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

.. only:: html

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

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

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

.. _sphx_glr_examples_multi_objective_plot_mnbi_fonseca.py:


Multi-objective Fonseca-Fleming example with the mNBI algorithm
===============================================================

In this example, the modified Normal Boundary Intersection algorithm (mNBI) is used to
solve the :class:`.FonsecaFleming` optimization problem :cite:`fonseca1995overview`:

.. math::

   \begin{aligned}
   \text{minimize the objective function }
   & f_1(x) = 1 - exp(-\sum_{i=1}^{d}((x_i - 1 / sqrt(d)) ^ 2)) \\
   & f_2(x) = 1 + exp(-\sum_{i=1}^{d}((x_i + 1 / sqrt(d)) ^ 2)) \\
   \text{with respect to the design variables }&x\\
   \text{subject to the bound constraint}
   & x\in[-4,4]^d
   \end{aligned}

We also show how the Pareto front can be refined.

.. GENERATED FROM PYTHON SOURCE LINES 40-51

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import execute_algo
    from gemseo import execute_post
    from gemseo.problems.analytical.fonseca_fleming import FonsecaFleming

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 52-58

Solve the Fonseca-Fleming optimization problem
----------------------------------------------
The 3 sub-optimization problems of mNBI are solved with SLSQP,
a gradient-based optimization algorithm from the NLOPT library,
with a maximum of 100 iterations.
The analytic gradients are provided.

.. GENERATED FROM PYTHON SOURCE LINES 58-67

.. code-block:: Python

    opt_problem = FonsecaFleming()
    result = execute_algo(
        opt_problem,
        "MNBI",
        max_iter=1000,
        sub_optim_max_iter=100,
        n_sub_optim=3,
        sub_optim_algo="NLOPT_SLSQP",
    )




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

 .. code-block:: none

        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize FonsecaFleming
        INFO - 13:53:09:    with respect to x
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09: Solving optimization problem with algorithm MNBI:
        INFO - 13:53:09: Searching for the individual optimum of each objective
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize f_0
        INFO - 13:53:09:    with respect to x
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:      1%|          | 6/1000 [00:00<00:03, 311.04 it/sec, obj=[3.45593287e-09 9.81688668e-01]]
        INFO - 13:53:09:      1%|          | 7/1000 [00:00<00:02, 341.27 it/sec, obj=[0.         0.98168436]]
        INFO - 13:53:09:      1%|          | 8/1000 [00:00<00:02, 369.28 it/sec, obj=[0.         0.98168436]]
        INFO - 13:53:09:      1%|          | 9/1000 [00:00<00:02, 408.97 it/sec, obj=[0.         0.98168436]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 11
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       Objective: 0.0
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | 0.577350268484795  |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | 0.577350268484795  |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | 0.5773502684847949 |      4      | float |
        INFO - 13:53:09:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize f_1
        INFO - 13:53:09:    with respect to x
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:      1%|          | 10/1000 [00:00<00:03, 254.45 it/sec, obj=[0.95084904 0.06744148]]
        INFO - 13:53:09:      1%|          | 11/1000 [00:00<00:03, 271.46 it/sec, obj=[0.99997026 0.77891095]]
        INFO - 13:53:09:      1%|          | 12/1000 [00:00<00:03, 293.59 it/sec, obj=[0.98859846 0.01317993]]
        INFO - 13:53:09:      1%|▏         | 13/1000 [00:00<00:03, 299.85 it/sec, obj=[9.81345634e-01 2.10356748e-05]]
        INFO - 13:53:09:      1%|▏         | 14/1000 [00:00<00:03, 314.07 it/sec, obj=[9.81688668e-01 3.45593287e-09]]
        INFO - 13:53:09:      2%|▏         | 15/1000 [00:00<00:03, 327.81 it/sec, obj=[0.98168436 0.        ]]
        INFO - 13:53:09:      2%|▏         | 16/1000 [00:00<00:02, 340.57 it/sec, obj=[0.98168436 0.        ]]
        INFO - 13:53:09:      2%|▏         | 17/1000 [00:00<00:02, 359.22 it/sec, obj=[0.98168436 0.        ]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 11
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       Objective: 0.0
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     |  -0.577350268484795 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     |  -0.577350268484795 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | -0.5773502684847949 |      4      | float |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.5 0.5]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    |   0   |     inf     | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:      2%|▏         | 18/1000 [00:00<00:03, 268.76 it/sec, obj=[0.63212056 0.63212056]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 4
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.1439142599466381
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [ 8.32667268e-17 -1.38777878e-16]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+------------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |         Value          | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+------------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | -6.407485192731112e-17 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | -6.407485192731112e-17 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | -6.407485192731112e-17 |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    |  -0.1439142599466381   |     inf     | float |
        INFO - 13:53:09:          +------+-------------+------------------------+-------------+-------+
        INFO - 13:53:09:      2%|▏         | 19/1000 [00:00<00:04, 229.35 it/sec, obj=[0.63212056 0.63212056]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: None
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 26
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       Objective: 0.8939534673502061
        INFO - 13:53:09:    Pareto efficient solutions:
        INFO - 13:53:09:       Pareto optimal points : 6 / 19
        INFO - 13:53:09:       Utopia point : [0. 0.]
        INFO - 13:53:09:       Compromise solution (closest to utopia) : [[0.06744148 0.95084904]
        INFO - 13:53:09:        [0.95084904 0.06744148]]
        INFO - 13:53:09:       Distance from utopia : 0.9532377715846151
        INFO - 13:53:09:       Objective values:
        INFO - 13:53:09:          +------+----------+----------+-----------+-----------+
        INFO - 13:53:09:          | name |        1 |        2 |         3 |         4 |
        INFO - 13:53:09:          +------+----------+----------+-----------+-----------+
        INFO - 13:53:09:          |    1 |        0 | 0.981684 | 0.0674415 |  0.950849 |
        INFO - 13:53:09:          |    2 | 0.981684 |        0 |  0.950849 | 0.0674415 |
        INFO - 13:53:09:          +------+----------+----------+-----------+-----------+
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +-------+-------------+---------+----------+----------+-----------+-------------+-------+
        INFO - 13:53:09:          |  name | lower_bound |       1 |        2 |        3 |         4 | upper_bound |  type |
        INFO - 13:53:09:          +-------+-------------+---------+----------+----------+-----------+-------------+-------+
        INFO - 13:53:09:          | x (1) |          -4 | 0.57735 | -0.57735 | 0.424791 | -0.424791 |           4 | float |
        INFO - 13:53:09:          | x (2) |          -4 | 0.57735 | -0.57735 | 0.424791 | -0.424791 |           4 | float |
        INFO - 13:53:09:          | x (3) |          -4 | 0.57735 | -0.57735 | 0.424791 | -0.424791 |           4 | float |
        INFO - 13:53:09:          +-------+-------------+---------+----------+----------+-----------+-------------+-------+




.. GENERATED FROM PYTHON SOURCE LINES 68-74

Display the Pareto front
^^^^^^^^^^^^^^^^^^^^^^^^
|g| detects the Pareto optimal points and the dominated ones.
The Fonseca-Fleming problem is interesting because
its Pareto front is not convex.
The mNBI algorithm successfully computes it.

.. GENERATED FROM PYTHON SOURCE LINES 74-77

.. code-block:: Python


    execute_post(opt_problem, "ParetoFront", save=False, show=True)




.. image-sg:: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_001.png
   :alt: Pareto front
   :srcset: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.pareto_front.ParetoFront object at 0x7f2d21d9a520>



.. GENERATED FROM PYTHON SOURCE LINES 78-81

Solve the Fonseca-Fleming optimization problem more finely
----------------------------------------------------------
The Pareto front is then refined with 10 sub-optimizations instead of 3.

.. GENERATED FROM PYTHON SOURCE LINES 81-90

.. code-block:: Python

    opt_problem = FonsecaFleming()
    result = execute_algo(
        opt_problem,
        "MNBI",
        max_iter=1000,
        sub_optim_max_iter=100,
        n_sub_optim=10,
        sub_optim_algo="NLOPT_SLSQP",
    )




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

 .. code-block:: none

        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize FonsecaFleming
        INFO - 13:53:09:    with respect to x
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09: Solving optimization problem with algorithm MNBI:
        INFO - 13:53:09: Searching for the individual optimum of each objective
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize f_0
        INFO - 13:53:09:    with respect to x
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:      1%|          | 6/1000 [00:00<00:03, 309.22 it/sec, obj=[3.45593287e-09 9.81688668e-01]]
        INFO - 13:53:09:      1%|          | 7/1000 [00:00<00:02, 339.32 it/sec, obj=[0.         0.98168436]]
        INFO - 13:53:09:      1%|          | 8/1000 [00:00<00:02, 366.90 it/sec, obj=[0.         0.98168436]]
        INFO - 13:53:09:      1%|          | 9/1000 [00:00<00:02, 406.42 it/sec, obj=[0.         0.98168436]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 11
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       Objective: 0.0
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | 0.577350268484795  |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | 0.577350268484795  |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | 0.5773502684847949 |      4      | float |
        INFO - 13:53:09:          +------+-------------+--------------------+-------------+-------+
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize f_1
        INFO - 13:53:09:    with respect to x
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:      1%|          | 10/1000 [00:00<00:03, 257.87 it/sec, obj=[0.95084904 0.06744148]]
        INFO - 13:53:09:      1%|          | 11/1000 [00:00<00:03, 275.31 it/sec, obj=[0.99997026 0.77891095]]
        INFO - 13:53:09:      1%|          | 12/1000 [00:00<00:03, 297.78 it/sec, obj=[0.98859846 0.01317993]]
        INFO - 13:53:09:      1%|▏         | 13/1000 [00:00<00:03, 304.12 it/sec, obj=[9.81345634e-01 2.10356748e-05]]
        INFO - 13:53:09:      1%|▏         | 14/1000 [00:00<00:03, 318.43 it/sec, obj=[9.81688668e-01 3.45593287e-09]]
        INFO - 13:53:09:      2%|▏         | 15/1000 [00:00<00:02, 332.03 it/sec, obj=[0.98168436 0.        ]]
        INFO - 13:53:09:      2%|▏         | 16/1000 [00:00<00:02, 344.93 it/sec, obj=[0.98168436 0.        ]]
        INFO - 13:53:09:      2%|▏         | 17/1000 [00:00<00:02, 363.65 it/sec, obj=[0.98168436 0.        ]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 11
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       Objective: 0.0
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     |  -0.577350268484795 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     |  -0.577350268484795 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | -0.5773502684847949 |      4      | float |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.11111111 0.88888889]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |   0   |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    |   0   |     inf     | float |
        INFO - 13:53:09:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:09:      2%|▏         | 18/1000 [00:00<00:03, 273.56 it/sec, obj=[0.90043834 0.20664322]]
        INFO - 13:53:09:      2%|▏         | 19/1000 [00:00<00:03, 281.78 it/sec, obj=[0.91873293 0.15869784]]
        INFO - 13:53:09:      2%|▏         | 20/1000 [00:00<00:03, 289.92 it/sec, obj=[0.91966962 0.15614908]]
        INFO - 13:53:09:      2%|▏         | 21/1000 [00:00<00:03, 296.43 it/sec, obj=[0.91967277 0.15614049]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 7
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.04794255057736304
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [-9.53889745e-14  1.10154941e-13]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | -0.3394642613023262  |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | -0.3394642613023261  |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     |  -0.339464261302326  |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.04794255057736304 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.22222222 0.77777778]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     | -0.3394642613023262  |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     | -0.3394642613023261  |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |  -0.339464261302326  |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.04794255057736304 |     inf     | float |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:      2%|▏         | 22/1000 [00:00<00:03, 247.47 it/sec, obj=[0.91967277 0.15614049]]
        INFO - 13:53:09:      2%|▏         | 23/1000 [00:00<00:03, 254.76 it/sec, obj=[0.84203912 0.33739501]]
        INFO - 13:53:09:      2%|▏         | 24/1000 [00:00<00:03, 261.73 it/sec, obj=[0.85527677 0.31046303]]
        INFO - 13:53:09:      2%|▎         | 25/1000 [00:00<00:03, 268.14 it/sec, obj=[0.85546004 0.31007996]]
        INFO - 13:53:09:      3%|▎         | 26/1000 [00:00<00:03, 274.26 it/sec, obj=[0.85546008 0.31007988]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 8
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.09364292443480814
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [ 1.03119223e-09 -4.66331571e-10]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | -0.2256025149680226  |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | -0.2256025149680226  |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | -0.2256025149680226  |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.09364292443480814 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.33333333 0.66666667]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     | -0.2256025149680226  |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     | -0.2256025149680226  |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     | -0.2256025149680226  |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.09364292443480814 |     inf     | float |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:      3%|▎         | 27/1000 [00:00<00:04, 238.86 it/sec, obj=[0.85546008 0.31007987]]
        INFO - 13:53:09:      3%|▎         | 28/1000 [00:00<00:03, 244.52 it/sec, obj=[0.77161692 0.45984451]]
        INFO - 13:53:09:      3%|▎         | 29/1000 [00:00<00:03, 249.83 it/sec, obj=[0.77767797 0.45048948]]
        INFO - 13:53:09:      3%|▎         | 30/1000 [00:00<00:03, 255.14 it/sec, obj=[0.77769345 0.45046533]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 6
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.1255364934686558
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [-9.90765803e-12 -5.96217520e-13]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | -0.1306276041616624 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | -0.1306276041616625 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | -0.1306276041616625 |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.1255364934686558 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.44444444 0.55555556]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     | -0.1306276041616624 |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     | -0.1306276041616625 |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     | -0.1306276041616625 |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.1255364934686558 |     inf     | float |
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:      3%|▎         | 31/1000 [00:00<00:04, 227.46 it/sec, obj=[0.77769345 0.45046533]]
        INFO - 13:53:09:      3%|▎         | 32/1000 [00:00<00:04, 231.99 it/sec, obj=[0.68170374 0.57895294]]
        INFO - 13:53:09:      3%|▎         | 33/1000 [00:00<00:04, 236.54 it/sec, obj=[0.68463821 0.57556413]]
        INFO - 13:53:09:      3%|▎         | 34/1000 [00:00<00:04, 241.11 it/sec, obj=[0.68463912 0.57556308]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 6
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.14185712248151133
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [1.02950981e-12 4.25381952e-13]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | -0.04287486268043029 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | -0.04287486268043034 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | -0.04287486268043035 |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.1418571224815113  |     inf     | float |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.55555556 0.44444444]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     | -0.04287486268043029 |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     | -0.04287486268043034 |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     | -0.04287486268043035 |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.1418571224815113  |     inf     | float |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:      4%|▎         | 35/1000 [00:00<00:04, 220.02 it/sec, obj=[0.68463912 0.57556308]]
        INFO - 13:53:09:      4%|▎         | 36/1000 [00:00<00:04, 224.06 it/sec, obj=[0.57513103 0.68501143]]
        INFO - 13:53:09:      4%|▎         | 37/1000 [00:00<00:04, 228.14 it/sec, obj=[0.5755631 0.6846391]]
        INFO - 13:53:09:      4%|▍         | 38/1000 [00:00<00:04, 232.07 it/sec, obj=[0.57556308 0.68463912]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 7
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.14185712248204044
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [1.42996726e-13 3.05810932e-13]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     | 0.04287486268025626 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     | 0.04287486268025616 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     | 0.04287486268025619 |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.1418571224820404 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.66666667 0.33333333]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     | 0.04287486268025626 |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     | 0.04287486268025616 |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     | 0.04287486268025619 |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.1418571224820404 |     inf     | float |
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:      4%|▍         | 39/1000 [00:00<00:04, 214.45 it/sec, obj=[0.57556308 0.68463912]]
        INFO - 13:53:09:      4%|▍         | 40/1000 [00:00<00:04, 217.97 it/sec, obj=[0.45294727 0.77609783]]
        INFO - 13:53:09:      4%|▍         | 41/1000 [00:00<00:04, 221.59 it/sec, obj=[0.45046707 0.77769234]]
        INFO - 13:53:09:      4%|▍         | 42/1000 [00:00<00:04, 225.10 it/sec, obj=[0.45046533 0.77769345]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 6
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.1255364934616085
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [1.48561718e-13 9.68516933e-13]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     |  0.1306276041658536 |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     |  0.1306276041658536 |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     |  0.1306276041658536 |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.1255364934616085 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.77777778 0.22222222]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |  0.1306276041658536 |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |  0.1306276041658536 |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |  0.1306276041658536 |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.1255364934616085 |     inf     | float |
        INFO - 13:53:09:       +------+-------------+---------------------+-------------+-------+
        INFO - 13:53:09:      4%|▍         | 43/1000 [00:00<00:04, 210.23 it/sec, obj=[0.45046533 0.77769345]]
        INFO - 13:53:09:      4%|▍         | 44/1000 [00:00<00:04, 213.48 it/sec, obj=[0.31697497 0.85214023]]
        INFO - 13:53:09:      4%|▍         | 45/1000 [00:00<00:04, 216.71 it/sec, obj=[0.31010616 0.85544751]]
        INFO - 13:53:09:      5%|▍         | 46/1000 [00:00<00:04, 219.92 it/sec, obj=[0.31007988 0.85546008]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 6
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.09364292499323551
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [ 8.56675841e-13 -2.60819144e-12]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     |  0.225602514270673   |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     |  0.2256025142706731  |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     |  0.225602514270673   |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.09364292499323551 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09: Solving mNBI sub-problem for beta = [0.88888889 0.11111111]
        INFO - 13:53:09: Optimization problem:
        INFO - 13:53:09:    minimize -t_extraction
        INFO - 13:53:09:    with respect to t, x
        INFO - 13:53:09:    subject to constraints:
        INFO - 13:53:09:       beta_sub_optim_constraint <= 0.0
        INFO - 13:53:09:    over the design space:
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:       | x[0] |      -4     |  0.225602514270673   |      4      | float |
        INFO - 13:53:09:       | x[1] |      -4     |  0.2256025142706731  |      4      | float |
        INFO - 13:53:09:       | x[2] |      -4     |  0.225602514270673   |      4      | float |
        INFO - 13:53:09:       | t    |     -inf    | -0.09364292499323551 |     inf     | float |
        INFO - 13:53:09:       +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:      5%|▍         | 47/1000 [00:00<00:04, 206.89 it/sec, obj=[0.31007988 0.85546008]]
        INFO - 13:53:09:      5%|▍         | 48/1000 [00:00<00:04, 210.01 it/sec, obj=[0.17146323 0.91399085]]
        INFO - 13:53:09:      5%|▍         | 49/1000 [00:00<00:04, 213.12 it/sec, obj=[0.15642562 0.91956815]]
        INFO - 13:53:09:      5%|▌         | 50/1000 [00:00<00:04, 215.90 it/sec, obj=[0.1561406  0.91967273]]
        INFO - 13:53:09:      5%|▌         | 51/1000 [00:00<00:04, 218.79 it/sec, obj=[0.15614049 0.91967277]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 7
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       The solution is feasible.
        INFO - 13:53:09:       Objective: 0.04794255057731033
        INFO - 13:53:09:       Standardized constraints:
        INFO - 13:53:09:          beta_sub_optim_constraint = [-1.83464355e-14  2.24126273e-14]
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | Name | Lower bound |        Value         | Upper bound | Type  |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:          | x[0] |      -4     |  0.3394642613024756  |      4      | float |
        INFO - 13:53:09:          | x[1] |      -4     |  0.3394642613024756  |      4      | float |
        INFO - 13:53:09:          | x[2] |      -4     |  0.3394642613024756  |      4      | float |
        INFO - 13:53:09:          | t    |     -inf    | -0.04794255057731033 |     inf     | float |
        INFO - 13:53:09:          +------+-------------+----------------------+-------------+-------+
        INFO - 13:53:09:      5%|▌         | 52/1000 [00:00<00:04, 208.79 it/sec, obj=[0.15614049 0.91967277]]
        INFO - 13:53:09: Optimization result:
        INFO - 13:53:09:    Optimizer info:
        INFO - 13:53:09:       Status: None
        INFO - 13:53:09:       Message: None
        INFO - 13:53:09:       Number of calls to the objective function by the optimizer: 80
        INFO - 13:53:09:    Solution:
        INFO - 13:53:09:       Objective: 0.8939534673502061
        INFO - 13:53:09:    Pareto efficient solutions:
        INFO - 13:53:09:       Pareto optimal points : 42 / 52
        INFO - 13:53:09:       Utopia point : [0. 0.]
        INFO - 13:53:09:       Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
        INFO - 13:53:09:       Distance from utopia : 0.8939534673502061
        INFO - 13:53:09:       Objective values:
        INFO - 13:53:09:          +------+----------+----------+----------+
        INFO - 13:53:09:          | name |        1 |        2 |        3 |
        INFO - 13:53:09:          +------+----------+----------+----------+
        INFO - 13:53:09:          |    1 |        0 | 0.981684 | 0.632121 |
        INFO - 13:53:09:          |    2 | 0.981684 |        0 | 0.632121 |
        INFO - 13:53:09:          +------+----------+----------+----------+
        INFO - 13:53:09:       Design space:
        INFO - 13:53:09:          +-------+-------------+---------+----------+---+-------------+-------+
        INFO - 13:53:09:          |  name | lower_bound |       1 |        2 | 3 | upper_bound |  type |
        INFO - 13:53:09:          +-------+-------------+---------+----------+---+-------------+-------+
        INFO - 13:53:09:          | x (1) |          -4 | 0.57735 | -0.57735 | 0 |           4 | float |
        INFO - 13:53:09:          | x (2) |          -4 | 0.57735 | -0.57735 | 0 |           4 | float |
        INFO - 13:53:09:          | x (3) |          -4 | 0.57735 | -0.57735 | 0 |           4 | float |
        INFO - 13:53:09:          +-------+-------------+---------+----------+---+-------------+-------+




.. GENERATED FROM PYTHON SOURCE LINES 91-94

Display the Pareto front
^^^^^^^^^^^^^^^^^^^^^^^^
We can clearly see the effect of the refinement.

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: Python


    execute_post(opt_problem, "ParetoFront", save=False, show=True)



.. image-sg:: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_002.png
   :alt: Pareto front
   :srcset: /examples/multi_objective/images/sphx_glr_plot_mnbi_fonseca_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.pareto_front.ParetoFront object at 0x7f2d246b47f0>




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

   **Total running time of the script:** (0 minutes 0.733 seconds)


.. _sphx_glr_download_examples_multi_objective_plot_mnbi_fonseca.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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