.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/multi_objective/plot_mnbi_binh_korn.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_binh_korn.py>`
        to download the full example code.

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

.. _sphx_glr_examples_multi_objective_plot_mnbi_binh_korn.py:


Multi-objective Binh-Korn example with the mNBI algorithm
=========================================================

In this example, the modified Normal Boundary Intersection (mNBI) algorithm is used
to solve the :class:`.BinhKorn` problem :cite:`binh1997mobes`:

.. math::

   \begin{aligned}
   \text{minimize the objective function } & f_1(x, y) = 4x^2 + 4y^2 \\
   & f_2(x, y) = (x-5)^2 + (y-5)^2 \\
   \text{with respect to the design variables }&x,\,y \\
   \text{subject to the general constraints }
   & g_1(x,y) = (x-5)^2 + y^2 \leq 25.0\\
   & g_2(x, y) = (x-8)^2 + (y+3)^2 \geq 7.7\\
   \text{subject to the bound constraints }
   & 0 \leq x \leq 5.0\\
   & 0 \leq y \leq 3.0
   \end{aligned}

.. GENERATED FROM PYTHON SOURCE LINES 42-56

.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo import configure_logger
    from gemseo import execute_algo
    from gemseo import execute_post
    from gemseo.problems.multiobjective_optimization.binh_korn import BinhKorn
    from gemseo.settings.opt import MNBI_Settings

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 57-63

Solve the Binh-Korn optimization problem
----------------------------------------
The 50 sub-optimization problems of mNBI are solved with SLSQP,
a gradient-based optimization algorithm from the NLOPT library,
with a maximum of 200 iterations.
The analytic gradients are provided.

.. GENERATED FROM PYTHON SOURCE LINES 63-71

.. code-block:: Python

    problem = BinhKorn()
    mnbi_settings = MNBI_Settings(
        max_iter=10000,
        sub_optim_max_iter=200,
        n_sub_optim=50,
        sub_optim_algo="NLOPT_SLSQP",
    )
    result = execute_algo(problem, settings_model=mnbi_settings)




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

 .. code-block:: none

        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
        INFO - 20:34:33:    with respect to x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 20:34:33:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |   1   |      5      | float |
        INFO - 20:34:33:       | y    |      0      |   1   |      3      | float |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33: Solving optimization problem with algorithm MNBI:
        INFO - 20:34:33: Searching for the individual optimum of each objective
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize f_0
        INFO - 20:34:33:    with respect to x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 20:34:33:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |   1   |      5      | float |
        INFO - 20:34:33:       | y    |      0      |   1   |      3      | float |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
       ERROR - 20:34:33: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: 0.0
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          ineq1 = [0.]
        INFO - 20:34:33:          ineq2 = [-59.3]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      |   0   |      5      | float |
        INFO - 20:34:33:          | y    |      0      |   0   |      3      | float |
        INFO - 20:34:33:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize f_1
        INFO - 20:34:33:    with respect to x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 20:34:33:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |   1   |      5      | float |
        INFO - 20:34:33:       | y    |      0      |   1   |      3      | float |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
       ERROR - 20:34:33: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: 4.0
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          ineq1 = [-22.]
        INFO - 20:34:33:          ineq2 = [-7.3]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      | 4.999999999999934 |      5      | float |
        INFO - 20:34:33:          | y    |      0      |         3         |      3      | float |
        INFO - 20:34:33:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [133.2244898    4.93877551]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |   1   |      5      | float |
        INFO - 20:34:33:       | y    |      0      |   1   |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    |   0   |     inf     | float |
        INFO - 20:34:33:       +------+-------------+-------+-------------+-------+
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: -0.01998643812378128
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          beta_sub_optim_constraint = [8.48468495e-09 2.12135087e-09]
        INFO - 20:34:33:          wrapped_ineq1 = [-21.98060064]
        INFO - 20:34:33:          wrapped_ineq2 = [-8.15508884]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      |  4.860718419626012  |      5      | float |
        INFO - 20:34:33:          | y    |      0      |  2.999999999999996  |      3      | float |
        INFO - 20:34:33:          | t    |     -inf    | 0.01998643812378128 |     inf     | float |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [130.44897959   5.87755102]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |  4.860718419626012  |      5      | float |
        INFO - 20:34:33:       | y    |      0      |  2.999999999999996  |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    | 0.01998643812378128 |     inf     | float |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: -0.03911696914200459
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          beta_sub_optim_constraint = [1.07045392e-06 2.67613453e-07]
        INFO - 20:34:33:          wrapped_ineq1 = [-21.92182929]
        INFO - 20:34:33:          wrapped_ineq2 = [-9.0557122]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      |   4.72040975072545  |      5      | float |
        INFO - 20:34:33:          | y    |      0      |          3          |      3      | float |
        INFO - 20:34:33:          | t    |     -inf    | 0.03911696914200459 |     inf     | float |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [127.67346939   6.81632653]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |   4.72040975072545  |      5      | float |
        INFO - 20:34:33:       | y    |      0      |          3          |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    | 0.03911696914200459 |     inf     | float |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
       ERROR - 20:34:33: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: -0.057372362603395656
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          beta_sub_optim_constraint = [1.11930942e-06 2.79827355e-07]
        INFO - 20:34:33:          wrapped_ineq1 = [-21.82280187]
        INFO - 20:34:33:          wrapped_ineq2 = [-10.00289263]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      |   4.57905091675667  |      5      | float |
        INFO - 20:34:33:          | y    |      0      |          3          |      3      | float |
        INFO - 20:34:33:          | t    |     -inf    | 0.05737236260339566 |     inf     | float |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [124.89795918   7.75510204]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |   4.57905091675667  |      5      | float |
        INFO - 20:34:33:       | y    |      0      |          3          |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    | 0.05737236260339566 |     inf     | float |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: -0.074732674761726
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          beta_sub_optim_constraint = [1.17118362e-06 2.92795885e-07]
        INFO - 20:34:33:          wrapped_ineq1 = [-21.68260071]
        INFO - 20:34:33:          wrapped_ineq2 = [-10.99769138]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      | 4.436617985224222 |      5      | float |
        INFO - 20:34:33:          | y    |      0      |         3         |      3      | float |
        INFO - 20:34:33:          | t    |     -inf    | 0.074732674761726 |     inf     | float |
        INFO - 20:34:33:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [122.12244898   8.69387755]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      | 4.436617985224222 |      5      | float |
        INFO - 20:34:33:       | y    |      0      |         3         |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    | 0.074732674761726 |     inf     | float |
        INFO - 20:34:33:       +------+-------------+-------------------+-------------+-------+
       ERROR - 20:34:33: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: -0.09117718665696596
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          beta_sub_optim_constraint = [1.22631340e-06 3.06578345e-07]
        INFO - 20:34:33:          wrapped_ineq1 = [-21.50027273]
        INFO - 20:34:33:          wrapped_ineq2 = [-12.04121071]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      |  4.293086093376062  |      5      | float |
        INFO - 20:34:33:          | y    |      0      |          3          |      3      | float |
        INFO - 20:34:33:          | t    |     -inf    | 0.09117718665696596 |     inf     | float |
        INFO - 20:34:33:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [119.34693878   9.63265306]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      |  4.293086093376062  |      5      | float |
        INFO - 20:34:33:       | y    |      0      |          3          |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    | 0.09117718665696596 |     inf     | float |
        INFO - 20:34:33:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:33: Optimization result:
        INFO - 20:34:33:    Optimizer info:
        INFO - 20:34:33:       Status: None
        INFO - 20:34:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:33:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:33:    Solution:
        INFO - 20:34:33:       The solution is feasible.
        INFO - 20:34:33:       Objective: -0.10668436745322656
        INFO - 20:34:33:       Standardized constraints:
        INFO - 20:34:33:          beta_sub_optim_constraint = [1.28495811e-06 3.21239565e-07]
        INFO - 20:34:33:          wrapped_ineq1 = [-21.27482752]
        INFO - 20:34:33:          wrapped_ineq2 = [-13.13459605]
        INFO - 20:34:33:       Design space:
        INFO - 20:34:33:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:33:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:33:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:33:          | x    |      0      | 4.148429404209126  |      5      | float |
        INFO - 20:34:33:          | y    |      0      | 2.999999999999998  |      3      | float |
        INFO - 20:34:33:          | t    |     -inf    | 0.1066843674532266 |     inf     | float |
        INFO - 20:34:33:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:33: Solving mNBI sub-problem for phi_beta = [116.57142857  10.57142857]
        INFO - 20:34:33: Optimization problem:
        INFO - 20:34:33:    minimize -t_extraction
        INFO - 20:34:33:    with respect to t, x, y
        INFO - 20:34:33:    under the inequality constraints
        INFO - 20:34:33:       wrapped_ineq1 <= 0.0
        INFO - 20:34:33:       wrapped_ineq2 <= 0.0
        INFO - 20:34:33:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:33:    over the design space:
        INFO - 20:34:33:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:33:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:33:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:33:       | x    |      0      | 4.148429404209126  |      5      | float |
        INFO - 20:34:33:       | y    |      0      | 2.999999999999998  |      3      | float |
        INFO - 20:34:33:       | t    |     -inf    | 0.1066843674532266 |     inf     | float |
        INFO - 20:34:33:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.12123182918922926
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.34740275e-06 3.36850684e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-21.00523523]
        INFO - 20:34:34:          wrapped_ineq2 = [-14.27903845]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 4.002621052169886  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.999999999999999  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1212318291892293 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [113.79591837  11.51020408]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 4.002621052169886  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.999999999999999  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1212318291892293 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.1347962782336722
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.41395998e-06 3.53490002e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-20.69042436]
        INFO - 20:34:34:          wrapped_ineq2 = [-15.47577713]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 3.855633084900768  |      5      | float |
        INFO - 20:34:34:          | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1347962782336722 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [111.02040816  12.44897959]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 3.855633084900768  |      5      | float |
        INFO - 20:34:34:       | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1347962782336722 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.1473534631473843
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.48497408e-06 3.71243520e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-20.32927934]
        INFO - 20:34:34:          wrapped_ineq2 = [-16.72610225]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 3.707436400674776  |      5      | float |
        INFO - 20:34:34:          | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1473534631473843 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [108.24489796  13.3877551 ]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 3.707436400674776  |      5      | float |
        INFO - 20:34:34:       | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1473534631473843 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.15887811862176143
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.56082414e-06 3.90206031e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-19.92063796]
        INFO - 20:34:34:          wrapped_ineq2 = [-18.03135795]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 3.558000681121583  |      5      | float |
        INFO - 20:34:34:          | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1588781186217614 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [105.46938776  14.32653061]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 3.558000681121583  |      5      | float |
        INFO - 20:34:34:       | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1588781186217614 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 51/10000 [00:00<00:17, 556.90 it/sec, obj=[86.63747507  6.07936207]]
        INFO - 20:34:34:      1%|          | 52/10000 [00:00<00:17, 561.05 it/sec, obj=[82.45608407  6.53467094]]
        INFO - 20:34:34:      1%|          | 53/10000 [00:00<00:17, 564.79 it/sec, obj=[82.4386183   6.53671139]]
        INFO - 20:34:34:      1%|          | 54/10000 [00:00<00:17, 568.47 it/sec, obj=[82.43861798  6.53671142]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.16934390512642403
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.64192927e-06 4.10482285e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-19.46328861]
        INFO - 20:34:34:          wrapped_ineq2 = [-19.39294547]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 3.407294318804734 |      5      | float |
        INFO - 20:34:34:          | y    |      0      |         3         |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.169343905126424 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [102.69387755  15.26530612]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 3.407294318804734 |      5      | float |
        INFO - 20:34:34:       | y    |      0      |         3         |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.169343905126424 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 55/10000 [00:00<00:17, 556.47 it/sec, obj=[82.43861798  6.53671142]]
        INFO - 20:34:34:      1%|          | 56/10000 [00:00<00:17, 558.81 it/sec, obj=[82.4386183   6.53671139]]
        INFO - 20:34:34:      1%|          | 57/10000 [00:00<00:17, 562.74 it/sec, obj=[78.4046267   7.04173918]]
        INFO - 20:34:34:      1%|          | 58/10000 [00:00<00:17, 566.20 it/sec, obj=[78.38750452  7.04403274]]
        INFO - 20:34:34:      1%|          | 59/10000 [00:00<00:17, 569.80 it/sec, obj=[78.38750419  7.04403278]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.1787233438577463
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.72875264e-06 4.32188164e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-18.95596726]
        INFO - 20:34:34:          wrapped_ineq2 = [-20.8123267]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  3.25528433915987  |      5      | float |
        INFO - 20:34:34:          | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1787233438577463 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [99.91836735 16.20408163]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  3.25528433915987  |      5      | float |
        INFO - 20:34:34:       | y    |      0      |         3          |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1787233438577463 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 60/10000 [00:00<00:17, 555.65 it/sec, obj=[78.38750419  7.04403278]]
        INFO - 20:34:34:      1%|          | 61/10000 [00:00<00:17, 559.28 it/sec, obj=[74.50478473  7.6000843 ]]
        INFO - 20:34:34:      1%|          | 62/10000 [00:00<00:17, 562.46 it/sec, obj=[74.48803564  7.60264575]]
        INFO - 20:34:34:      1%|          | 63/10000 [00:00<00:17, 565.77 it/sec, obj=[74.48803531  7.6026458 ]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.18698774653318131
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.82180674e-06 4.55451708e-07]
        INFO - 20:34:34:          wrapped_ineq1 = [-18.39735425]
        INFO - 20:34:34:          wrapped_ineq2 = [-22.29102785]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 3.101936316247944  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.999999999999999  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1869877465331813 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [97.14285714 17.14285714]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 3.101936316247944  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.999999999999999  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1869877465331813 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 64/10000 [00:00<00:17, 552.56 it/sec, obj=[74.48803531  7.6026458 ]]
        INFO - 20:34:34:      1%|          | 65/10000 [00:00<00:17, 555.83 it/sec, obj=[70.75658544  8.21055954]]
        INFO - 20:34:34:      1%|          | 66/10000 [00:00<00:17, 559.34 it/sec, obj=[70.74019853  8.21247029]]
        INFO - 20:34:34:      1%|          | 67/10000 [00:00<00:17, 562.84 it/sec, obj=[70.7397555   8.21235896]]
        INFO - 20:34:34:      1%|          | 68/10000 [00:00<00:17, 565.72 it/sec, obj=[70.73968192  8.21237138]]
        INFO - 20:34:34:      1%|          | 69/10000 [00:00<00:17, 568.86 it/sec, obj=[70.73968188  8.21237139]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.19414099622670417
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [2.67250769e-07 6.68126852e-08]
        INFO - 20:34:34:          wrapped_ineq1 = [-17.92018718]
        INFO - 20:34:34:          wrapped_ineq2 = [-23.5380477]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.973627520197292  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.973627389560434  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1941409962267042 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [94.36734694 18.08163265]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.973627520197292  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.973627389560434  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1941409962267042 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 70/10000 [00:00<00:17, 558.93 it/sec, obj=[70.73968188  8.21237139]]
        INFO - 20:34:34:      1%|          | 71/10000 [00:00<00:17, 560.99 it/sec, obj=[70.73968192  8.21237138]]
        INFO - 20:34:34:      1%|          | 72/10000 [00:00<00:17, 564.12 it/sec, obj=[67.10688455  8.85599137]]
        INFO - 20:34:34:      1%|          | 73/10000 [00:00<00:17, 567.27 it/sec, obj=[67.09022377  8.85523197]]
        INFO - 20:34:34:      1%|          | 74/10000 [00:00<00:17, 570.49 it/sec, obj=[67.08836417  8.8547516 ]]
        INFO - 20:34:34:      1%|          | 75/10000 [00:00<00:17, 573.18 it/sec, obj=[67.0880443  8.8548097]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.20058310774576443
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.59261866e-08 3.98157241e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-17.67673508]
        INFO - 20:34:34:          wrapped_ineq2 = [-24.24810451]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.895860068518814  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.895860068939334  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2005831077457644 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [91.59183673 19.02040816]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.895860068518814  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.895860068939334  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2005831077457644 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 76/10000 [00:00<00:17, 560.02 it/sec, obj=[67.0880443  8.8548097]]
        INFO - 20:34:34:      1%|          | 77/10000 [00:00<00:17, 562.79 it/sec, obj=[63.53594358  9.5256767 ]]
        INFO - 20:34:34:      1%|          | 78/10000 [00:00<00:17, 565.63 it/sec, obj=[63.51929686  9.52496401]]
        INFO - 20:34:34:      1%|          | 79/10000 [00:00<00:17, 568.45 it/sec, obj=[63.51742882  9.52448661]]
        INFO - 20:34:34:      1%|          | 80/10000 [00:00<00:17, 570.96 it/sec, obj=[63.51711681  9.52454701]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.20643176428316765
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.60213212e-08 4.00534717e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-17.4199899]
        INFO - 20:34:34:          wrapped_ineq2 = [-24.97359042]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.817736612798091  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.817736606382494  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2064317642831676 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [88.81632653 19.95918367]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.817736612798091  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.817736606382494  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2064317642831676 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 81/10000 [00:00<00:17, 559.96 it/sec, obj=[63.51711681  9.52454701]]
        INFO - 20:34:34:      1%|          | 82/10000 [00:00<00:17, 562.63 it/sec, obj=[60.04682873 10.22303763]]
        INFO - 20:34:34:      1%|          | 83/10000 [00:00<00:17, 565.37 it/sec, obj=[60.03019841 10.22237318]]
        INFO - 20:34:34:      1%|          | 84/10000 [00:00<00:17, 568.16 it/sec, obj=[60.02832235 10.22189905]]
        INFO - 20:34:34:      1%|          | 85/10000 [00:00<00:17, 570.36 it/sec, obj=[60.0280183  10.22196177]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.21167873709715218
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.60891247e-08 4.02227762e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-17.14976701]
        INFO - 20:34:34:          wrapped_ineq2 = [-25.71472011]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.739252146962356  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.739252133472566  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2116787370971522 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [86.04081633 20.89795918]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.739252146962356  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.739252133472566  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2116787370971522 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 86/10000 [00:00<00:17, 561.98 it/sec, obj=[60.0280183  10.22196177]]
        INFO - 20:34:34:      1%|          | 87/10000 [00:00<00:17, 563.56 it/sec, obj=[60.0280183  10.22196177]]
        INFO - 20:34:34:      1%|          | 88/10000 [00:00<00:17, 566.17 it/sec, obj=[56.64068487 10.94846138]]
        INFO - 20:34:34:      1%|          | 89/10000 [00:00<00:17, 568.68 it/sec, obj=[56.62407339 10.94784674]]
        INFO - 20:34:34:      1%|          | 90/10000 [00:00<00:17, 571.21 it/sec, obj=[56.62218975 10.9473762 ]]
        INFO - 20:34:34:      1%|          | 91/10000 [00:00<00:17, 573.34 it/sec, obj=[56.62189378 10.94744126]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.21631560710603964
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.61276361e-08 4.03189482e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-16.86587782]
        INFO - 20:34:34:          wrapped_ineq2 = [-26.47171246]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.660401619556324  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.660401598766817  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2163156071060396 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [83.26530612 21.83673469]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.660401619556324  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.660401598766817  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2163156071060396 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 92/10000 [00:00<00:17, 562.69 it/sec, obj=[56.62189377 10.94744126]]
        INFO - 20:34:34:      1%|          | 93/10000 [00:00<00:17, 564.99 it/sec, obj=[53.31868379 11.70234427]]
        INFO - 20:34:34:      1%|          | 94/10000 [00:00<00:17, 567.49 it/sec, obj=[53.30209371 11.70178107]]
        INFO - 20:34:34:      1%|          | 95/10000 [00:00<00:17, 569.99 it/sec, obj=[53.30020299 11.70131446]]
        INFO - 20:34:34:      1%|          | 96/10000 [00:00<00:17, 572.01 it/sec, obj=[53.29991518 11.70138187]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22033375703666092
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.61356368e-08 4.03389500e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-16.5681293]
        INFO - 20:34:34:          wrapped_ineq2 = [-27.24479154]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.581179860208634  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.581179831908805  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2203337570366609 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [80.48979592 22.7755102 ]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.581179860208634  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.581179831908805  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2203337570366609 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 97/10000 [00:00<00:17, 561.97 it/sec, obj=[53.29991518 11.70138187]]
        INFO - 20:34:34:      1%|          | 98/10000 [00:00<00:17, 564.15 it/sec, obj=[50.08202514 12.48509203]]
        INFO - 20:34:34:      1%|          | 99/10000 [00:00<00:17, 566.46 it/sec, obj=[50.06545915 12.48458197]]
        INFO - 20:34:34:      1%|          | 100/10000 [00:00<00:17, 568.78 it/sec, obj=[50.06356185 12.48411964]]
        INFO - 20:34:34:      1%|          | 101/10000 [00:00<00:17, 570.65 it/sec, obj=[50.06328232 12.48418943]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22372436483038086
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.61119189e-08 4.02796374e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-16.25632384]
        INFO - 20:34:34:          wrapped_ineq2 = [-28.03418671]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.501581575675593  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.501581539671863  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2237243648303809 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [77.71428571 23.71428571]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.501581575675593  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.501581539671863  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2237243648303809 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 102/10000 [00:00<00:17, 559.56 it/sec, obj=[50.06328232 12.48418943]]
        INFO - 20:34:34:      1%|          | 103/10000 [00:00<00:17, 561.65 it/sec, obj=[46.93193733 13.29712012]]
        INFO - 20:34:34:      1%|          | 104/10000 [00:00<00:17, 563.80 it/sec, obj=[46.91539824 13.29666496]]
        INFO - 20:34:34:      1%|          | 105/10000 [00:00<00:17, 565.86 it/sec, obj=[46.91349492 13.2962073 ]]
        INFO - 20:34:34:      1%|          | 106/10000 [00:00<00:17, 567.74 it/sec, obj=[46.91322377 13.29627947]]
       ERROR - 20:34:34: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22647839676434958
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.60554023e-08 4.01386124e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-15.93025908]
        INFO - 20:34:34:          wrapped_ineq2 = [-28.84013285]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.421601345713955  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.421601301831813  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2264783967643496 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [74.93877551 24.65306122]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.421601345713955  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.421601301831813  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2264783967643496 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 107/10000 [00:00<00:17, 558.37 it/sec, obj=[46.91322377 13.29627947]]
        INFO - 20:34:34:      1%|          | 108/10000 [00:00<00:17, 560.35 it/sec, obj=[43.86967855 14.13885408]]
        INFO - 20:34:34:      1%|          | 109/10000 [00:00<00:17, 562.44 it/sec, obj=[43.8531693  14.13845566]]
        INFO - 20:34:34:      1%|          | 110/10000 [00:00<00:17, 564.56 it/sec, obj=[43.85126056 14.13800305]]
        INFO - 20:34:34:      1%|          | 111/10000 [00:00<00:17, 566.30 it/sec, obj=[43.85099789 14.13807762]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22858660027279698
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.59653339e-08 3.99136368e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-15.58972776]
        INFO - 20:34:34:          wrapped_ineq2 = [-29.66287052]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.341233618773758 |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.341233566859697 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.228586600272797 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [72.16326531 25.59183673]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.341233618773758 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.341233566859697 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.228586600272797 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 112/10000 [00:00<00:17, 557.02 it/sec, obj=[43.85099789 14.13807762]]
        INFO - 20:34:34:      1%|          | 113/10000 [00:00<00:17, 558.83 it/sec, obj=[40.89653773 15.01072985]]
        INFO - 20:34:34:      1%|          | 114/10000 [00:00<00:17, 560.83 it/sec, obj=[40.88006141 15.01039006]]
        INFO - 20:34:34:      1%|          | 115/10000 [00:00<00:17, 562.84 it/sec, obj=[40.87814788 15.00994293]]
        INFO - 20:34:34:      1%|          | 116/10000 [00:00<00:17, 564.61 it/sec, obj=[40.8778938 15.0100199]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.2300394964522294
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.58414366e-08 3.96036626e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-15.23451757]
        INFO - 20:34:34:          wrapped_ineq2 = [-30.50264619]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.260472707501503  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.260472647424826  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2300394964522294 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [69.3877551  26.53061224]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.260472707501503  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.260472647424826  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2300394964522294 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 117/10000 [00:00<00:17, 556.62 it/sec, obj=[40.8778938 15.0100199]]
        INFO - 20:34:34:      1%|          | 118/10000 [00:00<00:17, 558.47 it/sec, obj=[38.01383568 15.91319413]]
        INFO - 20:34:34:      1%|          | 119/10000 [00:00<00:17, 560.39 it/sec, obj=[37.99739551 15.91291495]]
        INFO - 20:34:34:      1%|          | 120/10000 [00:00<00:17, 562.37 it/sec, obj=[37.99547788 15.91247373]]
        INFO - 20:34:34:      1%|          | 121/10000 [00:00<00:17, 564.02 it/sec, obj=[37.99523249 15.91255313]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.23082737223334543
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.56837494e-08 3.92091692e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-14.86441091]
        INFO - 20:34:34:          wrapped_ineq2 = [-31.35971238]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.179312784043387  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.179312715697836  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2308273722333454 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [66.6122449  27.46938776]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.179312784043387  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.179312715697836  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2308273722333454 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|          | 122/10000 [00:00<00:17, 556.21 it/sec, obj=[37.99523249 15.91255313]]
        INFO - 20:34:34:      1%|          | 123/10000 [00:00<00:17, 557.99 it/sec, obj=[35.22292611 16.84670478]]
        INFO - 20:34:34:      1%|          | 124/10000 [00:00<00:17, 559.83 it/sec, obj=[35.20652549 16.84648825]]
        INFO - 20:34:34:      1%|▏         | 125/10000 [00:00<00:17, 561.76 it/sec, obj=[35.20460449 16.84605342]]
        INFO - 20:34:34:      1%|▏         | 126/10000 [00:00<00:17, 563.35 it/sec, obj=[35.20436789 16.84613524]]
        INFO - 20:34:34:      1%|▏         | 127/10000 [00:00<00:17, 564.98 it/sec, obj=[35.20436789 16.84613524]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.2309402722013747
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.54922830e-08 3.87308674e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-14.47918481]
        INFO - 20:34:34:          wrapped_ineq2 = [-32.23432794]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.097747875137614  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.097747798442793  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2309402722013747 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [63.83673469 28.40816327]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.097747875137614  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.097747798442793  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2309402722013747 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|▏         | 128/10000 [00:00<00:17, 556.73 it/sec, obj=[35.20436789 16.84613524]]
        INFO - 20:34:34:      1%|▏         | 129/10000 [00:00<00:17, 558.30 it/sec, obj=[32.52519687 17.81173117]]
        INFO - 20:34:34:      1%|▏         | 130/10000 [00:00<00:17, 560.02 it/sec, obj=[32.50883935 17.81157943]]
        INFO - 20:34:34:      1%|▏         | 131/10000 [00:00<00:17, 561.77 it/sec, obj=[32.50691576 17.81115147]]
        INFO - 20:34:34:      1%|▏         | 132/10000 [00:00<00:17, 563.25 it/sec, obj=[32.50668806 17.81123573]]
        INFO - 20:34:34:      1%|▏         | 133/10000 [00:00<00:17, 564.80 it/sec, obj=[32.50668806 17.81123573]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.23036799004535574
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.52679220e-08 3.81699117e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-14.07861062]
        INFO - 20:34:34:          wrapped_ineq2 = [-33.12675824]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.015771856984091  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.015771771886646  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2303679900453557 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [61.06122449 29.34693878]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.015771856984091  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.015771771886646  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2303679900453557 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|▏         | 134/10000 [00:00<00:17, 557.66 it/sec, obj=[32.50668806 17.81123573]]
        INFO - 20:34:34:      1%|▏         | 135/10000 [00:00<00:17, 559.24 it/sec, obj=[29.92207113 18.80875463]]
        INFO - 20:34:34:      1%|▏         | 136/10000 [00:00<00:17, 560.84 it/sec, obj=[29.90576043 18.8086699 ]]
        INFO - 20:34:34:      1%|▏         | 137/10000 [00:00<00:17, 562.51 it/sec, obj=[29.90383509 18.80824933]]
        INFO - 20:34:34:      1%|▏         | 138/10000 [00:00<00:17, 563.90 it/sec, obj=[29.9036164  18.80833604]]
        INFO - 20:34:34:      1%|▏         | 139/10000 [00:00<00:17, 565.40 it/sec, obj=[29.9036164  18.80833604]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22910005961555657
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.50115760e-08 3.75289311e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-13.66245391]
        INFO - 20:34:34:          wrapped_ineq2 = [-34.03727539]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.933378449878997  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.933378356353534  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2291000596155566 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [58.28571429 30.28571429]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.933378449878997  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.933378356353534  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2291000596155566 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|▏         | 140/10000 [00:00<00:17, 560.58 it/sec, obj=[29.9036164  18.80833604]]
        INFO - 20:34:34:      1%|▏         | 141/10000 [00:00<00:17, 561.45 it/sec, obj=[29.9036164  18.80833604]]
        INFO - 20:34:34:      1%|▏         | 142/10000 [00:00<00:17, 562.97 it/sec, obj=[27.41500866 19.83826888]]
        INFO - 20:34:34:      1%|▏         | 143/10000 [00:00<00:17, 564.62 it/sec, obj=[27.39874869 19.83825346]]
        INFO - 20:34:34:      1%|▏         | 144/10000 [00:00<00:17, 566.29 it/sec, obj=[27.39682249 19.83784083]]
        INFO - 20:34:34:      1%|▏         | 145/10000 [00:00<00:17, 567.70 it/sec, obj=[27.3966129  19.83792999]]
        INFO - 20:34:34:      1%|▏         | 146/10000 [00:00<00:17, 569.11 it/sec, obj=[27.3966129  19.83792999]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22712574556687226
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.47244741e-08 3.68110342e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-13.23047421]
        INFO - 20:34:34:          wrapped_ineq2 = [-34.96615851]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.850561212600975  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.850561110650689  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2271257455668723 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [55.51020408 31.2244898 ]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.850561212600975  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.850561110650689  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2271257455668723 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      1%|▏         | 147/10000 [00:00<00:17, 558.49 it/sec, obj=[27.3966129  19.83792999]]
        INFO - 20:34:34:      1%|▏         | 148/10000 [00:00<00:17, 559.78 it/sec, obj=[25.00550716 20.90078046]]
        INFO - 20:34:34:      1%|▏         | 149/10000 [00:00<00:17, 561.23 it/sec, obj=[24.98930201 20.90083674]]
        INFO - 20:34:34:      2%|▏         | 150/10000 [00:00<00:17, 562.74 it/sec, obj=[24.98737592 20.90043263]]
        INFO - 20:34:34:      2%|▏         | 151/10000 [00:00<00:17, 563.72 it/sec, obj=[24.98717553 20.90052426]]
        INFO - 20:34:34:      2%|▏         | 152/10000 [00:00<00:17, 565.00 it/sec, obj=[24.98717553 20.90052426]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22443403356452646
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.44083359e-08 3.60209285e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-12.7824248]
        INFO - 20:34:34:          wrapped_ineq2 = [-35.91369398]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.767313536534702  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.767313426191696  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2244340335645265 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [52.73469388 32.16326531]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.767313536534702  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.767313426191696  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2244340335645265 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 153/10000 [00:00<00:17, 560.12 it/sec, obj=[24.98717553 20.90052426]]
        INFO - 20:34:34:      2%|▏         | 154/10000 [00:00<00:17, 560.95 it/sec, obj=[24.98717553 20.90052426]]
        INFO - 20:34:34:      2%|▏         | 155/10000 [00:00<00:17, 562.35 it/sec, obj=[22.69510365 21.99680919]]
        INFO - 20:34:34:      2%|▏         | 156/10000 [00:00<00:17, 563.82 it/sec, obj=[22.67895762 21.99693969]]
        INFO - 20:34:34:      2%|▏         | 157/10000 [00:00<00:17, 565.28 it/sec, obj=[22.67703266 21.9965447 ]]
        INFO - 20:34:34:      2%|▏         | 158/10000 [00:00<00:17, 566.56 it/sec, obj=[22.67684157 21.99663879]]
       ERROR - 20:34:34: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.2210136200267818
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.40650158e-08 3.51628948e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-12.31805248]
        INFO - 20:34:34:          wrapped_ineq2 = [-36.88017568]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.683628639516674  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.683628520841981  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2210136200267818 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [49.95918367 33.10204082]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.683628639516674  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.683628520841981  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2210136200267818 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 159/10000 [00:00<00:17, 560.02 it/sec, obj=[22.67684157 21.99663879]]
        INFO - 20:34:34:      2%|▏         | 160/10000 [00:00<00:17, 561.29 it/sec, obj=[20.48537592 23.12688872]]
        INFO - 20:34:34:      2%|▏         | 161/10000 [00:00<00:17, 562.70 it/sec, obj=[20.46929353 23.12709601]]
        INFO - 20:34:34:      2%|▏         | 162/10000 [00:00<00:17, 564.14 it/sec, obj=[20.46737079 23.1267108 ]]
        INFO - 20:34:34:      2%|▏         | 163/10000 [00:00<00:17, 565.37 it/sec, obj=[20.4671891  23.12680736]]
        INFO - 20:34:34:      2%|▏         | 164/10000 [00:00<00:17, 566.65 it/sec, obj=[20.4671891  23.12680736]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.21685290137763716
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.36969263e-08 3.42422446e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-11.83709732]
        INFO - 20:34:34:          wrapped_ineq2 = [-37.86590532]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  1.59949955938698  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.599499432470258  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2168529013776372 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [47.18367347 34.04081633]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  1.59949955938698  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.599499432470258  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2168529013776372 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 165/10000 [00:00<00:17, 562.46 it/sec, obj=[20.4671891  23.12680736]]
        INFO - 20:34:34:      2%|▏         | 166/10000 [00:00<00:17, 563.24 it/sec, obj=[20.4671891  23.12680736]]
        INFO - 20:34:34:      2%|▏         | 167/10000 [00:00<00:17, 564.58 it/sec, obj=[18.37794411 24.29156696]]
        INFO - 20:34:34:      2%|▏         | 168/10000 [00:00<00:17, 565.90 it/sec, obj=[18.36193008 24.29185378]]
        INFO - 20:34:34:      2%|▏         | 169/10000 [00:00<00:17, 567.29 it/sec, obj=[18.36001075 24.29147902]]
        INFO - 20:34:34:      2%|▏         | 170/10000 [00:00<00:17, 568.39 it/sec, obj=[18.35983854 24.29157804]]
        INFO - 20:34:34:      2%|▏         | 171/10000 [00:00<00:17, 569.57 it/sec, obj=[18.35983854 24.29157804]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.21193996278057933
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.33062201e-08 3.32653372e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-11.33929244]
        INFO - 20:34:34:          wrapped_ineq2 = [-38.87119268]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.514919147229693  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.514919012188628  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2119399627805793 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [44.40816327 34.97959184]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.514919147229693  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.514919012188628  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2119399627805793 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 172/10000 [00:00<00:17, 565.38 it/sec, obj=[18.35983854 24.29157804]]
        INFO - 20:34:34:      2%|▏         | 173/10000 [00:00<00:17, 566.12 it/sec, obj=[18.35983854 24.29157804]]
        INFO - 20:34:34:      2%|▏         | 174/10000 [00:00<00:17, 567.39 it/sec, obj=[16.37447224 25.49140673]]
        INFO - 20:34:34:      2%|▏         | 175/10000 [00:00<00:17, 568.72 it/sec, obj=[16.35853156 25.49177588]]
        INFO - 20:34:34:      2%|▏         | 176/10000 [00:00<00:17, 570.05 it/sec, obj=[16.35661687 25.4914123 ]]
        INFO - 20:34:34:      2%|▏         | 177/10000 [00:00<00:17, 571.15 it/sec, obj=[16.35645426 25.49151379]]
        INFO - 20:34:34:      2%|▏         | 178/10000 [00:00<00:17, 572.30 it/sec, obj=[16.35645426 25.49151379]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.2062625663224441
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.28956579e-08 3.22393312e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-10.8243637]
        INFO - 20:34:34:          wrapped_ineq2 = [-39.89635594]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  1.42988006028335  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.429879917262757  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2062625663224441 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [41.63265306 35.91836735]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  1.42988006028335  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.429879917262757  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2062625663224441 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 179/10000 [00:00<00:17, 567.55 it/sec, obj=[16.35645426 25.49151379]]
        INFO - 20:34:34:      2%|▏         | 180/10000 [00:00<00:17, 568.06 it/sec, obj=[16.35645426 25.49151379]]
        INFO - 20:34:34:      2%|▏         | 181/10000 [00:00<00:17, 569.26 it/sec, obj=[14.47666997 26.72698623]]
        INFO - 20:34:34:      2%|▏         | 182/10000 [00:00<00:17, 570.45 it/sec, obj=[14.46080786 26.72744066]]
        INFO - 20:34:34:      2%|▏         | 183/10000 [00:00<00:17, 571.66 it/sec, obj=[14.45889916 26.72708902]]
        INFO - 20:34:34:      2%|▏         | 184/10000 [00:00<00:17, 572.74 it/sec, obj=[14.45874622 26.72719297]]
        INFO - 20:34:34:      2%|▏         | 185/10000 [00:00<00:17, 573.87 it/sec, obj=[14.45874622 26.72719297]]
        INFO - 20:34:34:      2%|▏         | 186/10000 [00:00<00:17, 574.93 it/sec, obj=[14.45874622 26.72719297]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.19980813861420837
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.24679964e-08 3.11698045e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-10.29202946]
        INFO - 20:34:34:          wrapped_ineq2 = [-40.94172201]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.344374754501563  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.344374603672217  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1998081386142084 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [38.85714286 36.85714286]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.344374754501563  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.344374603672217  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1998081386142084 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 187/10000 [00:00<00:17, 569.16 it/sec, obj=[14.45874622 26.72719297]]
        INFO - 20:34:34:      2%|▏         | 188/10000 [00:00<00:17, 570.29 it/sec, obj=[12.68629432 27.99889971]]
        INFO - 20:34:34:      2%|▏         | 189/10000 [00:00<00:17, 571.47 it/sec, obj=[12.67051626 27.99944249]]
        INFO - 20:34:34:      2%|▏         | 190/10000 [00:00<00:17, 572.70 it/sec, obj=[12.66861499 27.99910359]]
        INFO - 20:34:34:      2%|▏         | 191/10000 [00:00<00:17, 573.67 it/sec, obj=[12.66847181 27.99921   ]]
       ERROR - 20:34:34: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.19256375777317306
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.20261276e-08 3.00653902e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-9.74200027]
        INFO - 20:34:34:          wrapped_ineq2 = [-42.00762687]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.258395476742429  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.258395318299658  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1925637577731731 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [36.08163265 37.79591837]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.258395476742429  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.258395318299658  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1925637577731731 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 192/10000 [00:00<00:17, 568.18 it/sec, obj=[12.66847181 27.99921   ]]
        INFO - 20:34:34:      2%|▏         | 193/10000 [00:00<00:17, 569.25 it/sec, obj=[11.00515155 29.30775805]]
        INFO - 20:34:34:      2%|▏         | 194/10000 [00:00<00:17, 570.43 it/sec, obj=[10.98946331 29.30839237]]
        INFO - 20:34:34:      2%|▏         | 195/10000 [00:00<00:17, 571.60 it/sec, obj=[10.98757099 29.30806707]]
        INFO - 20:34:34:      2%|▏         | 196/10000 [00:00<00:17, 572.64 it/sec, obj=[10.98743766 29.30817594]]
        INFO - 20:34:34:      2%|▏         | 197/10000 [00:00<00:17, 573.70 it/sec, obj=[10.98743766 29.30817594]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.18451613974837508
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.15728334e-08 2.89322699e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-9.17397857]
        INFO - 20:34:34:          wrapped_ineq2 = [-43.09441589]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.171934256563914  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.171934090725966  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1845161397483751 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [33.30612245 38.73469388]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.171934256563914  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.171934090725966  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1845161397483751 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 198/10000 [00:00<00:17, 567.97 it/sec, obj=[10.98743766 29.30817594]]
        INFO - 20:34:34:      2%|▏         | 199/10000 [00:00<00:17, 569.04 it/sec, obj=[ 9.43509909 30.65418945]]
        INFO - 20:34:34:      2%|▏         | 200/10000 [00:00<00:17, 570.14 it/sec, obj=[ 9.41950673 30.65491867]]
        INFO - 20:34:34:      2%|▏         | 201/10000 [00:00<00:17, 571.28 it/sec, obj=[ 9.41762501 30.65460787]]
        INFO - 20:34:34:      2%|▏         | 202/10000 [00:00<00:17, 572.16 it/sec, obj=[ 9.4175016  30.65471918]]
        INFO - 20:34:34:      2%|▏         | 203/10000 [00:00<00:17, 573.17 it/sec, obj=[ 9.4175016  30.65471918]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.17565162394828981
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.11113643e-08 2.77783130e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-8.58765836]
        INFO - 20:34:34:          wrapped_ineq2 = [-44.20244425]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.084982897600546  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.084982724606786  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1756516239482898 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [30.53061224 39.67346939]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.084982897600546  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.084982724606786  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1756516239482898 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 204/10000 [00:00<00:17, 568.53 it/sec, obj=[ 9.4175016  30.65471918]]
        INFO - 20:34:34:      2%|▏         | 205/10000 [00:00<00:17, 569.51 it/sec, obj=[ 7.97804763 32.03884013]]
        INFO - 20:34:34:      2%|▏         | 206/10000 [00:00<00:17, 570.56 it/sec, obj=[ 7.96255753 32.03966771]]
        INFO - 20:34:34:      2%|▏         | 207/10000 [00:00<00:17, 571.64 it/sec, obj=[ 7.96068815 32.03937238]]
        INFO - 20:34:34:      2%|▏         | 208/10000 [00:00<00:17, 572.57 it/sec, obj=[ 7.96057475 32.03948612]]
        INFO - 20:34:34:      2%|▏         | 209/10000 [00:00<00:17, 573.42 it/sec, obj=[ 7.96057475 32.03948612]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.16595615812678902
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.06442215e-08 2.66106248e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-7.98272487]
        INFO - 20:34:34:          wrapped_ineq2 = [-45.33207732]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.9975329684950597 |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 0.9975327886040215 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.165956158126789  |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [27.75510204 40.6122449 ]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 0.9975329684950597 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 0.9975327886040215 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.165956158126789  |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 210/10000 [00:00<00:17, 568.76 it/sec, obj=[ 7.96057475 32.03948612]]
        INFO - 20:34:34:      2%|▏         | 211/10000 [00:00<00:17, 569.76 it/sec, obj=[ 6.63596326 33.46237501]]
        INFO - 20:34:34:      2%|▏         | 212/10000 [00:00<00:17, 570.83 it/sec, obj=[ 6.62058212 33.46330461]]
        INFO - 20:34:34:      2%|▏         | 213/10000 [00:00<00:17, 571.70 it/sec, obj=[ 6.61872696 33.46302576]]
        INFO - 20:34:34:      2%|▏         | 214/10000 [00:00<00:17, 572.60 it/sec, obj=[ 6.61862363 33.46314191]]
        INFO - 20:34:34:      2%|▏         | 215/10000 [00:00<00:17, 573.04 it/sec, obj=[ 6.61862363 33.46314191]]
        INFO - 20:34:34:      2%|▏         | 216/10000 [00:00<00:17, 573.89 it/sec, obj=[ 6.61862363 33.46314191]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.15541528248005268
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [1.01742508e-08 2.54357690e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-7.3588542]
        INFO - 20:34:34:          wrapped_ineq2 = [-46.48369104]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.9095757933566083 |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 0.9095756068439402 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1554152824800527 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [24.97959184 41.55102041]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 0.9095757933566083 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 0.9095756068439402 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1554152824800527 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 217/10000 [00:00<00:17, 570.44 it/sec, obj=[ 6.61862363 33.46314191]]
        INFO - 20:34:34:      2%|▏         | 218/10000 [00:00<00:17, 570.89 it/sec, obj=[ 6.61862363 33.46314191]]
        INFO - 20:34:34:      2%|▏         | 219/10000 [00:00<00:17, 571.86 it/sec, obj=[ 5.41086973 34.92547856]]
        INFO - 20:34:34:      2%|▏         | 220/10000 [00:00<00:17, 572.85 it/sec, obj=[ 5.39560462 34.92651398]]
        INFO - 20:34:34:      2%|▏         | 221/10000 [00:00<00:17, 573.88 it/sec, obj=[ 5.39376567 34.92625268]]
        INFO - 20:34:34:      2%|▏         | 222/10000 [00:00<00:17, 574.77 it/sec, obj=[ 5.39367249 34.92637122]]
        INFO - 20:34:34:      2%|▏         | 223/10000 [00:00<00:16, 575.67 it/sec, obj=[ 5.39367249 34.92637122]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.14401411290347046
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [9.70410241e-09 2.42604159e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-6.71571295]
        INFO - 20:34:34:          wrapped_ineq2 = [-47.6576724]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.8211024417149247 |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 0.8211022488712774 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1440141129034705 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [22.20408163 42.48979592]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 0.8211024417149247 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 0.8211022488712774 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1440141129034705 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 224/10000 [00:00<00:17, 572.19 it/sec, obj=[ 5.39367249 34.92637122]]
        INFO - 20:34:34:      2%|▏         | 225/10000 [00:00<00:17, 572.66 it/sec, obj=[ 5.39367249 34.92637122]]
        INFO - 20:34:34:      2%|▏         | 226/10000 [00:00<00:17, 573.54 it/sec, obj=[ 4.30485089 36.42885552]]
        INFO - 20:34:34:      2%|▏         | 227/10000 [00:00<00:17, 574.53 it/sec, obj=[ 4.28970922 36.43000074]]
        INFO - 20:34:34:      2%|▏         | 228/10000 [00:00<00:16, 575.47 it/sec, obj=[ 4.28788864 36.42975814]]
        INFO - 20:34:34:      2%|▏         | 229/10000 [00:00<00:16, 576.26 it/sec, obj=[ 4.28780567 36.42987905]]
        INFO - 20:34:34:      2%|▏         | 230/10000 [00:00<00:16, 577.11 it/sec, obj=[ 4.28780567 36.42987905]]
       ERROR - 20:34:34: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.13173732335367283
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [9.23635923e-09 2.30908626e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-6.05295781]
        INFO - 20:34:34:          wrapped_ineq2 = [-48.85441989]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.7321037179375566 |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 0.7321035190664417 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1317373233536728 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [19.42857143 43.42857143]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 0.7321037179375566 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 0.7321035190664417 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1317373233536728 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 231/10000 [00:00<00:17, 571.57 it/sec, obj=[ 4.28780567 36.42987905]]
        INFO - 20:34:34:      2%|▏         | 232/10000 [00:00<00:17, 572.48 it/sec, obj=[ 3.32005317 37.97323185]]
        INFO - 20:34:34:      2%|▏         | 233/10000 [00:00<00:17, 573.46 it/sec, obj=[ 3.30504278 37.97449102]]
        INFO - 20:34:34:      2%|▏         | 234/10000 [00:00<00:17, 574.41 it/sec, obj=[ 3.30324284 37.97426832]]
        INFO - 20:34:34:      2%|▏         | 235/10000 [00:00<00:16, 575.23 it/sec, obj=[ 3.30317013 37.97439158]]
        INFO - 20:34:34:      2%|▏         | 236/10000 [00:00<00:16, 576.12 it/sec, obj=[ 3.30317013 37.97439158]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.1185691272565207
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [8.77297524e-09 2.19327045e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-5.37023516]
        INFO - 20:34:34:          wrapped_ineq2 = [-50.07434394]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.6425701500746512 |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 0.6425699454903127 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1185691272565207 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [16.65306122 44.36734694]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 0.6425701500746512 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 0.6425699454903127 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1185691272565207 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 237/10000 [00:00<00:17, 571.92 it/sec, obj=[ 3.30317013 37.97439158]]
        INFO - 20:34:34:      2%|▏         | 238/10000 [00:00<00:17, 572.81 it/sec, obj=[ 2.45868826 39.55935553]]
        INFO - 20:34:34:      2%|▏         | 239/10000 [00:00<00:17, 573.77 it/sec, obj=[ 2.44381739 39.56073302]]
        INFO - 20:34:34:      2%|▏         | 240/10000 [00:00<00:16, 574.73 it/sec, obj=[ 2.44204056 39.56053151]]
        INFO - 20:34:34:      2%|▏         | 241/10000 [00:00<00:16, 575.54 it/sec, obj=[ 2.44197816 39.56065708]]
        INFO - 20:34:34:      2%|▏         | 242/10000 [00:00<00:16, 576.40 it/sec, obj=[ 2.44197816 39.56065708]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.10449325789723277
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [8.31663449e-09 2.07913864e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-4.66718063]
        INFO - 20:34:34:          wrapped_ineq2 = [-51.3178675]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.552491978093023  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 0.552491768118351  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.1044932578972328 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [13.87755102 45.30612245]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 0.552491978093023  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 0.552491768118351  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.1044932578972328 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:      2%|▏         | 243/10000 [00:00<00:17, 572.35 it/sec, obj=[ 2.44197816 39.56065708]]
        INFO - 20:34:34:      2%|▏         | 244/10000 [00:00<00:17, 573.16 it/sec, obj=[ 1.72303596 41.18799761]]
        INFO - 20:34:34:      2%|▏         | 245/10000 [00:00<00:16, 574.06 it/sec, obj=[ 1.70831329 41.18949797]]
        INFO - 20:34:34:      2%|▏         | 246/10000 [00:00<00:16, 575.01 it/sec, obj=[ 1.70656219 41.18931901]]
        INFO - 20:34:34:      2%|▏         | 247/10000 [00:00<00:16, 575.79 it/sec, obj=[ 1.70651014 41.18944686]]
        INFO - 20:34:34:      2%|▏         | 248/10000 [00:00<00:16, 576.62 it/sec, obj=[ 1.70651014 41.18944686]]
        INFO - 20:34:34:      2%|▏         | 249/10000 [00:00<00:16, 577.42 it/sec, obj=[ 1.70651014 41.18944686]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.08949294772366469
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [7.86864796e-09 1.96713668e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-3.94341862]
        INFO - 20:34:34:          wrapped_ineq2 = [-52.58542653]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  0.4618591414580615 |      5      | float |
        INFO - 20:34:34:          | y    |      0      |  0.4618589264225835 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.08949294772366469 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [11.10204082 46.24489796]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  0.4618591414580615 |      5      | float |
        INFO - 20:34:34:       | y    |      0      |  0.4618589264225835 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.08949294772366469 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:      2%|▎         | 250/10000 [00:00<00:17, 572.89 it/sec, obj=[ 1.70651014 41.18944686]]
        INFO - 20:34:34:      3%|▎         | 251/10000 [00:00<00:16, 573.71 it/sec, obj=[ 1.11544708 42.85995314]]
        INFO - 20:34:34:      3%|▎         | 252/10000 [00:00<00:16, 574.61 it/sec, obj=[ 1.10088177 42.86158114]]
        INFO - 20:34:34:      3%|▎         | 253/10000 [00:00<00:16, 575.52 it/sec, obj=[ 1.09915921 42.86142618]]
        INFO - 20:34:34:      3%|▎         | 254/10000 [00:00<00:16, 576.30 it/sec, obj=[ 1.09911754 42.86155626]]
        INFO - 20:34:34:      3%|▎         | 255/10000 [00:00<00:16, 577.07 it/sec, obj=[ 1.09911754 42.86155626]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.07355090648824657
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [7.43066231e-09 1.85767357e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-3.19856184]
        INFO - 20:34:34:          wrapped_ineq2 = [-53.87747056]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  0.3706612660188607 |      5      | float |
        INFO - 20:34:34:          | y    |      0      |  0.3706610462568307 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.07355090648824657 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [ 8.32653061 47.18367347]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  0.3706612660188607 |      5      | float |
        INFO - 20:34:34:       | y    |      0      |  0.3706610462568307 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.07355090648824657 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:      3%|▎         | 256/10000 [00:00<00:16, 573.39 it/sec, obj=[ 1.09911754 42.86155626]]
        INFO - 20:34:34:      3%|▎         | 257/10000 [00:00<00:16, 574.21 it/sec, obj=[ 0.63834664 44.57604226]]
        INFO - 20:34:34:      3%|▎         | 258/10000 [00:00<00:16, 575.03 it/sec, obj=[ 0.62394835 44.57780289]]
        INFO - 20:34:34:      3%|▎         | 259/10000 [00:00<00:16, 575.92 it/sec, obj=[ 0.62225734 44.57767347]]
        INFO - 20:34:34:      3%|▎         | 260/10000 [00:00<00:16, 576.66 it/sec, obj=[ 0.62222607 44.57780576]]
        INFO - 20:34:34:      3%|▎         | 261/10000 [00:00<00:16, 577.40 it/sec, obj=[ 0.62222607 44.57780576]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.05664929814788619
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [7.00442992e-09 1.75109216e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-2.43221075]
        INFO - 20:34:34:          wrapped_ineq2 = [-55.19446335]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  0.2788876501480995 |      5      | float |
        INFO - 20:34:34:          | y    |      0      |  0.2788874259967131 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.05664929814788619 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [ 5.55102041 48.12244898]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  0.2788876501480995 |      5      | float |
        INFO - 20:34:34:       | y    |      0      |  0.2788874259967131 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.05664929814788619 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:      3%|▎         | 262/10000 [00:00<00:16, 574.81 it/sec, obj=[ 0.62222607 44.57780576]]
        INFO - 20:34:34:      3%|▎         | 263/10000 [00:00<00:16, 575.24 it/sec, obj=[ 0.62222607 44.57780576]]
        INFO - 20:34:34:      3%|▎         | 264/10000 [00:00<00:16, 576.08 it/sec, obj=[ 0.29423714 46.33711132]]
        INFO - 20:34:34:      3%|▎         | 265/10000 [00:00<00:16, 576.92 it/sec, obj=[ 0.28001607 46.33900984]]
        INFO - 20:34:34:      3%|▎         | 266/10000 [00:00<00:16, 577.80 it/sec, obj=[ 0.27835982 46.3389076 ]]
        INFO - 20:34:34:      3%|▎         | 267/10000 [00:00<00:16, 578.16 it/sec, obj=[ 0.27833898 46.33904203]]
        INFO - 20:34:34:      3%|▎         | 268/10000 [00:00<00:16, 578.84 it/sec, obj=[ 0.27833898 46.33904203]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.038769716434479316
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [6.59059385e-09 1.64767378e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-1.64395306]
        INFO - 20:34:34:          wrapped_ineq2 = [-56.53688344]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  0.1865272500842602 |      5      | float |
        INFO - 20:34:34:          | y    |      0      |  0.1865270218820104 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.03876971643447932 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [ 2.7755102  49.06122449]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  0.1865272500842602 |      5      | float |
        INFO - 20:34:34:       | y    |      0      |  0.1865270218820104 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.03876971643447932 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:      3%|▎         | 269/10000 [00:00<00:16, 575.21 it/sec, obj=[ 0.27833898 46.33904203]]
        INFO - 20:34:34:      3%|▎         | 270/10000 [00:00<00:16, 575.99 it/sec, obj=[ 0.08570212 48.14403408]]
        INFO - 20:34:34:      3%|▎         | 271/10000 [00:00<00:16, 576.83 it/sec, obj=[ 0.07166903 48.14607599]]
        INFO - 20:34:34:      3%|▎         | 272/10000 [00:00<00:16, 577.68 it/sec, obj=[ 0.07005101 48.14600266]]
        INFO - 20:34:34:      3%|▎         | 273/10000 [00:00<00:16, 578.37 it/sec, obj=[ 0.07004059 48.14613918]]
        INFO - 20:34:34:      3%|▎         | 274/10000 [00:00<00:16, 579.12 it/sec, obj=[ 0.07004059 48.14613918]]
        INFO - 20:34:34:      3%|▎         | 275/10000 [00:00<00:16, 579.87 it/sec, obj=[ 0.07004059 48.14613918]]
        INFO - 20:34:34:      3%|▎         | 276/10000 [00:00<00:16, 580.61 it/sec, obj=[ 0.07004059 48.14613918]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.01989315900133865
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [6.19085672e-09 1.54771107e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-0.83336312]
        INFO - 20:34:34:          wrapped_ineq2 = [-57.9052249]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |        Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 0.09356866441943447 |      5      | float |
        INFO - 20:34:34:          | y    |      0      |  0.0935684325046217 |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.01989315900133865 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+---------------------+-------------+-------+
        INFO - 20:34:34:      3%|▎         | 277/10000 [00:00<00:18, 524.02 it/sec, obj=[ 0.07004059 48.14613918]]
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: None
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: 30.28780069872395
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          ineq1 = [-10.82436312]
        INFO - 20:34:34:          ineq2 = [-39.89635695]
        INFO - 20:34:34:    Pareto efficient solutions:
        INFO - 20:34:34:       Pareto optimal points : 203 / 277
        INFO - 20:34:34:       Utopia point : [0. 4.]
        INFO - 20:34:34:       Compromise solution (closest to utopia) : [[14.45889916 26.72708902]]
        INFO - 20:34:34:       Distance from utopia : 26.936598526003834
        INFO - 20:34:34:       Objective values:
        INFO - 20:34:34:          +------+----+-----+---------+
        INFO - 20:34:34:          | name |  1 |   2 |       3 |
        INFO - 20:34:34:          +------+----+-----+---------+
        INFO - 20:34:34:          |    1 |  0 | 136 | 14.4589 |
        INFO - 20:34:34:          |    2 | 50 |   4 | 26.7271 |
        INFO - 20:34:34:          +------+----+-----+---------+
        INFO - 20:34:34:       Constraint values:
        INFO - 20:34:34:          +------+-------+------+----------+
        INFO - 20:34:34:          | name |     1 |    2 |        3 |
        INFO - 20:34:34:          +------+-------+------+----------+
        INFO - 20:34:34:          |    1 |     0 |  -22 | -10.2918 |
        INFO - 20:34:34:          |    2 | -59.3 | -7.3 | -40.9422 |
        INFO - 20:34:34:          +------+-------+------+----------+
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +-------+-------------+---+---+---------+-------------+-------+
        INFO - 20:34:34:          |  name | lower_bound | 1 | 2 |       3 | upper_bound |  type |
        INFO - 20:34:34:          +-------+-------------+---+---+---------+-------------+-------+
        INFO - 20:34:34:          | x (1) |           0 | 0 | 5 | 1.34434 |           5 | float |
        INFO - 20:34:34:          | y (1) |           0 | 0 | 3 | 1.34442 |           3 | float |
        INFO - 20:34:34:          +-------+-------------+---+---+---------+-------------+-------+




.. GENERATED FROM PYTHON SOURCE LINES 72-75

Display the Pareto front
------------------------
|g| detects the Pareto optimal points and the dominated ones.

.. GENERATED FROM PYTHON SOURCE LINES 75-77

.. code-block:: Python

    execute_post(problem, post_name="ParetoFront", save=False, show=True)




.. image-sg:: /examples/multi_objective/images/sphx_glr_plot_mnbi_binh_korn_001.png
   :alt: Pareto front
   :srcset: /examples/multi_objective/images/sphx_glr_plot_mnbi_binh_korn_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.pareto_front.ParetoFront object at 0x785917dec7a0>



.. GENERATED FROM PYTHON SOURCE LINES 78-83

Refine the Pareto front in the user specified area
--------------------------------------------------
The Pareto front is then refined with 5 new sub-optimizations.
The ``custom_anchor_points`` argument corresponds to the bounds of
both objectives in order to define the refinement area.

.. GENERATED FROM PYTHON SOURCE LINES 83-92

.. code-block:: Python

    mnbi_settings = MNBI_Settings(
        max_iter=10000,
        sub_optim_max_iter=200,
        n_sub_optim=5,
        sub_optim_algo="NLOPT_SLSQP",
        custom_anchor_points=[array([44.5, 14]), array([29.4, 19])],
    )

    execute_algo(problem, settings_model=mnbi_settings)




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

 .. code-block:: none

        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
        INFO - 20:34:34:    with respect to x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 20:34:34:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.429879988721573 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.429879988721184 |      3      | float |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34: Solving optimization problem with algorithm MNBI:
     WARNING - 20:34:34: Option `custom_anchor_points` was set. The resulting Pareto front might be incomplete.
        INFO - 20:34:34: Searching for the individual optimum of each objective
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize f_0
        INFO - 20:34:34:    with respect to x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 20:34:34:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.429879988721573 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.429879988721184 |      3      | float |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
       ERROR - 20:34:34: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: 0.0
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          ineq1 = [0.]
        INFO - 20:34:34:          ineq2 = [-59.3]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |   0   |      5      | float |
        INFO - 20:34:34:          | y    |      0      |   0   |      3      | float |
        INFO - 20:34:34:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize f_1
        INFO - 20:34:34:    with respect to x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
        INFO - 20:34:34:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.429879988721573 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.429879988721184 |      3      | float |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
       ERROR - 20:34:34: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
        return _nlopt.opt_optimize(self, *args)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: 4.0
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          ineq1 = [-22.]
        INFO - 20:34:34:          ineq2 = [-7.3]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |   5   |      5      | float |
        INFO - 20:34:34:          | y    |      0      |   3   |      3      | float |
        INFO - 20:34:34:          +------+-------------+-------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [63.01630435 28.68566176]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value       | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.429879988721573 |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.429879988721184 |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    |         0         |     inf     | float |
        INFO - 20:34:34:       +------+-------------+-------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.23006624766887837
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [2.35958401e-05 5.89896004e-06]
        INFO - 20:34:34:          wrapped_ineq1 = [-13.95717111]
        INFO - 20:34:34:          wrapped_ineq2 = [-33.39411594]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 1.991452157953277  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 1.991468771474438  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2300662476688784 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [65.50652174 27.84338235]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 1.991452157953277  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 1.991468771474438  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2300662476688784 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.23079497225296655
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [3.84877907e-09 9.62177893e-10]
        INFO - 20:34:34:          wrapped_ineq1 = [-14.32145361]
        INFO - 20:34:34:          wrapped_ineq2 = [-32.58771023]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      |  2.06513935996432  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.065139414923385  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2307949722529666 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [67.99673913 27.00110294]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      |  2.06513935996432  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.065139414923385  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2307949722529666 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.23096895870405437
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [3.93921695e-09 9.84808679e-10]
        INFO - 20:34:34:          wrapped_ineq1 = [-14.67324895]
        INFO - 20:34:34:          wrapped_ineq2 = [-31.7958384]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.138485442599787  |      5      | float |
        INFO - 20:34:34:          | y    |      0      |  2.1384854919883   |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2309689587040544 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [70.48695652 26.15882353]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.138485442599787  |      5      | float |
        INFO - 20:34:34:       | y    |      0      |  2.1384854919883   |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2309689587040544 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.2305955098019026
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [4.02403089e-09 1.00601660e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-15.01278173]
        INFO - 20:34:34:          wrapped_ineq2 = [-31.01819989]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.211503064031537  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.211503107833047  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2305955098019026 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Solving mNBI sub-problem for phi_beta = [72.97717391 25.31654412]
        INFO - 20:34:34: Optimization problem:
        INFO - 20:34:34:    minimize -t_extraction
        INFO - 20:34:34:    with respect to t, x, y
        INFO - 20:34:34:    under the inequality constraints
        INFO - 20:34:34:       wrapped_ineq1 <= 0.0
        INFO - 20:34:34:       wrapped_ineq2 <= 0.0
        INFO - 20:34:34:       beta_sub_optim_constraint <= 0.0
        INFO - 20:34:34:    over the design space:
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:       | x    |      0      | 2.211503064031537  |      5      | float |
        INFO - 20:34:34:       | y    |      0      | 2.211503107833047  |      3      | float |
        INFO - 20:34:34:       | t    |     -inf    | 0.2305955098019026 |     inf     | float |
        INFO - 20:34:34:       +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: -0.22968191496902265
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          beta_sub_optim_constraint = [4.09995593e-09 1.02497921e-09]
        INFO - 20:34:34:          wrapped_ineq1 = [-15.34021524]
        INFO - 20:34:34:          wrapped_ineq2 = [-30.25460517]
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | Name | Lower bound |       Value        | Upper bound | Type  |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34:          | x    |      0      | 2.284196597883743  |      5      | float |
        INFO - 20:34:34:          | y    |      0      | 2.284196636140467  |      3      | float |
        INFO - 20:34:34:          | t    |     -inf    | 0.2296819149690227 |     inf     | float |
        INFO - 20:34:34:          +------+-------------+--------------------+-------------+-------+
        INFO - 20:34:34: Optimization result:
        INFO - 20:34:34:    Optimizer info:
        INFO - 20:34:34:       Status: None
        INFO - 20:34:34:       Message: None
        INFO - 20:34:34:       Number of calls to the objective function by the optimizer: 0
        INFO - 20:34:34:    Solution:
        INFO - 20:34:34:       The solution is feasible.
        INFO - 20:34:34:       Objective: 30.28780069872395
        INFO - 20:34:34:       Standardized constraints:
        INFO - 20:34:34:          ineq1 = [-10.82436312]
        INFO - 20:34:34:          ineq2 = [-39.89635695]
        INFO - 20:34:34:    Pareto efficient solutions:
        INFO - 20:34:34:       Pareto optimal points : 226 / 312
        INFO - 20:34:34:       Utopia point : [0. 4.]
        INFO - 20:34:34:       Compromise solution (closest to utopia) : [[14.45889916 26.72708902]]
        INFO - 20:34:34:       Distance from utopia : 26.936598526003834
        INFO - 20:34:34:       Objective values:
        INFO - 20:34:34:          +------+----+-----+---------+
        INFO - 20:34:34:          | name |  1 |   2 |       3 |
        INFO - 20:34:34:          +------+----+-----+---------+
        INFO - 20:34:34:          |    1 |  0 | 136 | 14.4589 |
        INFO - 20:34:34:          |    2 | 50 |   4 | 26.7271 |
        INFO - 20:34:34:          +------+----+-----+---------+
        INFO - 20:34:34:       Constraint values:
        INFO - 20:34:34:          +------+-------+------+----------+
        INFO - 20:34:34:          | name |     1 |    2 |        3 |
        INFO - 20:34:34:          +------+-------+------+----------+
        INFO - 20:34:34:          |    1 |     0 |  -22 | -10.2918 |
        INFO - 20:34:34:          |    2 | -59.3 | -7.3 | -40.9422 |
        INFO - 20:34:34:          +------+-------+------+----------+
        INFO - 20:34:34:       Design space:
        INFO - 20:34:34:          +-------+-------------+---+---+---------+-------------+-------+
        INFO - 20:34:34:          |  name | lower_bound | 1 | 2 |       3 | upper_bound |  type |
        INFO - 20:34:34:          +-------+-------------+---+---+---------+-------------+-------+
        INFO - 20:34:34:          | x (1) |           0 | 0 | 5 | 1.34434 |           5 | float |
        INFO - 20:34:34:          | y (1) |           0 | 0 | 3 | 1.34442 |           3 | float |
        INFO - 20:34:34:          +-------+-------------+---+---+---------+-------------+-------+


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='margin: 1em;'>Optimization result:<br/><ul><li>Design variables: [1.42987999 1.42987999]</li><li>Objective function: 30.28780069872395</li><li>Feasible solution: True</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 93-96

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

.. GENERATED FROM PYTHON SOURCE LINES 96-98

.. code-block:: Python


    execute_post(problem, post_name="ParetoFront", save=False, show=True)



.. image-sg:: /examples/multi_objective/images/sphx_glr_plot_mnbi_binh_korn_002.png
   :alt: Pareto front
   :srcset: /examples/multi_objective/images/sphx_glr_plot_mnbi_binh_korn_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.pareto_front.ParetoFront object at 0x78592fb293a0>




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

   **Total running time of the script:** (0 minutes 0.975 seconds)


.. _sphx_glr_download_examples_multi_objective_plot_mnbi_binh_korn.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_binh_korn.ipynb <plot_mnbi_binh_korn.ipynb>`

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

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

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

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


.. only:: html

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

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