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

In this example, the modified Normal Boundary Intersection (mNBI) algorithm is used to solve the BinhKorn problem [BK97]:

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

from numpy import array

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

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.

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)
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
    INFO - 16:21:06:    with respect to x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
    INFO - 16:21:06:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |   1   |      5      | float |
    INFO - 16:21:06:       | y    |      0      |   1   |      3      | float |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06: Solving optimization problem with algorithm MNBI:
    INFO - 16:21:06: Searching for the individual optimum of each objective
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize f_0
    INFO - 16:21:06:    with respect to x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
    INFO - 16:21:06:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |   1   |      5      | float |
    INFO - 16:21:06:       | y    |      0      |   1   |      3      | float |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: 2.606494387870873e-24
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          ineq1 = [-8.07531819e-12]
    INFO - 16:21:06:          ineq2 = [-59.3]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |         Value         | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 8.072320589320757e-13 |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 3.635071051258422e-26 |      3      | float |
    INFO - 16:21:06:          +------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize f_1
    INFO - 16:21:06:    with respect to x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
    INFO - 16:21:06:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |   1   |      5      | float |
    INFO - 16:21:06:       | y    |      0      |   1   |      3      | float |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: 4.0
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          ineq1 = [-22.]
    INFO - 16:21:06:          ineq2 = [-7.3]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 4.999999999999934 |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3         |      3      | float |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [133.2244898    4.93877551]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |   1   |      5      | float |
    INFO - 16:21:06:       | y    |      0      |   1   |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    |   0   |     inf     | float |
    INFO - 16:21:06:       +------+-------------+-------+-------------+-------+
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.01998643812377874
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [8.48439630e-09 2.12122098e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.98060064]
    INFO - 16:21:06:          wrapped_ineq2 = [-8.15508884]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  4.860718419626012  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.01998643812377874 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [130.44897959   5.87755102]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  4.860718419626012  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.01998643812377874 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.03911696914200524
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.07045397e-06 2.67613498e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.92182929]
    INFO - 16:21:06:          wrapped_ineq2 = [-9.0557122]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  4.720409750725449  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.03911696914200524 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [127.67346939   6.81632653]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  4.720409750725449  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.03911696914200524 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.05737236260339593
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.11930950e-06 2.79827399e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.82280187]
    INFO - 16:21:06:          wrapped_ineq2 = [-10.00289263]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  4.579050916756671  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.05737236260339593 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [124.89795918   7.75510204]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  4.579050916756671  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.05737236260339593 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.07473267476172492
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.17118353e-06 2.92795888e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.68260071]
    INFO - 16:21:06:          wrapped_ineq2 = [-10.99769138]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  4.436617985224224  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.07473267476172492 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [122.12244898   8.69387755]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  4.436617985224224  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.07473267476172492 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.09117718665696382
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.22631329e-06 3.06578325e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.50027273]
    INFO - 16:21:06:          wrapped_ineq2 = [-12.04121071]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  4.293086093376068  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.09117718665696382 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [119.34693878   9.63265306]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  4.293086093376068  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |          3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.09117718665696382 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.10668436745322431
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.28495818e-06 3.21239564e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.27482752]
    INFO - 16:21:06:          wrapped_ineq2 = [-13.13459605]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 4.148429404209136  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1066843674532243 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [116.57142857  10.57142857]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 4.148429404209136  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1066843674532243 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.12123182918922668
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.34740280e-06 3.36850713e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-21.00523523]
    INFO - 16:21:06:          wrapped_ineq2 = [-14.27903845]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 4.002621052169897  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1212318291892267 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [113.79591837  11.51020408]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 4.002621052169897  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1212318291892267 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.134796278233669
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.41396002e-06 3.53490051e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-20.69042436]
    INFO - 16:21:06:          wrapped_ineq2 = [-15.47577713]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 3.855633084900785 |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.999999999999999 |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.134796278233669 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [111.02040816  12.44897959]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 3.855633084900785 |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.999999999999999 |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.134796278233669 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.14735346314737857
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.48497395e-06 3.71243494e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-20.32927934]
    INFO - 16:21:06:          wrapped_ineq2 = [-16.72610225]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 3.707436400674799  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1473534631473786 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [108.24489796  13.3877551 ]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 3.707436400674799  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1473534631473786 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 51/10000 [00:00<00:19, 521.91 it/sec, feas=True, obj=[86.65525741  6.07756089]]
    INFO - 16:21:06:      1%|          | 52/10000 [00:00<00:18, 524.86 it/sec, feas=True, obj=[86.63747539  6.07936204]]
    INFO - 16:21:06:      1%|          | 53/10000 [00:00<00:18, 527.87 it/sec, feas=True, obj=[86.63747507  6.07936207]]
    INFO - 16:21:06:      1%|          | 54/10000 [00:00<00:18, 531.44 it/sec, feas=True, obj=[86.63747507  6.07936207]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.15887811862175563
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.56082417e-06 3.90206043e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-19.92063796]
    INFO - 16:21:06:          wrapped_ineq2 = [-18.03135795]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 3.558000681121612  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1588781186217556 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [105.46938776  14.32653061]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 3.558000681121612  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1588781186217556 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 55/10000 [00:00<00:19, 516.84 it/sec, feas=True, obj=[86.63747507  6.07936207]]
    INFO - 16:21:06:      1%|          | 56/10000 [00:00<00:19, 520.89 it/sec, feas=True, obj=[82.45608407  6.53467094]]
    INFO - 16:21:06:      1%|          | 57/10000 [00:00<00:18, 523.58 it/sec, feas=True, obj=[82.4386183   6.53671139]]
    INFO - 16:21:06:      1%|          | 58/10000 [00:00<00:18, 526.48 it/sec, feas=True, obj=[82.43861798  6.53671142]]
    INFO - 16:21:06:      1%|          | 59/10000 [00:00<00:18, 529.38 it/sec, feas=True, obj=[82.43861798  6.53671142]]
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.16934390512641784
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.64192933e-06 4.10482341e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-19.46328861]
    INFO - 16:21:06:          wrapped_ineq2 = [-19.39294547]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 3.407294318804767  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1693439051264178 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [102.69387755  15.26530612]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 3.407294318804767  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1693439051264178 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 60/10000 [00:00<00:19, 517.15 it/sec, feas=True, obj=[82.43861798  6.53671142]]
    INFO - 16:21:06:      1%|          | 61/10000 [00:00<00:19, 519.31 it/sec, feas=True, obj=[82.4386183   6.53671139]]
    INFO - 16:21:06:      1%|          | 62/10000 [00:00<00:19, 522.96 it/sec, feas=True, obj=[78.4046267   7.04173918]]
    INFO - 16:21:06:      1%|          | 63/10000 [00:00<00:18, 525.37 it/sec, feas=True, obj=[78.38750452  7.04403274]]
    INFO - 16:21:06:      1%|          | 64/10000 [00:00<00:18, 527.92 it/sec, feas=True, obj=[78.38750419  7.04403278]]
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.1787233438577375
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.72875259e-06 4.32188139e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-18.95596726]
    INFO - 16:21:06:          wrapped_ineq2 = [-20.8123267]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 3.255284339159914  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1787233438577375 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [99.91836735 16.20408163]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 3.255284339159914  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1787233438577375 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 65/10000 [00:00<00:19, 517.09 it/sec, feas=True, obj=[78.38750419  7.04403278]]
    INFO - 16:21:06:      1%|          | 66/10000 [00:00<00:19, 519.40 it/sec, feas=True, obj=[78.38750452  7.04403274]]
    INFO - 16:21:06:      1%|          | 67/10000 [00:00<00:18, 522.84 it/sec, feas=True, obj=[74.50478473  7.6000843 ]]
    INFO - 16:21:06:      1%|          | 68/10000 [00:00<00:18, 525.15 it/sec, feas=True, obj=[74.48803564  7.60264575]]
    INFO - 16:21:06:      1%|          | 69/10000 [00:00<00:18, 527.55 it/sec, feas=True, obj=[74.48803531  7.6026458 ]]
    INFO - 16:21:06:      1%|          | 70/10000 [00:00<00:18, 530.23 it/sec, feas=True, obj=[74.48803531  7.6026458 ]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.18698774653317168
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.82180682e-06 4.55451687e-07]
    INFO - 16:21:06:          wrapped_ineq1 = [-18.39735425]
    INFO - 16:21:06:          wrapped_ineq2 = [-22.29102785]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 3.101936316247999  |      5      | float |
    INFO - 16:21:06:          | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1869877465331717 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [97.14285714 17.14285714]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 3.101936316247999  |      5      | float |
    INFO - 16:21:06:       | y    |      0      |         3          |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1869877465331717 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 71/10000 [00:00<00:19, 521.52 it/sec, feas=True, obj=[74.48803531  7.6026458 ]]
    INFO - 16:21:06:      1%|          | 72/10000 [00:00<00:18, 523.36 it/sec, feas=True, obj=[74.48803564  7.60264575]]
    INFO - 16:21:06:      1%|          | 73/10000 [00:00<00:18, 526.51 it/sec, feas=True, obj=[70.75658544  8.21055954]]
    INFO - 16:21:06:      1%|          | 74/10000 [00:00<00:18, 529.36 it/sec, feas=True, obj=[70.74019853  8.21247029]]
    INFO - 16:21:06:      1%|          | 75/10000 [00:00<00:18, 532.13 it/sec, feas=True, obj=[70.7397555   8.21235896]]
    INFO - 16:21:06:      1%|          | 76/10000 [00:00<00:18, 534.19 it/sec, feas=True, obj=[70.73968192  8.21237138]]
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.19414099622669317
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [2.67250751e-07 6.68126674e-08]
    INFO - 16:21:06:          wrapped_ineq1 = [-17.92018718]
    INFO - 16:21:06:          wrapped_ineq2 = [-23.5380477]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 2.973627520197323  |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.973627389560465  |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.1941409962266932 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [94.36734694 18.08163265]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 2.973627520197323  |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.973627389560465  |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.1941409962266932 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 77/10000 [00:00<00:18, 524.70 it/sec, feas=True, obj=[70.73968188  8.21237139]]
    INFO - 16:21:06:      1%|          | 78/10000 [00:00<00:18, 526.48 it/sec, feas=True, obj=[70.73968192  8.21237138]]
    INFO - 16:21:06:      1%|          | 79/10000 [00:00<00:18, 529.43 it/sec, feas=True, obj=[67.10688455  8.85599137]]
    INFO - 16:21:06:      1%|          | 80/10000 [00:00<00:18, 532.04 it/sec, feas=True, obj=[67.09022377  8.85523197]]
    INFO - 16:21:06:      1%|          | 81/10000 [00:00<00:18, 534.65 it/sec, feas=True, obj=[67.08836417  8.8547516 ]]
    INFO - 16:21:06:      1%|          | 82/10000 [00:00<00:18, 536.53 it/sec, feas=True, obj=[67.0880443  8.8548097]]
    INFO - 16:21:06:      1%|          | 83/10000 [00:00<00:18, 538.54 it/sec, feas=True, obj=[67.0880443  8.8548097]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.20058310774575158
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.5926144e-08 3.9815280e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-17.67673508]
    INFO - 16:21:06:          wrapped_ineq2 = [-24.24810451]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 2.895860068518851  |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.895860068939371  |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.2005831077457516 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [91.59183673 19.02040816]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 2.895860068518851  |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.895860068939371  |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.2005831077457516 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 84/10000 [00:00<00:18, 529.86 it/sec, feas=True, obj=[67.0880443  8.8548097]]
    INFO - 16:21:06:      1%|          | 85/10000 [00:00<00:18, 531.04 it/sec, feas=True, obj=[67.0880443  8.8548097]]
    INFO - 16:21:06:      1%|          | 86/10000 [00:00<00:18, 533.66 it/sec, feas=True, obj=[63.53594358  9.5256767 ]]
    INFO - 16:21:06:      1%|          | 87/10000 [00:00<00:18, 536.07 it/sec, feas=True, obj=[63.51929686  9.52496401]]
    INFO - 16:21:06:      1%|          | 88/10000 [00:00<00:18, 538.38 it/sec, feas=True, obj=[63.51742882  9.52448661]]
    INFO - 16:21:06:      1%|          | 89/10000 [00:00<00:18, 540.08 it/sec, feas=True, obj=[63.51711681  9.52454701]]
    INFO - 16:21:06:      1%|          | 90/10000 [00:00<00:18, 541.73 it/sec, feas=True, obj=[63.51711681  9.52454701]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.20643176428315416
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.60213638e-08 4.00533295e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-17.4199899]
    INFO - 16:21:06:          wrapped_ineq2 = [-24.97359042]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 2.817736612798133  |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.817736606382536  |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.2064317642831542 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [88.81632653 19.95918367]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 2.817736612798133  |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.817736606382536  |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.2064317642831542 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 91/10000 [00:00<00:18, 534.17 it/sec, feas=True, obj=[63.51711681  9.52454701]]
    INFO - 16:21:06:      1%|          | 92/10000 [00:00<00:18, 535.66 it/sec, feas=True, obj=[63.51711681  9.52454701]]
    INFO - 16:21:06:      1%|          | 93/10000 [00:00<00:18, 538.10 it/sec, feas=True, obj=[60.04682873 10.22303763]]
    INFO - 16:21:06:      1%|          | 94/10000 [00:00<00:18, 540.28 it/sec, feas=True, obj=[60.03019841 10.22237318]]
    INFO - 16:21:06:      1%|          | 95/10000 [00:00<00:18, 542.49 it/sec, feas=True, obj=[60.02832235 10.22189905]]
    INFO - 16:21:06:      1%|          | 96/10000 [00:00<00:18, 543.96 it/sec, feas=True, obj=[60.0280183  10.22196177]]
    INFO - 16:21:06:      1%|          | 97/10000 [00:00<00:18, 545.63 it/sec, feas=True, obj=[60.0280183  10.22196177]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.21167873709713758
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.60890927e-08 4.02229539e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-17.14976701]
    INFO - 16:21:06:          wrapped_ineq2 = [-25.71472011]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  2.7392521469624   |      5      | float |
    INFO - 16:21:06:          | y    |      0      |  2.73925213347261  |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.2116787370971376 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [86.04081633 20.89795918]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  2.7392521469624   |      5      | float |
    INFO - 16:21:06:       | y    |      0      |  2.73925213347261  |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.2116787370971376 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 98/10000 [00:00<00:18, 535.50 it/sec, feas=True, obj=[60.0280183  10.22196177]]
    INFO - 16:21:06:      1%|          | 99/10000 [00:00<00:18, 537.76 it/sec, feas=True, obj=[56.64068487 10.94846138]]
    INFO - 16:21:06:      1%|          | 100/10000 [00:00<00:18, 539.27 it/sec, feas=True, obj=[56.62407339 10.94784674]]
    INFO - 16:21:06:      1%|          | 101/10000 [00:00<00:18, 541.21 it/sec, feas=True, obj=[56.62218975 10.9473762 ]]
    INFO - 16:21:06:      1%|          | 102/10000 [00:00<00:18, 542.63 it/sec, feas=True, obj=[56.62189378 10.94744126]]
    INFO - 16:21:06:      1%|          | 103/10000 [00:00<00:18, 544.17 it/sec, feas=True, obj=[56.62189377 10.94744126]]
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.21631560710602385
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.61276645e-08 4.03191258e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-16.86587782]
    INFO - 16:21:06:          wrapped_ineq2 = [-26.47171246]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 2.660401619556375  |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.660401598766867  |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.2163156071060238 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [83.26530612 21.83673469]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 2.660401619556375  |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.660401598766867  |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.2163156071060238 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 104/10000 [00:00<00:18, 536.66 it/sec, feas=True, obj=[56.62189377 10.94744126]]
    INFO - 16:21:06:      1%|          | 105/10000 [00:00<00:18, 537.93 it/sec, feas=True, obj=[56.62189378 10.94744126]]
    INFO - 16:21:06:      1%|          | 106/10000 [00:00<00:18, 540.07 it/sec, feas=True, obj=[53.31868379 11.70234427]]
    INFO - 16:21:06:      1%|          | 107/10000 [00:00<00:18, 541.93 it/sec, feas=True, obj=[53.30209371 11.70178107]]
    INFO - 16:21:06:      1%|          | 108/10000 [00:00<00:18, 543.85 it/sec, feas=True, obj=[53.30020299 11.70131446]]
    INFO - 16:21:06:      1%|          | 109/10000 [00:00<00:18, 545.21 it/sec, feas=True, obj=[53.29991518 11.70138187]]
    INFO - 16:21:06:      1%|          | 110/10000 [00:00<00:18, 546.64 it/sec, feas=True, obj=[53.29991518 11.70138187]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.22033375703664396
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.61356439e-08 4.03392342e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-16.5681293]
    INFO - 16:21:06:          wrapped_ineq2 = [-27.24479154]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      |  2.58117986020869 |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.581179831908861 |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.220333757036644 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [80.48979592 22.7755102 ]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      |  2.58117986020869 |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.581179831908861 |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.220333757036644 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 111/10000 [00:00<00:18, 538.19 it/sec, feas=True, obj=[53.29991518 11.70138187]]
    INFO - 16:21:06:      1%|          | 112/10000 [00:00<00:18, 540.12 it/sec, feas=True, obj=[50.08202514 12.48509203]]
    INFO - 16:21:06:      1%|          | 113/10000 [00:00<00:18, 541.91 it/sec, feas=True, obj=[50.06545915 12.48458197]]
    INFO - 16:21:06:      1%|          | 114/10000 [00:00<00:18, 543.69 it/sec, feas=True, obj=[50.06356185 12.48411964]]
    INFO - 16:21:06:      1%|          | 115/10000 [00:00<00:18, 544.57 it/sec, feas=True, obj=[50.06328232 12.48418943]]
   ERROR - 16:21:06: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.22372436483036234
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.61118621e-08 4.02798683e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-16.25632384]
    INFO - 16:21:06:          wrapped_ineq2 = [-28.03418671]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 2.501581575675654  |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.501581539671924  |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.2237243648303623 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [77.71428571 23.71428571]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 2.501581575675654  |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.501581539671924  |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.2237243648303623 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 116/10000 [00:00<00:18, 537.81 it/sec, feas=True, obj=[50.06328232 12.48418943]]
    INFO - 16:21:06:      1%|          | 117/10000 [00:00<00:18, 538.96 it/sec, feas=True, obj=[50.06328232 12.48418943]]
    INFO - 16:21:06:      1%|          | 118/10000 [00:00<00:18, 540.89 it/sec, feas=True, obj=[46.93193733 13.29712012]]
    INFO - 16:21:06:      1%|          | 119/10000 [00:00<00:18, 542.61 it/sec, feas=True, obj=[46.91539824 13.29666496]]
    INFO - 16:21:06:      1%|          | 120/10000 [00:00<00:18, 544.26 it/sec, feas=True, obj=[46.91349492 13.2962073 ]]
    INFO - 16:21:06:      1%|          | 121/10000 [00:00<00:18, 545.50 it/sec, feas=True, obj=[46.91322377 13.29627947]]
    INFO - 16:21:06:      1%|          | 122/10000 [00:00<00:18, 546.78 it/sec, feas=True, obj=[46.91322377 13.29627947]]
    INFO - 16:21:06: Optimization result:
    INFO - 16:21:06:    Optimizer info:
    INFO - 16:21:06:       Status: None
    INFO - 16:21:06:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:06:    Solution:
    INFO - 16:21:06:       The solution is feasible.
    INFO - 16:21:06:       Objective: -0.22647839676432904
    INFO - 16:21:06:       Standardized constraints:
    INFO - 16:21:06:          beta_sub_optim_constraint = [1.60553384e-08 4.01382039e-09]
    INFO - 16:21:06:          wrapped_ineq1 = [-15.93025908]
    INFO - 16:21:06:          wrapped_ineq2 = [-28.84013285]
    INFO - 16:21:06:       Design space:
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:          | x    |      0      | 2.421601345714025 |      5      | float |
    INFO - 16:21:06:          | y    |      0      | 2.421601301831883 |      3      | float |
    INFO - 16:21:06:          | t    |     -inf    | 0.226478396764329 |     inf     | float |
    INFO - 16:21:06:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06: Solving mNBI sub-problem for phi_beta = [74.93877551 24.65306122]
    INFO - 16:21:06: Optimization problem:
    INFO - 16:21:06:    minimize -t_extraction
    INFO - 16:21:06:    with respect to t, x, y
    INFO - 16:21:06:    under the inequality constraints
    INFO - 16:21:06:       wrapped_ineq1 <= 0.0
    INFO - 16:21:06:       wrapped_ineq2 <= 0.0
    INFO - 16:21:06:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:06:    over the design space:
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:       | x    |      0      | 2.421601345714025 |      5      | float |
    INFO - 16:21:06:       | y    |      0      | 2.421601301831883 |      3      | float |
    INFO - 16:21:06:       | t    |     -inf    | 0.226478396764329 |     inf     | float |
    INFO - 16:21:06:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:06:      1%|          | 123/10000 [00:00<00:18, 539.17 it/sec, feas=True, obj=[46.91322377 13.29627947]]
    INFO - 16:21:06:      1%|          | 124/10000 [00:00<00:18, 541.01 it/sec, feas=True, obj=[43.86967855 14.13885408]]
    INFO - 16:21:06:      1%|▏         | 125/10000 [00:00<00:18, 542.60 it/sec, feas=True, obj=[43.8531693  14.13845566]]
    INFO - 16:21:07:      1%|▏         | 126/10000 [00:00<00:18, 544.19 it/sec, feas=True, obj=[43.85126056 14.13800305]]
    INFO - 16:21:07:      1%|▏         | 127/10000 [00:00<00:18, 545.31 it/sec, feas=True, obj=[43.85099789 14.13807762]]
    INFO - 16:21:07:      1%|▏         | 128/10000 [00:00<00:18, 546.51 it/sec, feas=True, obj=[43.85099789 14.13807762]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.22858660027277578
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.59653304e-08 3.99134947e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-15.58972776]
    INFO - 16:21:07:          wrapped_ineq2 = [-29.66287052]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.341233618773835  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.341233566859774  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2285866002727758 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [72.16326531 25.59183673]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.341233618773835  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.341233566859774  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2285866002727758 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      1%|▏         | 129/10000 [00:00<00:18, 535.30 it/sec, feas=True, obj=[43.85099789 14.13807762]]
    INFO - 16:21:07:      1%|▏         | 130/10000 [00:00<00:18, 537.01 it/sec, feas=True, obj=[40.89653773 15.01072985]]
    INFO - 16:21:07:      1%|▏         | 131/10000 [00:00<00:18, 538.57 it/sec, feas=True, obj=[40.88006141 15.01039006]]
    INFO - 16:21:07:      1%|▏         | 132/10000 [00:00<00:18, 540.10 it/sec, feas=True, obj=[40.87814788 15.00994293]]
    INFO - 16:21:07:      1%|▏         | 133/10000 [00:00<00:18, 541.20 it/sec, feas=True, obj=[40.8778938 15.0100199]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23003949645220786
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.58415503e-08 3.96038580e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-15.23451757]
    INFO - 16:21:07:          wrapped_ineq2 = [-30.50264619]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.260472707501587  |      5      | float |
    INFO - 16:21:07:          | y    |      0      |  2.26047264742491  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2300394964522079 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [69.3877551  26.53061224]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.260472707501587  |      5      | float |
    INFO - 16:21:07:       | y    |      0      |  2.26047264742491  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2300394964522079 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      1%|▏         | 134/10000 [00:00<00:18, 533.65 it/sec, feas=True, obj=[40.8778938 15.0100199]]
    INFO - 16:21:07:      1%|▏         | 135/10000 [00:00<00:18, 535.24 it/sec, feas=True, obj=[38.01383568 15.91319413]]
    INFO - 16:21:07:      1%|▏         | 136/10000 [00:00<00:18, 536.68 it/sec, feas=True, obj=[37.99739551 15.91291495]]
    INFO - 16:21:07:      1%|▏         | 137/10000 [00:00<00:18, 538.15 it/sec, feas=True, obj=[37.99547788 15.91247373]]
    INFO - 16:21:07:      1%|▏         | 138/10000 [00:00<00:18, 539.20 it/sec, feas=True, obj=[37.99523249 15.91255313]]
    INFO - 16:21:07:      1%|▏         | 139/10000 [00:00<00:18, 540.35 it/sec, feas=True, obj=[37.99523249 15.91255313]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23082737223332214
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.56837352e-08 3.92091692e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-14.86441091]
    INFO - 16:21:07:          wrapped_ineq2 = [-31.35971238]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.179312784043477  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.179312715697926  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2308273722333221 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [66.6122449  27.46938776]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.179312784043477  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.179312715697926  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2308273722333221 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      1%|▏         | 140/10000 [00:00<00:18, 532.95 it/sec, feas=True, obj=[37.99523249 15.91255313]]
    INFO - 16:21:07:      1%|▏         | 141/10000 [00:00<00:18, 534.51 it/sec, feas=True, obj=[35.22292611 16.84670478]]
    INFO - 16:21:07:      1%|▏         | 142/10000 [00:00<00:18, 535.92 it/sec, feas=True, obj=[35.20652549 16.84648825]]
    INFO - 16:21:07:      1%|▏         | 143/10000 [00:00<00:18, 537.37 it/sec, feas=True, obj=[35.20460449 16.84605342]]
    INFO - 16:21:07:      1%|▏         | 144/10000 [00:00<00:18, 538.38 it/sec, feas=True, obj=[35.20436789 16.84613524]]
    INFO - 16:21:07:      1%|▏         | 145/10000 [00:00<00:18, 539.45 it/sec, feas=True, obj=[35.20436789 16.84613524]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23094027220135074
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.54923363e-08 3.87309385e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-14.47918481]
    INFO - 16:21:07:          wrapped_ineq2 = [-32.23432794]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.097747875137713  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.097747798442891  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2309402722013507 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [63.83673469 28.40816327]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.097747875137713  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.097747798442891  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2309402722013507 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      1%|▏         | 146/10000 [00:00<00:18, 532.58 it/sec, feas=True, obj=[35.20436789 16.84613524]]
    INFO - 16:21:07:      1%|▏         | 147/10000 [00:00<00:18, 534.10 it/sec, feas=True, obj=[32.52519687 17.81173117]]
    INFO - 16:21:07:      1%|▏         | 148/10000 [00:00<00:18, 535.44 it/sec, feas=True, obj=[32.50883935 17.81157943]]
    INFO - 16:21:07:      1%|▏         | 149/10000 [00:00<00:18, 536.86 it/sec, feas=True, obj=[32.50691576 17.81115147]]
    INFO - 16:21:07:      2%|▏         | 150/10000 [00:00<00:18, 537.88 it/sec, feas=True, obj=[32.50668806 17.81123573]]
    INFO - 16:21:07:      2%|▏         | 151/10000 [00:00<00:18, 538.89 it/sec, feas=True, obj=[32.50668806 17.81123573]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.2303679900453309
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.52679540e-08 3.81701248e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-14.07861062]
    INFO - 16:21:07:          wrapped_ineq2 = [-33.12675824]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.015771856984196  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.015771771886752  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2303679900453309 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [61.06122449 29.34693878]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.015771856984196  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.015771771886752  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2303679900453309 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 152/10000 [00:00<00:18, 532.52 it/sec, feas=True, obj=[32.50668806 17.81123573]]
    INFO - 16:21:07:      2%|▏         | 153/10000 [00:00<00:18, 533.95 it/sec, feas=True, obj=[29.92207113 18.80875463]]
    INFO - 16:21:07:      2%|▏         | 154/10000 [00:00<00:18, 535.25 it/sec, feas=True, obj=[29.90576043 18.8086699 ]]
    INFO - 16:21:07:      2%|▏         | 155/10000 [00:00<00:18, 536.55 it/sec, feas=True, obj=[29.90383509 18.80824933]]
    INFO - 16:21:07:      2%|▏         | 156/10000 [00:00<00:18, 537.50 it/sec, feas=True, obj=[29.9036164  18.80833604]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.22910005961553107
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.50116506e-08 3.75290909e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-13.66245391]
    INFO - 16:21:07:          wrapped_ineq2 = [-34.03727539]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.933378449879112  |      5      | float |
    INFO - 16:21:07:          | y    |      0      |  1.93337835635365  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2291000596155311 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [58.28571429 30.28571429]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.933378449879112  |      5      | float |
    INFO - 16:21:07:       | y    |      0      |  1.93337835635365  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2291000596155311 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 157/10000 [00:00<00:18, 532.70 it/sec, feas=True, obj=[29.9036164  18.80833604]]
    INFO - 16:21:07:      2%|▏         | 158/10000 [00:00<00:18, 533.59 it/sec, feas=True, obj=[29.9036164  18.80833604]]
    INFO - 16:21:07:      2%|▏         | 159/10000 [00:00<00:18, 535.04 it/sec, feas=True, obj=[27.41500866 19.83826888]]
    INFO - 16:21:07:      2%|▏         | 160/10000 [00:00<00:18, 536.33 it/sec, feas=True, obj=[27.39874869 19.83825346]]
    INFO - 16:21:07:      2%|▏         | 161/10000 [00:00<00:18, 537.61 it/sec, feas=True, obj=[27.39682249 19.83784083]]
    INFO - 16:21:07:      2%|▏         | 162/10000 [00:00<00:18, 538.57 it/sec, feas=True, obj=[27.3966129  19.83792999]]
    INFO - 16:21:07:      2%|▏         | 163/10000 [00:00<00:18, 539.57 it/sec, feas=True, obj=[27.3966129  19.83792999]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.22712574556684564
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.47244776e-08 3.68111586e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-13.23047421]
    INFO - 16:21:07:          wrapped_ineq2 = [-34.96615851]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.850561212601098  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.850561110650811  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2271257455668456 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [55.51020408 31.2244898 ]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.850561212601098  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.850561110650811  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2271257455668456 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 164/10000 [00:00<00:18, 535.14 it/sec, feas=True, obj=[27.3966129  19.83792999]]
    INFO - 16:21:07:      2%|▏         | 165/10000 [00:00<00:18, 535.92 it/sec, feas=True, obj=[27.3966129  19.83792999]]
    INFO - 16:21:07:      2%|▏         | 166/10000 [00:00<00:18, 537.28 it/sec, feas=True, obj=[25.00550716 20.90078046]]
    INFO - 16:21:07:      2%|▏         | 167/10000 [00:00<00:18, 538.50 it/sec, feas=True, obj=[24.98930201 20.90083674]]
    INFO - 16:21:07:      2%|▏         | 168/10000 [00:00<00:18, 539.74 it/sec, feas=True, obj=[24.98737592 20.90043263]]
    INFO - 16:21:07:      2%|▏         | 169/10000 [00:00<00:18, 540.57 it/sec, feas=True, obj=[24.98717553 20.90052426]]
    INFO - 16:21:07:      2%|▏         | 170/10000 [00:00<00:18, 541.49 it/sec, feas=True, obj=[24.98717553 20.90052426]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.22443403356449895
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.44083501e-08 3.60207864e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-12.7824248]
    INFO - 16:21:07:          wrapped_ineq2 = [-35.91369398]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.767313536534835 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.767313426191829 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.224434033564499 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [52.73469388 32.16326531]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.767313536534835 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.767313426191829 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.224434033564499 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 171/10000 [00:00<00:18, 536.11 it/sec, feas=True, obj=[24.98717553 20.90052426]]
    INFO - 16:21:07:      2%|▏         | 172/10000 [00:00<00:18, 537.39 it/sec, feas=True, obj=[22.69510365 21.99680919]]
    INFO - 16:21:07:      2%|▏         | 173/10000 [00:00<00:18, 538.60 it/sec, feas=True, obj=[22.67895762 21.99693969]]
    INFO - 16:21:07:      2%|▏         | 174/10000 [00:00<00:18, 539.77 it/sec, feas=True, obj=[22.67703266 21.9965447 ]]
    INFO - 16:21:07:      2%|▏         | 175/10000 [00:00<00:18, 540.64 it/sec, feas=True, obj=[22.67684157 21.99663879]]
    INFO - 16:21:07:      2%|▏         | 176/10000 [00:00<00:18, 541.53 it/sec, feas=True, obj=[22.67684157 21.99663879]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.22101362002675384
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.40650478e-08 3.51627705e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-12.31805248]
    INFO - 16:21:07:          wrapped_ineq2 = [-36.88017568]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.683628639516817  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.683628520842123  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2210136200267538 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [49.95918367 33.10204082]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.683628639516817  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.683628520842123  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2210136200267538 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 177/10000 [00:00<00:18, 535.90 it/sec, feas=True, obj=[22.67684157 21.99663879]]
    INFO - 16:21:07:      2%|▏         | 178/10000 [00:00<00:18, 537.00 it/sec, feas=True, obj=[20.48537592 23.12688872]]
    INFO - 16:21:07:      2%|▏         | 179/10000 [00:00<00:18, 538.11 it/sec, feas=True, obj=[20.46929353 23.12709601]]
    INFO - 16:21:07:      2%|▏         | 180/10000 [00:00<00:18, 539.24 it/sec, feas=True, obj=[20.46737079 23.1267108 ]]
    INFO - 16:21:07:      2%|▏         | 181/10000 [00:00<00:18, 540.06 it/sec, feas=True, obj=[20.4671891  23.12680736]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.21685290137760832
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.36968623e-08 3.42420314e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-11.83709732]
    INFO - 16:21:07:          wrapped_ineq2 = [-37.86590532]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.599499559387131  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.599499432470409  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2168529013776083 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [47.18367347 34.04081633]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.599499559387131  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.599499432470409  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2168529013776083 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 182/10000 [00:00<00:18, 535.91 it/sec, feas=True, obj=[20.4671891  23.12680736]]
    INFO - 16:21:07:      2%|▏         | 183/10000 [00:00<00:18, 536.62 it/sec, feas=True, obj=[20.4671891  23.12680736]]
    INFO - 16:21:07:      2%|▏         | 184/10000 [00:00<00:18, 537.78 it/sec, feas=True, obj=[18.37794411 24.29156696]]
    INFO - 16:21:07:      2%|▏         | 185/10000 [00:00<00:18, 538.92 it/sec, feas=True, obj=[18.36193008 24.29185378]]
    INFO - 16:21:07:      2%|▏         | 186/10000 [00:00<00:18, 540.03 it/sec, feas=True, obj=[18.36001075 24.29147902]]
    INFO - 16:21:07:      2%|▏         | 187/10000 [00:00<00:18, 540.87 it/sec, feas=True, obj=[18.35983854 24.29157804]]
    INFO - 16:21:07:      2%|▏         | 188/10000 [00:00<00:18, 541.73 it/sec, feas=True, obj=[18.35983854 24.29157804]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.21193996278055047
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.33061775e-08 3.32653549e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-11.33929244]
    INFO - 16:21:07:          wrapped_ineq2 = [-38.87119268]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.514919147229853  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.514919012188789  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2119399627805505 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [44.40816327 34.97959184]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.514919147229853  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.514919012188789  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2119399627805505 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 189/10000 [00:00<00:18, 538.22 it/sec, feas=True, obj=[18.35983854 24.29157804]]
    INFO - 16:21:07:      2%|▏         | 190/10000 [00:00<00:18, 538.89 it/sec, feas=True, obj=[18.35983854 24.29157804]]
    INFO - 16:21:07:      2%|▏         | 191/10000 [00:00<00:18, 540.07 it/sec, feas=True, obj=[16.37447224 25.49140673]]
    INFO - 16:21:07:      2%|▏         | 192/10000 [00:00<00:18, 541.13 it/sec, feas=True, obj=[16.35853156 25.49177588]]
    INFO - 16:21:07:      2%|▏         | 193/10000 [00:00<00:18, 542.19 it/sec, feas=True, obj=[16.35661687 25.4914123 ]]
    INFO - 16:21:07:      2%|▏         | 194/10000 [00:00<00:18, 542.69 it/sec, feas=True, obj=[16.35645426 25.49151379]]
    INFO - 16:21:07:      2%|▏         | 195/10000 [00:00<00:18, 543.43 it/sec, feas=True, obj=[16.35645426 25.49151379]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.20626256632241502
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.28956223e-08 3.22391358e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-10.8243637]
    INFO - 16:21:07:          wrapped_ineq2 = [-39.89635594]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.429880060283522 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.429879917262929 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.206262566322415 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [41.63265306 35.91836735]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.429880060283522 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.429879917262929 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.206262566322415 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 196/10000 [00:00<00:18, 538.82 it/sec, feas=True, obj=[16.35645426 25.49151379]]
    INFO - 16:21:07:      2%|▏         | 197/10000 [00:00<00:18, 539.90 it/sec, feas=True, obj=[14.47666997 26.72698623]]
    INFO - 16:21:07:      2%|▏         | 198/10000 [00:00<00:18, 540.91 it/sec, feas=True, obj=[14.46080786 26.72744066]]
    INFO - 16:21:07:      2%|▏         | 199/10000 [00:00<00:18, 541.93 it/sec, feas=True, obj=[14.45889916 26.72708902]]
    INFO - 16:21:07:      2%|▏         | 200/10000 [00:00<00:18, 542.62 it/sec, feas=True, obj=[14.45874622 26.72719297]]
    INFO - 16:21:07:      2%|▏         | 201/10000 [00:00<00:18, 543.38 it/sec, feas=True, obj=[14.45874622 26.72719297]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.19980813861417973
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.24679929e-08 3.11700354e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-10.29202946]
    INFO - 16:21:07:          wrapped_ineq2 = [-40.94172201]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.344374754501743  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.344374603672398  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1998081386141797 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [38.85714286 36.85714286]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.344374754501743  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.344374603672398  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1998081386141797 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 202/10000 [00:00<00:18, 538.65 it/sec, feas=True, obj=[14.45874622 26.72719297]]
    INFO - 16:21:07:      2%|▏         | 203/10000 [00:00<00:18, 539.75 it/sec, feas=True, obj=[12.68629432 27.99889971]]
    INFO - 16:21:07:      2%|▏         | 204/10000 [00:00<00:18, 540.74 it/sec, feas=True, obj=[12.67051626 27.99944249]]
    INFO - 16:21:07:      2%|▏         | 205/10000 [00:00<00:18, 541.71 it/sec, feas=True, obj=[12.66861499 27.99910359]]
    INFO - 16:21:07:      2%|▏         | 206/10000 [00:00<00:18, 542.45 it/sec, feas=True, obj=[12.66847181 27.99921   ]]
    INFO - 16:21:07:      2%|▏         | 207/10000 [00:00<00:18, 543.21 it/sec, feas=True, obj=[12.66847181 27.99921   ]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.1925637577731446
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.20261561e-08 3.00654257e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-9.74200027]
    INFO - 16:21:07:          wrapped_ineq2 = [-42.00762687]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.258395476742623  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.258395318299852  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1925637577731446 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [36.08163265 37.79591837]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.258395476742623  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.258395318299852  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1925637577731446 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 208/10000 [00:00<00:18, 538.57 it/sec, feas=True, obj=[12.66847181 27.99921   ]]
    INFO - 16:21:07:      2%|▏         | 209/10000 [00:00<00:18, 539.61 it/sec, feas=True, obj=[11.00515155 29.30775805]]
    INFO - 16:21:07:      2%|▏         | 210/10000 [00:00<00:18, 540.48 it/sec, feas=True, obj=[10.98946331 29.30839237]]
    INFO - 16:21:07:      2%|▏         | 211/10000 [00:00<00:18, 541.44 it/sec, feas=True, obj=[10.98757099 29.30806707]]
    INFO - 16:21:07:      2%|▏         | 212/10000 [00:00<00:18, 542.15 it/sec, feas=True, obj=[10.98743766 29.30817594]]
    INFO - 16:21:07:      2%|▏         | 213/10000 [00:00<00:18, 542.85 it/sec, feas=True, obj=[10.98743766 29.30817594]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.18451613974834757
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.15729790e-08 2.89322877e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-9.17397857]
    INFO - 16:21:07:          wrapped_ineq2 = [-43.09441589]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.171934256564121  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.171934090726174  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1845161397483476 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [33.30612245 38.73469388]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.171934256564121  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.171934090726174  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1845161397483476 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 214/10000 [00:00<00:18, 538.71 it/sec, feas=True, obj=[10.98743766 29.30817594]]
    INFO - 16:21:07:      2%|▏         | 215/10000 [00:00<00:18, 539.76 it/sec, feas=True, obj=[ 9.43509909 30.65418945]]
    INFO - 16:21:07:      2%|▏         | 216/10000 [00:00<00:18, 540.68 it/sec, feas=True, obj=[ 9.41950673 30.65491867]]
    INFO - 16:21:07:      2%|▏         | 217/10000 [00:00<00:18, 541.62 it/sec, feas=True, obj=[ 9.41762501 30.65460787]]
    INFO - 16:21:07:      2%|▏         | 218/10000 [00:00<00:18, 542.29 it/sec, feas=True, obj=[ 9.4175016  30.65471918]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.1756516239482621
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.11113714e-08 2.77783130e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-8.58765836]
    INFO - 16:21:07:          wrapped_ineq2 = [-44.20244425]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.084982897600763  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.084982724607004  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1756516239482621 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [30.53061224 39.67346939]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.084982897600763  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.084982724607004  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1756516239482621 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 219/10000 [00:00<00:18, 538.69 it/sec, feas=True, obj=[ 9.4175016  30.65471918]]
    INFO - 16:21:07:      2%|▏         | 220/10000 [00:00<00:18, 539.29 it/sec, feas=True, obj=[ 9.4175016  30.65471918]]
    INFO - 16:21:07:      2%|▏         | 221/10000 [00:00<00:18, 540.33 it/sec, feas=True, obj=[ 7.97804763 32.03884013]]
    INFO - 16:21:07:      2%|▏         | 222/10000 [00:00<00:18, 541.26 it/sec, feas=True, obj=[ 7.96255753 32.03966771]]
    INFO - 16:21:07:      2%|▏         | 223/10000 [00:00<00:18, 542.19 it/sec, feas=True, obj=[ 7.96068815 32.03937238]]
    INFO - 16:21:07:      2%|▏         | 224/10000 [00:00<00:18, 542.82 it/sec, feas=True, obj=[ 7.96057475 32.03948612]]
    INFO - 16:21:07:      2%|▏         | 225/10000 [00:00<00:17, 543.54 it/sec, feas=True, obj=[ 7.96057475 32.03948612]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.16595615812676265
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.06443210e-08 2.66108291e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-7.98272487]
    INFO - 16:21:07:          wrapped_ineq2 = [-45.33207732]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.9975329684952907 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.9975327886042522 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1659561581267626 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [27.75510204 40.6122449 ]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.9975329684952907 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.9975327886042522 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1659561581267626 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 226/10000 [00:00<00:18, 540.34 it/sec, feas=True, obj=[ 7.96057475 32.03948612]]
    INFO - 16:21:07:      2%|▏         | 227/10000 [00:00<00:18, 540.88 it/sec, feas=True, obj=[ 7.96057475 32.03948612]]
    INFO - 16:21:07:      2%|▏         | 228/10000 [00:00<00:18, 541.83 it/sec, feas=True, obj=[ 6.63596326 33.46237501]]
    INFO - 16:21:07:      2%|▏         | 229/10000 [00:00<00:18, 542.69 it/sec, feas=True, obj=[ 6.62058212 33.46330461]]
    INFO - 16:21:07:      2%|▏         | 230/10000 [00:00<00:17, 543.57 it/sec, feas=True, obj=[ 6.61872696 33.46302576]]
    INFO - 16:21:07:      2%|▏         | 231/10000 [00:00<00:17, 544.16 it/sec, feas=True, obj=[ 6.61862363 33.46314191]]
    INFO - 16:21:07:      2%|▏         | 232/10000 [00:00<00:17, 544.86 it/sec, feas=True, obj=[ 6.61862363 33.46314191]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.15541528248002634
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [1.01742152e-08 2.54355470e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-7.3588542]
    INFO - 16:21:07:          wrapped_ineq2 = [-46.48369104]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.9095757933568522 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.909575606844184  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1554152824800263 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [24.97959184 41.55102041]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.9095757933568522 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.909575606844184  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1554152824800263 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 233/10000 [00:00<00:18, 540.75 it/sec, feas=True, obj=[ 6.61862363 33.46314191]]
    INFO - 16:21:07:      2%|▏         | 234/10000 [00:00<00:18, 541.68 it/sec, feas=True, obj=[ 5.41086973 34.92547856]]
    INFO - 16:21:07:      2%|▏         | 235/10000 [00:00<00:17, 542.53 it/sec, feas=True, obj=[ 5.39560462 34.92651398]]
    INFO - 16:21:07:      2%|▏         | 236/10000 [00:00<00:17, 543.39 it/sec, feas=True, obj=[ 5.39376567 34.92625268]]
    INFO - 16:21:07:      2%|▏         | 237/10000 [00:00<00:17, 543.98 it/sec, feas=True, obj=[ 5.39367249 34.92637122]]
    INFO - 16:21:07:      2%|▏         | 238/10000 [00:00<00:17, 544.63 it/sec, feas=True, obj=[ 5.39367249 34.92637122]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.1440141129034469
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [9.70430136e-09 2.42605491e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-6.71571295]
    INFO - 16:21:07:          wrapped_ineq2 = [-47.6576724]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.8211024417151838 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.8211022488715362 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1440141129034469 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [22.20408163 42.48979592]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.8211024417151838 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.8211022488715362 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1440141129034469 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 239/10000 [00:00<00:18, 540.85 it/sec, feas=True, obj=[ 5.39367249 34.92637122]]
    INFO - 16:21:07:      2%|▏         | 240/10000 [00:00<00:18, 541.78 it/sec, feas=True, obj=[ 4.30485089 36.42885552]]
    INFO - 16:21:07:      2%|▏         | 241/10000 [00:00<00:17, 542.59 it/sec, feas=True, obj=[ 4.28970922 36.43000074]]
    INFO - 16:21:07:      2%|▏         | 242/10000 [00:00<00:17, 543.40 it/sec, feas=True, obj=[ 4.28788864 36.42975814]]
    INFO - 16:21:07:      2%|▏         | 243/10000 [00:00<00:17, 544.01 it/sec, feas=True, obj=[ 4.28780567 36.42987905]]
    INFO - 16:21:07:      2%|▏         | 244/10000 [00:00<00:17, 544.62 it/sec, feas=True, obj=[ 4.28780567 36.42987905]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.13173732335364916
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [9.23629528e-09 2.30908004e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-6.05295781]
    INFO - 16:21:07:          wrapped_ineq2 = [-48.85441989]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.7321037179378262 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.7321035190667113 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1317373233536492 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [19.42857143 43.42857143]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.7321037179378262 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.7321035190667113 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1317373233536492 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      2%|▏         | 245/10000 [00:00<00:18, 541.70 it/sec, feas=True, obj=[ 4.28780567 36.42987905]]
    INFO - 16:21:07:      2%|▏         | 246/10000 [00:00<00:17, 542.21 it/sec, feas=True, obj=[ 4.28780567 36.42987905]]
    INFO - 16:21:07:      2%|▏         | 247/10000 [00:00<00:17, 543.09 it/sec, feas=True, obj=[ 3.32005317 37.97323185]]
    INFO - 16:21:07:      2%|▏         | 248/10000 [00:00<00:17, 543.90 it/sec, feas=True, obj=[ 3.30504278 37.97449102]]
    INFO - 16:21:07:      2%|▏         | 249/10000 [00:00<00:17, 544.72 it/sec, feas=True, obj=[ 3.30324284 37.97426832]]
    INFO - 16:21:07:      2%|▎         | 250/10000 [00:00<00:17, 545.29 it/sec, feas=True, obj=[ 3.30317013 37.97439158]]
    INFO - 16:21:07:      3%|▎         | 251/10000 [00:00<00:17, 545.91 it/sec, feas=True, obj=[ 3.30317013 37.97439158]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.11856912725650058
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [8.77319550e-09 2.19329177e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-5.37023516]
    INFO - 16:21:07:          wrapped_ineq2 = [-50.07434394]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.6425701500749383 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.6425699454906001 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1185691272565006 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [16.65306122 44.36734694]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.6425701500749383 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.6425699454906001 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1185691272565006 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 252/10000 [00:00<00:17, 542.10 it/sec, feas=True, obj=[ 3.30317013 37.97439158]]
    INFO - 16:21:07:      3%|▎         | 253/10000 [00:00<00:17, 542.98 it/sec, feas=True, obj=[ 2.45868826 39.55935553]]
    INFO - 16:21:07:      3%|▎         | 254/10000 [00:00<00:17, 543.78 it/sec, feas=True, obj=[ 2.44381739 39.56073302]]
    INFO - 16:21:07:      3%|▎         | 255/10000 [00:00<00:17, 544.58 it/sec, feas=True, obj=[ 2.44204056 39.56053151]]
    INFO - 16:21:07:      3%|▎         | 256/10000 [00:00<00:17, 545.11 it/sec, feas=True, obj=[ 2.44197816 39.56065708]]
    INFO - 16:21:07:      3%|▎         | 257/10000 [00:00<00:17, 545.74 it/sec, feas=True, obj=[ 2.44197816 39.56065708]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.10449325789721346
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [8.31667002e-09 2.07914130e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-4.66718063]
    INFO - 16:21:07:          wrapped_ineq2 = [-51.3178675]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.5524919780933236 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.5524917681186522 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.1044932578972135 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [13.87755102 45.30612245]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.5524919780933236 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.5524917681186522 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.1044932578972135 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 258/10000 [00:00<00:17, 541.98 it/sec, feas=True, obj=[ 2.44197816 39.56065708]]
    INFO - 16:21:07:      3%|▎         | 259/10000 [00:00<00:17, 542.82 it/sec, feas=True, obj=[ 1.72303596 41.18799761]]
    INFO - 16:21:07:      3%|▎         | 260/10000 [00:00<00:17, 543.58 it/sec, feas=True, obj=[ 1.70831329 41.18949797]]
    INFO - 16:21:07:      3%|▎         | 261/10000 [00:00<00:17, 544.34 it/sec, feas=True, obj=[ 1.70656219 41.18931901]]
    INFO - 16:21:07:      3%|▎         | 262/10000 [00:00<00:17, 544.89 it/sec, feas=True, obj=[ 1.70651014 41.18944686]]
    INFO - 16:21:07:      3%|▎         | 263/10000 [00:00<00:17, 545.48 it/sec, feas=True, obj=[ 1.70651014 41.18944686]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.0894929477236469
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [7.86855203e-09 1.96713046e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-3.94341862]
    INFO - 16:21:07:          wrapped_ineq2 = [-52.58542653]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.461859141458376  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.4618589264228979 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.0894929477236469 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [11.10204082 46.24489796]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.461859141458376  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.4618589264228979 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.0894929477236469 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 264/10000 [00:00<00:17, 542.42 it/sec, feas=True, obj=[ 1.70651014 41.18944686]]
    INFO - 16:21:07:      3%|▎         | 265/10000 [00:00<00:17, 542.91 it/sec, feas=True, obj=[ 1.70651014 41.18944686]]
    INFO - 16:21:07:      3%|▎         | 266/10000 [00:00<00:17, 543.76 it/sec, feas=True, obj=[ 1.11544708 42.85995314]]
    INFO - 16:21:07:      3%|▎         | 267/10000 [00:00<00:17, 544.49 it/sec, feas=True, obj=[ 1.10088177 42.86158114]]
    INFO - 16:21:07:      3%|▎         | 268/10000 [00:00<00:17, 545.24 it/sec, feas=True, obj=[ 1.09915921 42.86142618]]
    INFO - 16:21:07:      3%|▎         | 269/10000 [00:00<00:17, 545.77 it/sec, feas=True, obj=[ 1.09911754 42.86155626]]
    INFO - 16:21:07:      3%|▎         | 270/10000 [00:00<00:17, 546.37 it/sec, feas=True, obj=[ 1.09911754 42.86155626]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.07355090648823236
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [7.43070672e-09 1.85765536e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-3.19856184]
    INFO - 16:21:07:          wrapped_ineq2 = [-53.87747056]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      |  0.3706612660191941 |      5      | float |
    INFO - 16:21:07:          | y    |      0      |  0.3706610462571641 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.07355090648823236 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [ 8.32653061 47.18367347]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      |  0.3706612660191941 |      5      | float |
    INFO - 16:21:07:       | y    |      0      |  0.3706610462571641 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.07355090648823236 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 271/10000 [00:00<00:17, 543.00 it/sec, feas=True, obj=[ 1.09911754 42.86155626]]
    INFO - 16:21:07:      3%|▎         | 272/10000 [00:00<00:17, 543.80 it/sec, feas=True, obj=[ 0.63834664 44.57604226]]
    INFO - 16:21:07:      3%|▎         | 273/10000 [00:00<00:17, 544.33 it/sec, feas=True, obj=[ 0.62394835 44.57780289]]
    INFO - 16:21:07:      3%|▎         | 274/10000 [00:00<00:17, 545.02 it/sec, feas=True, obj=[ 0.62225734 44.57767347]]
    INFO - 16:21:07:      3%|▎         | 275/10000 [00:00<00:17, 545.50 it/sec, feas=True, obj=[ 0.62222607 44.57780576]]
    INFO - 16:21:07:      3%|▎         | 276/10000 [00:00<00:17, 546.02 it/sec, feas=True, obj=[ 0.62222607 44.57780576]]
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.05664929814787476
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [7.00443525e-09 1.75108239e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-2.43221075]
    INFO - 16:21:07:          wrapped_ineq2 = [-55.19446335]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      |  0.278887650148449  |      5      | float |
    INFO - 16:21:07:          | y    |      0      |  0.2788874259970627 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.05664929814787476 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [ 5.55102041 48.12244898]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      |  0.278887650148449  |      5      | float |
    INFO - 16:21:07:       | y    |      0      |  0.2788874259970627 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.05664929814787476 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 277/10000 [00:00<00:17, 543.36 it/sec, feas=True, obj=[ 0.62222607 44.57780576]]
    INFO - 16:21:07:      3%|▎         | 278/10000 [00:00<00:17, 543.83 it/sec, feas=True, obj=[ 0.62222607 44.57780576]]
    INFO - 16:21:07:      3%|▎         | 279/10000 [00:00<00:17, 544.61 it/sec, feas=True, obj=[ 0.29423714 46.33711132]]
    INFO - 16:21:07:      3%|▎         | 280/10000 [00:00<00:17, 545.30 it/sec, feas=True, obj=[ 0.28001607 46.33900984]]
    INFO - 16:21:07:      3%|▎         | 281/10000 [00:00<00:17, 546.02 it/sec, feas=True, obj=[ 0.27835982 46.3389076 ]]
    INFO - 16:21:07:      3%|▎         | 282/10000 [00:00<00:17, 546.51 it/sec, feas=True, obj=[ 0.27833898 46.33904203]]
    INFO - 16:21:07:      3%|▎         | 283/10000 [00:00<00:17, 547.06 it/sec, feas=True, obj=[ 0.27833898 46.33904203]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.0387697164344738
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [6.59095267e-09 1.64769687e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-1.64395306]
    INFO - 16:21:07:          wrapped_ineq2 = [-56.53688344]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.1865272500846318 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.1865270218823821 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.0387697164344738 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [ 2.7755102  49.06122449]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 0.1865272500846318 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 0.1865270218823821 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.0387697164344738 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 284/10000 [00:00<00:17, 544.68 it/sec, feas=True, obj=[ 0.27833898 46.33904203]]
    INFO - 16:21:07:      3%|▎         | 285/10000 [00:00<00:17, 545.14 it/sec, feas=True, obj=[ 0.27833898 46.33904203]]
    INFO - 16:21:07:      3%|▎         | 286/10000 [00:00<00:17, 545.93 it/sec, feas=True, obj=[ 0.08570212 48.14403408]]
    INFO - 16:21:07:      3%|▎         | 287/10000 [00:00<00:17, 546.64 it/sec, feas=True, obj=[ 0.07166903 48.14607599]]
    INFO - 16:21:07:      3%|▎         | 288/10000 [00:00<00:17, 547.35 it/sec, feas=True, obj=[ 0.07005101 48.14600266]]
    INFO - 16:21:07:      3%|▎         | 289/10000 [00:00<00:17, 546.14 it/sec, feas=True, obj=[ 0.07004059 48.14613918]]
    INFO - 16:21:07:      3%|▎         | 290/10000 [00:00<00:17, 546.56 it/sec, feas=True, obj=[ 0.07004059 48.14613918]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.019893159001336508
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [6.19114759e-09 1.54771496e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-0.83336312]
    INFO - 16:21:07:          wrapped_ineq2 = [-57.9052249]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 0.09356866441982352 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 0.09356843250501073 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.01989315900133651 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+---------------------+-------------+-------+
    INFO - 16:21:07:      3%|▎         | 291/10000 [00:00<00:19, 497.68 it/sec, feas=True, obj=[ 0.07004059 48.14613918]]
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: None
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: 30.287800698724006
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          ineq1 = [-10.82436312]
    INFO - 16:21:07:          ineq2 = [-39.89635695]
    INFO - 16:21:07:    Pareto efficient solutions:
    INFO - 16:21:07:       Pareto optimal points : 213 / 291
    INFO - 16:21:07:       Utopia point : [2.60649439e-24 4.00000000e+00]
    INFO - 16:21:07:       Compromise solution (closest to utopia) : [[14.45889916 26.72708902]]
    INFO - 16:21:07:       Distance from utopia : 26.93659852600369
    INFO - 16:21:07:       Objective values:
    INFO - 16:21:07:          +------+-------------+-----+---------+
    INFO - 16:21:07:          | name |           1 |   2 |       3 |
    INFO - 16:21:07:          +------+-------------+-----+---------+
    INFO - 16:21:07:          |    1 | 2.60649e-24 | 136 | 14.4589 |
    INFO - 16:21:07:          |    2 |          50 |   4 | 26.7271 |
    INFO - 16:21:07:          +------+-------------+-----+---------+
    INFO - 16:21:07:       Constraint values:
    INFO - 16:21:07:          +------+--------------+------+----------+
    INFO - 16:21:07:          | name |            1 |    2 |        3 |
    INFO - 16:21:07:          +------+--------------+------+----------+
    INFO - 16:21:07:          |    1 | -8.07532e-12 |  -22 | -10.2918 |
    INFO - 16:21:07:          |    2 |        -59.3 | -7.3 | -40.9422 |
    INFO - 16:21:07:          +------+--------------+------+----------+
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +-------+-------------+-------------+---+---------+-------------+-------+
    INFO - 16:21:07:          |  name | lower_bound |           1 | 2 |       3 | upper_bound |  type |
    INFO - 16:21:07:          +-------+-------------+-------------+---+---------+-------------+-------+
    INFO - 16:21:07:          | x (1) |           0 | 8.07232e-13 | 5 | 1.34434 |           5 | float |
    INFO - 16:21:07:          | y (1) |           0 | 3.63507e-26 | 3 | 1.34442 |           3 | float |
    INFO - 16:21:07:          +-------+-------------+-------------+---+---------+-------------+-------+

Display the Pareto front#

GEMSEO detects the Pareto optimal points and the dominated ones.

execute_post(problem, post_name="ParetoFront", save=False, show=True)
Pareto front
<gemseo.post.pareto_front.ParetoFront object at 0x7c2f8f9cc7a0>

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.

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)
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2)
    INFO - 16:21:07:    with respect to x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
    INFO - 16:21:07:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.429879988721743 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.429879988721355 |      3      | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Solving optimization problem with algorithm MNBI:
 WARNING - 16:21:07: Option `custom_anchor_points` was set. The resulting Pareto front might be incomplete.
    INFO - 16:21:07: Searching for the individual optimum of each objective
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize f_0
    INFO - 16:21:07:    with respect to x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
    INFO - 16:21:07:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.429879988721743 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.429879988721355 |      3      | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: 1.946427143038124e-21
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          ineq1 = [-2.20587992e-10]
    INFO - 16:21:07:          ineq2 = [-59.3]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |         Value         | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      |  2.20591655726034e-11 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.093800925524851e-24 |      3      | float |
    INFO - 16:21:07:          +------+-------------+-----------------------+-------------+-------+
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize f_1
    INFO - 16:21:07:    with respect to x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0
    INFO - 16:21:07:       ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.429879988721743 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.429879988721355 |      3      | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: 4.0
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          ineq1 = [-22.]
    INFO - 16:21:07:          ineq2 = [-7.3]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 4.999999999999998 |      5      | float |
    INFO - 16:21:07:          | y    |      0      |         3         |      3      | float |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [63.01630435 28.68566176]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.429879988721743 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.429879988721355 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    |         0         |     inf     | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23006624766814543
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [2.35958406e-05 5.89896008e-06]
    INFO - 16:21:07:          wrapped_ineq1 = [-13.95717111]
    INFO - 16:21:07:          wrapped_ineq2 = [-33.39411594]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 1.991452157953268  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 1.991468771474431  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2300662476681454 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [65.50652174 27.84338235]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 1.991452157953268  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 1.991468771474431  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2300662476681454 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23079497225227696
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [3.84877552e-09 9.62177893e-10]
    INFO - 16:21:07:          wrapped_ineq1 = [-14.32145361]
    INFO - 16:21:07:          wrapped_ineq2 = [-32.58771023]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.065139359964297 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.065139414923363 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.230794972252277 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [67.99673913 27.00110294]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.065139359964297 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.065139414923363 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.230794972252277 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
   ERROR - 16:21:07: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 399, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
    return _nlopt.opt_optimize(self, *args)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23096895870340897
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [3.93919564e-09 9.84785586e-10]
    INFO - 16:21:07:          wrapped_ineq1 = [-14.67324895]
    INFO - 16:21:07:          wrapped_ineq2 = [-31.7958384]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.138485442599762 |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.138485491988275 |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.230968958703409 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [70.48695652 26.15882353]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.138485442599762 |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.138485491988275 |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.230968958703409 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+-------------------+-------------+-------+
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.23059550980130075
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [4.02404865e-09 1.00601838e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-15.01278173]
    INFO - 16:21:07:          wrapped_ineq2 = [-31.01819989]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.211503064031514  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.211503107833023  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2305955098013008 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Solving mNBI sub-problem for phi_beta = [72.97717391 25.31654412]
    INFO - 16:21:07: Optimization problem:
    INFO - 16:21:07:    minimize -t_extraction
    INFO - 16:21:07:    with respect to t, x, y
    INFO - 16:21:07:    under the inequality constraints
    INFO - 16:21:07:       wrapped_ineq1 <= 0.0
    INFO - 16:21:07:       wrapped_ineq2 <= 0.0
    INFO - 16:21:07:       beta_sub_optim_constraint <= 0.0
    INFO - 16:21:07:    over the design space:
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:       | x    |      0      | 2.211503064031514  |      5      | float |
    INFO - 16:21:07:       | y    |      0      | 2.211503107833023  |      3      | float |
    INFO - 16:21:07:       | t    |     -inf    | 0.2305955098013008 |     inf     | float |
    INFO - 16:21:07:       +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: -0.22968191496846257
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          beta_sub_optim_constraint = [4.09991330e-09 1.02499875e-09]
    INFO - 16:21:07:          wrapped_ineq1 = [-15.34021524]
    INFO - 16:21:07:          wrapped_ineq2 = [-30.25460517]
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07:          | x    |      0      | 2.284196597883724  |      5      | float |
    INFO - 16:21:07:          | y    |      0      | 2.284196636140448  |      3      | float |
    INFO - 16:21:07:          | t    |     -inf    | 0.2296819149684626 |     inf     | float |
    INFO - 16:21:07:          +------+-------------+--------------------+-------------+-------+
    INFO - 16:21:07: Optimization result:
    INFO - 16:21:07:    Optimizer info:
    INFO - 16:21:07:       Status: None
    INFO - 16:21:07:       Message: None
    INFO - 16:21:07:    Solution:
    INFO - 16:21:07:       The solution is feasible.
    INFO - 16:21:07:       Objective: 30.287800698724006
    INFO - 16:21:07:       Standardized constraints:
    INFO - 16:21:07:          ineq1 = [-10.82436312]
    INFO - 16:21:07:          ineq2 = [-39.89635695]
    INFO - 16:21:07:    Pareto efficient solutions:
    INFO - 16:21:07:       Pareto optimal points : 237 / 328
    INFO - 16:21:07:       Utopia point : [2.60649439e-24 4.00000000e+00]
    INFO - 16:21:07:       Compromise solution (closest to utopia) : [[14.45889916 26.72708902]]
    INFO - 16:21:07:       Distance from utopia : 26.93659852600369
    INFO - 16:21:07:       Objective values:
    INFO - 16:21:07:          +------+-------------+-----+---------+
    INFO - 16:21:07:          | name |           1 |   2 |       3 |
    INFO - 16:21:07:          +------+-------------+-----+---------+
    INFO - 16:21:07:          |    1 | 2.60649e-24 | 136 | 14.4589 |
    INFO - 16:21:07:          |    2 |          50 |   4 | 26.7271 |
    INFO - 16:21:07:          +------+-------------+-----+---------+
    INFO - 16:21:07:       Constraint values:
    INFO - 16:21:07:          +------+--------------+------+----------+
    INFO - 16:21:07:          | name |            1 |    2 |        3 |
    INFO - 16:21:07:          +------+--------------+------+----------+
    INFO - 16:21:07:          |    1 | -8.07532e-12 |  -22 | -10.2918 |
    INFO - 16:21:07:          |    2 |        -59.3 | -7.3 | -40.9422 |
    INFO - 16:21:07:          +------+--------------+------+----------+
    INFO - 16:21:07:       Design space:
    INFO - 16:21:07:          +-------+-------------+-------------+---+---------+-------------+-------+
    INFO - 16:21:07:          |  name | lower_bound |           1 | 2 |       3 | upper_bound |  type |
    INFO - 16:21:07:          +-------+-------------+-------------+---+---------+-------------+-------+
    INFO - 16:21:07:          | x (1) |           0 | 8.07232e-13 | 5 | 1.34434 |           5 | float |
    INFO - 16:21:07:          | y (1) |           0 | 3.63507e-26 | 3 | 1.34442 |           3 | float |
    INFO - 16:21:07:          +-------+-------------+-------------+---+---------+-------------+-------+
Optimization result:
  • Design variables: [1.42987999 1.42987999]
  • Objective function: 30.287800698724006
  • Feasible solution: True


Display the Pareto front#

We can clearly see the effect of the local refinement.

execute_post(problem, post_name="ParetoFront", save=False, show=True)
Pareto front
<gemseo.post.pareto_front.ParetoFront object at 0x7c2f8fa28050>

Total running time of the script: (0 minutes 1.029 seconds)

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