        INFO - 20:38:27:     11%|█         | 11/100 [00:00<00:00, 1686.98 it/sec, obj=1.6]
        INFO - 20:38:27:     12%|█▏        | 12/100 [00:00<00:00, 1679.91 it/sec, obj=1.7]
        INFO - 20:38:27:     13%|█▎        | 13/100 [00:00<00:00, 1678.39 it/sec, obj=1.54]
        INFO - 20:38:27:     14%|█▍        | 14/100 [00:00<00:00, 1671.70 it/sec, obj=1.72]
        INFO - 20:38:27:     15%|█▌        | 15/100 [00:00<00:00, 1671.44 it/sec, obj=1.68]
        INFO - 20:38:27:     16%|█▌        | 16/100 [00:00<00:00, 1667.34 it/sec, obj=1.81]
        INFO - 20:38:27:     17%|█▋        | 17/100 [00:00<00:00, 1662.47 it/sec, obj=1.45]
        INFO - 20:38:27:     18%|█▊        | 18/100 [00:00<00:00, 1661.51 it/sec, obj=1.51]
        INFO - 20:38:27:     19%|█▉        | 19/100 [00:00<00:00, 1657.34 it/sec, obj=1.47]
        INFO - 20:38:27:     20%|██        | 20/100 [00:00<00:00, 1656.88 it/sec, obj=1.42]
        INFO - 20:38:27:     21%|██        | 21/100 [00:00<00:00, 1652.32 it/sec, obj=1.42]
        INFO - 20:38:27:     22%|██▏       | 22/100 [00:00<00:00, 1648.97 it/sec, obj=1.42]
        INFO - 20:38:27:     23%|██▎       | 23/100 [00:00<00:00, 1648.85 it/sec, obj=1.41]
        INFO - 20:38:27:     24%|██▍       | 24/100 [00:00<00:00, 1646.65 it/sec, obj=1.41]
        INFO - 20:38:27:     25%|██▌       | 25/100 [00:00<00:00, 1644.52 it/sec, obj=1.41]
        INFO - 20:38:27:     26%|██▌       | 26/100 [00:00<00:00, 1644.06 it/sec, obj=1.41]
        INFO - 20:38:27:     27%|██▋       | 27/100 [00:00<00:00, 1639.40 it/sec, obj=1.41]
        INFO - 20:38:27:     28%|██▊       | 28/100 [00:00<00:00, 1637.35 it/sec, obj=1.41]
        INFO - 20:38:27:     29%|██▉       | 29/100 [00:00<00:00, 1637.03 it/sec, obj=1.41]
        INFO - 20:38:27:     30%|███       | 30/100 [00:00<00:00, 1634.65 it/sec, obj=1.41]
        INFO - 20:38:27:     31%|███       | 31/100 [00:00<00:00, 1634.86 it/sec, obj=1.41]
        INFO - 20:38:27:     32%|███▏      | 32/100 [00:00<00:00, 1634.27 it/sec, obj=1.41]
        INFO - 20:38:27:     33%|███▎      | 33/100 [00:00<00:00, 1629.74 it/sec, obj=1.41]
        INFO - 20:38:27:     34%|███▍      | 34/100 [00:00<00:00, 1629.99 it/sec, obj=1.41]
        INFO - 20:38:27:     35%|███▌      | 35/100 [00:00<00:00, 1628.58 it/sec, obj=1.41]
        INFO - 20:38:27:     36%|███▌      | 36/100 [00:00<00:00, 1628.33 it/sec, obj=1.41]
        INFO - 20:38:27:     37%|███▋      | 37/100 [00:00<00:00, 1628.91 it/sec, obj=1.41]
        INFO - 20:38:27:     38%|███▊      | 38/100 [00:00<00:00, 1627.99 it/sec, obj=1.41]
        INFO - 20:38:27:     39%|███▉      | 39/100 [00:00<00:00, 1628.60 it/sec, obj=1.41]
        INFO - 20:38:27:     40%|████      | 40/100 [00:00<00:00, 1627.26 it/sec, obj=1.41]
        INFO - 20:38:27:     41%|████      | 41/100 [00:00<00:00, 1626.01 it/sec, obj=1.41]
        INFO - 20:38:27:     42%|████▏     | 42/100 [00:00<00:00, 1626.89 it/sec, obj=1.41]
        INFO - 20:38:27:     43%|████▎     | 43/100 [00:00<00:00, 1626.12 it/sec, obj=1.41]
        INFO - 20:38:27:     44%|████▍     | 44/100 [00:00<00:00, 1627.12 it/sec, obj=1.41]
        INFO - 20:38:27:     45%|████▌     | 45/100 [00:00<00:00, 1625.97 it/sec, obj=1.41]
        INFO - 20:38:27:     46%|████▌     | 46/100 [00:00<00:00, 1625.12 it/sec, obj=1.41]
        INFO - 20:38:27:     47%|████▋     | 47/100 [00:00<00:00, 1625.85 it/sec, obj=1.41]
        INFO - 20:38:27:     48%|████▊     | 48/100 [00:00<00:00, 1624.81 it/sec, obj=1.41]
        INFO - 20:38:27:     49%|████▉     | 49/100 [00:00<00:00, 1624.08 it/sec, obj=1.41]
        INFO - 20:38:27:     50%|█████     | 50/100 [00:00<00:00, 1624.63 it/sec, obj=1.41]
        INFO - 20:38:27:     51%|█████     | 51/100 [00:00<00:00, 1620.02 it/sec, obj=1.41]
        INFO - 20:38:27:     52%|█████▏    | 52/100 [00:00<00:00, 1618.82 it/sec, obj=1.41]
        INFO - 20:38:27:     53%|█████▎    | 53/100 [00:00<00:00, 1618.81 it/sec, obj=1.41]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 1.4142135623730954
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-1. -1.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | Name | Lower bound |         Value         | Upper bound | Type  |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27:          | x[0] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          | x[1] |      0      | 1.110223024625157e-16 |      1      | float |
        INFO - 20:38:27:          +------+-------------+-----------------------+-------------+-------+
        INFO - 20:38:27: *** End MDOScenario execution ***
        INFO - 20:38:27:     44%|████▍     | 4/9 [00:00<00:00, 24.93 it/sec, obj=1.41]
        INFO - 20:38:27: *** Start MDOScenario execution ***
        INFO - 20:38:27: MDOScenario
        INFO - 20:38:27:    Disciplines: f(x,y) g(x,y)
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(x)
        INFO - 20:38:27:    with respect to x
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(x) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | x[0] |      0      |  None |      1      | float |
        INFO - 20:38:27:       | x[1] |      0      |  None |      1      | float |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 20:38:27:      1%|          | 1/100 [00:00<00:00, 2659.67 it/sec, obj=2.71]
        INFO - 20:38:27:      2%|▏         | 2/100 [00:00<00:00, 2007.80 it/sec, obj=2.9]
        INFO - 20:38:27:      3%|▎         | 3/100 [00:00<00:00, 2092.27 it/sec, obj=2.9]
        INFO - 20:38:27:      4%|▍         | 4/100 [00:00<00:00, 2119.94 it/sec, obj=2.56]
        INFO - 20:38:27:      5%|▌         | 5/100 [00:00<00:00, 2127.36 it/sec, obj=2.5]
        INFO - 20:38:27:      6%|▌         | 6/100 [00:00<00:00, 2149.46 it/sec, obj=2.25]
        INFO - 20:38:27:      7%|▋         | 7/100 [00:00<00:00, 2016.77 it/sec, obj=2]
        INFO - 20:38:27:      8%|▊         | 8/100 [00:00<00:00, 1956.64 it/sec, obj=2.2]
        INFO - 20:38:27:      9%|▉         | 9/100 [00:00<00:00, 1907.37 it/sec, obj=2.08]
        INFO - 20:38:27:     10%|█         | 10/100 [00:00<00:00, 1870.04 it/sec, obj=2.01]
        INFO - 20:38:27:     11%|█         | 11/100 [00:00<00:00, 1898.81 it/sec, obj=2.01]
        INFO - 20:38:27:     12%|█▏        | 12/100 [00:00<00:00, 1927.09 it/sec, obj=2.02]
        INFO - 20:38:27:     13%|█▎        | 13/100 [00:00<00:00, 1942.64 it/sec, obj=2.01]
        INFO - 20:38:27:     14%|█▍        | 14/100 [00:00<00:00, 1962.12 it/sec, obj=2]
        INFO - 20:38:27:     15%|█▌        | 15/100 [00:00<00:00, 1925.29 it/sec, obj=2]
        INFO - 20:38:27:     16%|█▌        | 16/100 [00:00<00:00, 1896.48 it/sec, obj=2]
        INFO - 20:38:27:     17%|█▋        | 17/100 [00:00<00:00, 1912.84 it/sec, obj=2]
        INFO - 20:38:27:     18%|█▊        | 18/100 [00:00<00:00, 1925.46 it/sec, obj=2]
        INFO - 20:38:27:     19%|█▉        | 19/100 [00:00<00:00, 1941.67 it/sec, obj=2]
        INFO - 20:38:27:     20%|██        | 20/100 [00:00<00:00, 1957.67 it/sec, obj=2]
        INFO - 20:38:27:     21%|██        | 21/100 [00:00<00:00, 1965.25 it/sec, obj=2]
        INFO - 20:38:27:     22%|██▏       | 22/100 [00:00<00:00, 1936.92 it/sec, obj=2]
        INFO - 20:38:27:     23%|██▎       | 23/100 [00:00<00:00, 1919.67 it/sec, obj=2]
        INFO - 20:38:27:     24%|██▍       | 24/100 [00:00<00:00, 1896.84 it/sec, obj=2]
        INFO - 20:38:27:     25%|██▌       | 25/100 [00:00<00:00, 1881.46 it/sec, obj=2]
        INFO - 20:38:27:     26%|██▌       | 26/100 [00:00<00:00, 1837.25 it/sec, obj=2]
        INFO - 20:38:27:     27%|██▋       | 27/100 [00:00<00:00, 1824.37 it/sec, obj=2]
        INFO - 20:38:27:     28%|██▊       | 28/100 [00:00<00:00, 1813.89 it/sec, obj=2]
        INFO - 20:38:27:     29%|██▉       | 29/100 [00:00<00:00, 1808.00 it/sec, obj=2]
        INFO - 20:38:27:     30%|███       | 30/100 [00:00<00:00, 1798.66 it/sec, obj=2]
        INFO - 20:38:27:     31%|███       | 31/100 [00:00<00:00, 1789.92 it/sec, obj=2]
        INFO - 20:38:27:     32%|███▏      | 32/100 [00:00<00:00, 1784.69 it/sec, obj=2]
        INFO - 20:38:27:     33%|███▎      | 33/100 [00:00<00:00, 1777.02 it/sec, obj=2]
        INFO - 20:38:27:     34%|███▍      | 34/100 [00:00<00:00, 1772.26 it/sec, obj=2]
        INFO - 20:38:27:     35%|███▌      | 35/100 [00:00<00:00, 1765.51 it/sec, obj=2]
        INFO - 20:38:27:     36%|███▌      | 36/100 [00:00<00:00, 1759.25 it/sec, obj=2]
        INFO - 20:38:27:     37%|███▋      | 37/100 [00:00<00:00, 1755.97 it/sec, obj=2]
        INFO - 20:38:27:     38%|███▊      | 38/100 [00:00<00:00, 1745.92 it/sec, obj=2]
        INFO - 20:38:27:     39%|███▉      | 39/100 [00:00<00:00, 1741.47 it/sec, obj=2]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 2.0
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-2.  0.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:          +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:          | x[0] |      0      |   0   |      1      | float |
        INFO - 20:38:27:          | x[1] |      0      |   0   |      1      | float |
        INFO - 20:38:27:          +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: *** End MDOScenario execution ***
        INFO - 20:38:27:     56%|█████▌    | 5/9 [00:00<00:00, 26.91 it/sec, obj=2]
        INFO - 20:38:27: *** Start MDOScenario execution ***
        INFO - 20:38:27: MDOScenario
        INFO - 20:38:27:    Disciplines: f(x,y) g(x,y)
        INFO - 20:38:27:    MDO formulation: DisciplinaryOpt
        INFO - 20:38:27: Optimization problem:
        INFO - 20:38:27:    minimize f(x)
        INFO - 20:38:27:    with respect to x
        INFO - 20:38:27:    under the inequality constraints
        INFO - 20:38:27:       g(x) <= 2
        INFO - 20:38:27:    over the design space:
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:       | x[0] |      0      |  None |      1      | float |
        INFO - 20:38:27:       | x[1] |      0      |  None |      1      | float |
        INFO - 20:38:27:       +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: Solving optimization problem with algorithm NLOPT_COBYLA:
        INFO - 20:38:27:      1%|          | 1/100 [00:00<00:00, 2882.68 it/sec, obj=2.94]
        INFO - 20:38:27:      2%|▏         | 2/100 [00:00<00:00, 2002.05 it/sec, obj=3.14]
        INFO - 20:38:27:      3%|▎         | 3/100 [00:00<00:00, 2122.27 it/sec, obj=3.14]
        INFO - 20:38:27:      4%|▍         | 4/100 [00:00<00:00, 2111.67 it/sec, obj=2.8]
        INFO - 20:38:27:      5%|▌         | 5/100 [00:00<00:00, 2123.27 it/sec, obj=2.74]
        INFO - 20:38:27:      6%|▌         | 6/100 [00:00<00:00, 2143.05 it/sec, obj=2.49]
        INFO - 20:38:27:      7%|▋         | 7/100 [00:00<00:00, 1986.07 it/sec, obj=2.24]
        INFO - 20:38:27:      8%|▊         | 8/100 [00:00<00:00, 1907.80 it/sec, obj=2.44]
        INFO - 20:38:27:      9%|▉         | 9/100 [00:00<00:00, 1857.53 it/sec, obj=2.32]
        INFO - 20:38:27:     10%|█         | 10/100 [00:00<00:00, 1815.32 it/sec, obj=2.25]
        INFO - 20:38:27:     11%|█         | 11/100 [00:00<00:00, 1837.12 it/sec, obj=2.25]
        INFO - 20:38:27:     12%|█▏        | 12/100 [00:00<00:00, 1864.14 it/sec, obj=2.25]
        INFO - 20:38:27:     13%|█▎        | 13/100 [00:00<00:00, 1884.56 it/sec, obj=2.24]
        INFO - 20:38:27:     14%|█▍        | 14/100 [00:00<00:00, 1902.92 it/sec, obj=2.24]
        INFO - 20:38:27:     15%|█▌        | 15/100 [00:00<00:00, 1870.23 it/sec, obj=2.24]
        INFO - 20:38:27:     16%|█▌        | 16/100 [00:00<00:00, 1851.28 it/sec, obj=2.24]
        INFO - 20:38:27:     17%|█▋        | 17/100 [00:00<00:00, 1864.82 it/sec, obj=2.24]
        INFO - 20:38:27:     18%|█▊        | 18/100 [00:00<00:00, 1883.95 it/sec, obj=2.24]
        INFO - 20:38:27:     19%|█▉        | 19/100 [00:00<00:00, 1897.33 it/sec, obj=2.24]
        INFO - 20:38:27:     20%|██        | 20/100 [00:00<00:00, 1913.11 it/sec, obj=2.24]
        INFO - 20:38:27:     21%|██        | 21/100 [00:00<00:00, 1926.01 it/sec, obj=2.24]
        INFO - 20:38:27:     22%|██▏       | 22/100 [00:00<00:00, 1903.43 it/sec, obj=2.24]
        INFO - 20:38:27:     23%|██▎       | 23/100 [00:00<00:00, 1885.74 it/sec, obj=2.24]
        INFO - 20:38:27:     24%|██▍       | 24/100 [00:00<00:00, 1870.44 it/sec, obj=2.24]
        INFO - 20:38:27:     25%|██▌       | 25/100 [00:00<00:00, 1855.95 it/sec, obj=2.24]
        INFO - 20:38:27:     26%|██▌       | 26/100 [00:00<00:00, 1843.68 it/sec, obj=2.24]
        INFO - 20:38:27:     27%|██▋       | 27/100 [00:00<00:00, 1835.52 it/sec, obj=2.24]
        INFO - 20:38:27:     28%|██▊       | 28/100 [00:00<00:00, 1824.29 it/sec, obj=2.24]
        INFO - 20:38:27:     29%|██▉       | 29/100 [00:00<00:00, 1815.04 it/sec, obj=2.24]
        INFO - 20:38:27:     30%|███       | 30/100 [00:00<00:00, 1808.51 it/sec, obj=2.24]
        INFO - 20:38:27:     31%|███       | 31/100 [00:00<00:00, 1800.43 it/sec, obj=2.24]
        INFO - 20:38:27:     32%|███▏      | 32/100 [00:00<00:00, 1795.29 it/sec, obj=2.24]
        INFO - 20:38:27:     33%|███▎      | 33/100 [00:00<00:00, 1787.32 it/sec, obj=2.24]
        INFO - 20:38:27:     34%|███▍      | 34/100 [00:00<00:00, 1780.00 it/sec, obj=2.24]
        INFO - 20:38:27:     35%|███▌      | 35/100 [00:00<00:00, 1775.21 it/sec, obj=2.24]
        INFO - 20:38:27:     36%|███▌      | 36/100 [00:00<00:00, 1768.17 it/sec, obj=2.24]
        INFO - 20:38:27:     37%|███▋      | 37/100 [00:00<00:00, 1763.01 it/sec, obj=2.24]
        INFO - 20:38:27:     38%|███▊      | 38/100 [00:00<00:00, 1758.99 it/sec, obj=2.24]
        INFO - 20:38:27:     39%|███▉      | 39/100 [00:00<00:00, 1753.30 it/sec, obj=2.24]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 2.23606797749979
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-1.  0.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:38:27:          +------+-------------+-------+-------------+-------+
        INFO - 20:38:27:          | x[0] |      0      |   0   |      1      | float |
        INFO - 20:38:27:          | x[1] |      0      |   0   |      1      | float |
        INFO - 20:38:27:          +------+-------------+-------+-------------+-------+
        INFO - 20:38:27: *** End MDOScenario execution ***
        INFO - 20:38:27:     67%|██████▋   | 6/9 [00:00<00:00, 28.43 it/sec, obj=2.24]
        INFO - 20:38:27: Optimization result:
        INFO - 20:38:27:    Optimizer info:
        INFO - 20:38:27:       Status: None
        INFO - 20:38:27:       Message: None
        INFO - 20:38:27:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:38:27:    Solution:
        INFO - 20:38:27:       The solution is feasible.
        INFO - 20:38:27:       Objective: 2.3125318484214635e-15
        INFO - 20:38:27:       Standardized constraints:
        INFO - 20:38:27:          [g-2] = [-2. -2.]
        INFO - 20:38:27:       Design space:
        INFO - 20:38:27:          +------+-------------+-------+-------------+---------+
        INFO - 20:38:27:          | Name | Lower bound | Value | Upper bound | Type    |
        INFO - 20:38:27:          +------+-------------+-------+-------------+---------+
        INFO - 20:38:27:          | y[0] |      0      |   0   |      1      | integer |
        INFO - 20:38:27:          | y[1] |      0      |   0   |      2      | integer |
        INFO - 20:38:27:          +------+-------------+-------+-------------+---------+
        INFO - 20:38:27: *** End DOEScenario execution ***




.. GENERATED FROM PYTHON SOURCE LINES 268-279

.. tip::

   In a :class:`.DOEScenario`, we know a priori the samples that will be evaluated.
   This means we can run the outer scenario in parallel if we set the setting
   ``n_processes`` to at least 2. Note that if you are running the outer scenario in
   parallel and requesting the databases of the continuous optimizations on the disk,
   you will need to instantiate the :class:`.MDOScenarioAdapter` with the argument
   ``naming="UUID"``, which is multiprocessing-safe.
   Running in parallel also means that the option ``keep_opt_history`` will not work
   because we are unable to copy the databases from the sub-processes to the main
   process.

.. GENERATED FROM PYTHON SOURCE LINES 282-289

Plot the objective and constraint history for the scenario.
-----------------------------------------------------------
At the end of the optimization we see the results of the problem. The optimal
solution would be in this case the iteration of the DOE that gave the minimum for
:math:`f(x,y)` while respecting the constraint :math;`g(x,y)`. The full problem
optimal result will contain the values for :math:`x`, :math:`y`, :math:`f`, and
:math:`g`.

.. GENERATED FROM PYTHON SOURCE LINES 289-290

.. code-block:: Python

    outer_scenario.post_process(OptHistoryView_Settings(save=False, show=True))



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/mdo/images/sphx_glr_plot_mixed_optimization_001.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/mdo/images/sphx_glr_plot_mixed_optimization_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/mdo/images/sphx_glr_plot_mixed_optimization_002.png
         :alt: Evolution of the objective value
         :srcset: /examples/mdo/images/sphx_glr_plot_mixed_optimization_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/mdo/images/sphx_glr_plot_mixed_optimization_003.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/mdo/images/sphx_glr_plot_mixed_optimization_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/mdo/images/sphx_glr_plot_mixed_optimization_004.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/mdo/images/sphx_glr_plot_mixed_optimization_004.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x78592cfba330>




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

   **Total running time of the script:** (0 minutes 0.589 seconds)


.. _sphx_glr_download_examples_mdo_plot_mixed_optimization.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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