Note
Go to the end to download the full example code.
Multi-objective Fonseca-Fleming example with the mNBI algorithm#
In this example, the modified Normal Boundary Intersection algorithm (mNBI) is used to
solve the FonsecaFleming optimization problem [FF95]:
\[\begin{split}\begin{aligned}
\text{minimize the objective function }
& f_1(x) = 1 - exp(-\sum_{i=1}^{d}((x_i - 1 / sqrt(d)) ^ 2)) \\
& f_2(x) = 1 + exp(-\sum_{i=1}^{d}((x_i + 1 / sqrt(d)) ^ 2)) \\
\text{with respect to the design variables }&x\\
\text{subject to the bound constraint}
& x\in[-4,4]^d
\end{aligned}\end{split}\]
We also show how the Pareto front can be refined.
from __future__ import annotations
from gemseo import configure_logger
from gemseo import execute_algo
from gemseo import execute_post
from gemseo.algos.opt.mnbi.settings.mnbi_settings import MNBI_Settings
from gemseo.problems.multiobjective_optimization.fonseca_fleming import FonsecaFleming
configure_logger()
<RootLogger root (INFO)>
Solve the Fonseca-Fleming optimization problem#
The 3 sub-optimization problems of mNBI are solved with SLSQP, a gradient-based optimization algorithm from the NLOPT library, with a maximum of 100 iterations. The analytic gradients are provided.
opt_problem = FonsecaFleming()
mnbi_settings = MNBI_Settings(
max_iter=1000,
sub_optim_max_iter=100,
n_sub_optim=3,
sub_optim_algo="NLOPT_SLSQP",
)
result = execute_algo(opt_problem, settings_model=mnbi_settings)
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize FonsecaFleming
INFO - 08:36:10: with respect to x
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: Solving optimization problem with algorithm MNBI:
INFO - 08:36:10: Searching for the individual optimum of each objective
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize f_0
INFO - 08:36:10: with respect to x
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: 1%| | 6/1000 [00:00<00:01, 598.18 it/sec, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 08:36:10: 1%| | 7/1000 [00:00<00:01, 616.41 it/sec, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 08:36:10: 1%| | 8/1000 [00:00<00:01, 632.08 it/sec, obj=[9.01501096e-14 9.81684376e-01]]
INFO - 08:36:10: 1%| | 9/1000 [00:00<00:01, 644.00 it/sec, obj=[8.15628010e-10 9.81684362e-01]]
INFO - 08:36:10: 1%| | 10/1000 [00:00<00:01, 697.11 it/sec, obj=[7.07334191e-12 9.81684374e-01]]
INFO - 08:36:10: 1%| | 11/1000 [00:00<00:01, 697.71 it/sec, obj=[4.27435864e-14 9.81684376e-01]]
INFO - 08:36:10: 1%| | 12/1000 [00:00<00:01, 651.05 it/sec, obj=[0. 0.98168436]]
INFO - 08:36:10: 1%|▏ | 13/1000 [00:00<00:01, 660.00 it/sec, obj=[0. 0.98168436]]
INFO - 08:36:10: 1%|▏ | 14/1000 [00:00<00:01, 698.39 it/sec, obj=[0. 0.98168436]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 17
INFO - 08:36:10: Solution:
INFO - 08:36:10: Objective: 0.0
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.5773502684895009 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.5773502684994094 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.5773502684993135 | 4 | float |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize f_1
INFO - 08:36:10: with respect to x
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: 2%|▏ | 15/1000 [00:00<00:01, 562.50 it/sec, obj=[1. 1.]]
INFO - 08:36:10: 2%|▏ | 16/1000 [00:00<00:01, 592.01 it/sec, obj=[0.99999998 0.9931056 ]]
INFO - 08:36:10: 2%|▏ | 17/1000 [00:00<00:01, 597.51 it/sec, obj=[0.99688636 0.14955784]]
INFO - 08:36:10: 2%|▏ | 18/1000 [00:00<00:01, 578.55 it/sec, obj=[0.9492493 0.07206897]]
INFO - 08:36:10: 2%|▏ | 19/1000 [00:00<00:01, 586.07 it/sec, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 08:36:10: 2%|▏ | 20/1000 [00:00<00:01, 592.97 it/sec, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 08:36:10: 2%|▏ | 21/1000 [00:00<00:01, 598.88 it/sec, obj=[9.81684376e-01 9.24815780e-14]]
INFO - 08:36:10: 2%|▏ | 22/1000 [00:00<00:01, 605.30 it/sec, obj=[9.81684362e-01 8.52572346e-10]]
INFO - 08:36:10: 2%|▏ | 23/1000 [00:00<00:01, 626.61 it/sec, obj=[9.81684374e-01 7.39219796e-12]]
INFO - 08:36:10: 2%|▏ | 24/1000 [00:00<00:01, 628.74 it/sec, obj=[9.81684376e-01 4.29656311e-14]]
INFO - 08:36:10: 2%|▎ | 25/1000 [00:00<00:01, 612.94 it/sec, obj=[0.98168436 0. ]]
INFO - 08:36:10: 3%|▎ | 26/1000 [00:00<00:01, 617.70 it/sec, obj=[0.98168436 0. ]]
INFO - 08:36:10: 3%|▎ | 27/1000 [00:00<00:01, 636.10 it/sec, obj=[0.98168436 0. ]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 17
INFO - 08:36:10: Solution:
INFO - 08:36:10: Objective: 0.0
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.5773502685200489 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.5773502685300462 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.5773502685281993 | 4 | float |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: | t | -inf | 0 | inf | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: 3%|▎ | 28/1000 [00:00<00:01, 538.12 it/sec, obj=[0.63212056 0.63212056]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 4
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.14391425994444806
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [ 8.16013923e-15 -4.96824804e-15]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+------------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+------------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -9.676703882632864e-13 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -9.676703882632864e-13 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -9.676703882632864e-13 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.1439142599444481 | inf | float |
INFO - 08:36:10: +------+-------------+------------------------+-------------+-------+
INFO - 08:36:10: 3%|▎ | 29/1000 [00:00<00:02, 384.41 it/sec, obj=[0.63212056 0.63212056]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: None
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 36
INFO - 08:36:10: Solution:
INFO - 08:36:10: Objective: 0.8939534673502061
INFO - 08:36:10: Pareto efficient solutions:
INFO - 08:36:10: Pareto optimal points : 9 / 29
INFO - 08:36:10: Utopia point : [0. 0.]
INFO - 08:36:10: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 08:36:10: Distance from utopia : 0.8939534673502061
INFO - 08:36:10: Objective values:
INFO - 08:36:10: +------+----------+----------+----------+
INFO - 08:36:10: | name | 1 | 2 | 3 |
INFO - 08:36:10: +------+----------+----------+----------+
INFO - 08:36:10: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 08:36:10: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 08:36:10: +------+----------+----------+----------+
INFO - 08:36:10: Design space:
INFO - 08:36:10: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 08:36:10: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 08:36:10: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 08:36:10: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 08:36:10: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 08:36:10: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 08:36:10: +-------+-------------+---------+----------+---+-------------+-------+
Display the Pareto front#
GEMSEO detects the Pareto optimal points and the dominated ones. The Fonseca-Fleming problem is interesting because its Pareto front is not convex. The mNBI algorithm successfully computes it.
execute_post(opt_problem, post_name="ParetoFront", save=False, show=True)
<gemseo.post.pareto_front.ParetoFront object at 0x7f25228a0cd0>
Solve the Fonseca-Fleming optimization problem more finely#
The Pareto front is then refined with 10 sub-optimizations instead of 3.
opt_problem = FonsecaFleming()
mnbi_settings.n_sub_optim = 10
result = execute_algo(opt_problem, settings_model=mnbi_settings)
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize FonsecaFleming
INFO - 08:36:10: with respect to x
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: Solving optimization problem with algorithm MNBI:
INFO - 08:36:10: Searching for the individual optimum of each objective
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize f_0
INFO - 08:36:10: with respect to x
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: 1%| | 6/1000 [00:00<00:01, 565.08 it/sec, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 08:36:10: 1%| | 7/1000 [00:00<00:01, 585.91 it/sec, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 08:36:10: 1%| | 8/1000 [00:00<00:01, 602.56 it/sec, obj=[9.01501096e-14 9.81684376e-01]]
INFO - 08:36:10: 1%| | 9/1000 [00:00<00:01, 617.65 it/sec, obj=[8.15628010e-10 9.81684362e-01]]
INFO - 08:36:10: 1%| | 10/1000 [00:00<00:01, 670.12 it/sec, obj=[7.07334191e-12 9.81684374e-01]]
INFO - 08:36:10: 1%| | 11/1000 [00:00<00:01, 670.60 it/sec, obj=[4.27435864e-14 9.81684376e-01]]
INFO - 08:36:10: 1%| | 12/1000 [00:00<00:01, 615.45 it/sec, obj=[0. 0.98168436]]
INFO - 08:36:10: 1%|▏ | 13/1000 [00:00<00:01, 612.29 it/sec, obj=[0. 0.98168436]]
INFO - 08:36:10: 1%|▏ | 14/1000 [00:00<00:01, 648.51 it/sec, obj=[0. 0.98168436]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 17
INFO - 08:36:10: Solution:
INFO - 08:36:10: Objective: 0.0
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.5773502684895009 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.5773502684994094 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.5773502684993135 | 4 | float |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize f_1
INFO - 08:36:10: with respect to x
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: 2%|▏ | 15/1000 [00:00<00:01, 526.33 it/sec, obj=[1. 1.]]
INFO - 08:36:10: 2%|▏ | 16/1000 [00:00<00:01, 554.44 it/sec, obj=[0.99999998 0.9931056 ]]
INFO - 08:36:10: 2%|▏ | 17/1000 [00:00<00:01, 561.39 it/sec, obj=[0.99688636 0.14955784]]
INFO - 08:36:10: 2%|▏ | 18/1000 [00:00<00:01, 541.30 it/sec, obj=[0.9492493 0.07206897]]
INFO - 08:36:10: 2%|▏ | 19/1000 [00:00<00:01, 546.06 it/sec, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 08:36:10: 2%|▏ | 20/1000 [00:00<00:01, 553.75 it/sec, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 08:36:10: 2%|▏ | 21/1000 [00:00<00:01, 560.69 it/sec, obj=[9.81684376e-01 9.24815780e-14]]
INFO - 08:36:10: 2%|▏ | 22/1000 [00:00<00:01, 568.07 it/sec, obj=[9.81684362e-01 8.52572346e-10]]
INFO - 08:36:10: 2%|▏ | 23/1000 [00:00<00:01, 588.51 it/sec, obj=[9.81684374e-01 7.39219796e-12]]
INFO - 08:36:10: 2%|▏ | 24/1000 [00:00<00:01, 591.75 it/sec, obj=[9.81684376e-01 4.29656311e-14]]
INFO - 08:36:10: 2%|▎ | 25/1000 [00:00<00:01, 579.04 it/sec, obj=[0.98168436 0. ]]
INFO - 08:36:10: 3%|▎ | 26/1000 [00:00<00:01, 584.38 it/sec, obj=[0.98168436 0. ]]
INFO - 08:36:10: 3%|▎ | 27/1000 [00:00<00:01, 602.09 it/sec, obj=[0.98168436 0. ]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 17
INFO - 08:36:10: Solution:
INFO - 08:36:10: Objective: 0.0
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.5773502685200489 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.5773502685300462 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.5773502685281993 | 4 | float |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0 | 4 | float |
INFO - 08:36:10: | t | -inf | 0 | inf | float |
INFO - 08:36:10: +------+-------------+-------+-------------+-------+
INFO - 08:36:10: 3%|▎ | 28/1000 [00:00<00:01, 518.17 it/sec, obj=[0.90043834 0.20664322]]
INFO - 08:36:10: 3%|▎ | 29/1000 [00:00<00:01, 519.76 it/sec, obj=[0.91873293 0.15869784]]
INFO - 08:36:10: 3%|▎ | 30/1000 [00:00<00:01, 520.92 it/sec, obj=[0.91966962 0.15614908]]
INFO - 08:36:10: 3%|▎ | 31/1000 [00:00<00:01, 522.20 it/sec, obj=[0.91967277 0.15614049]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 7
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.047942550573600556
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [ 6.93889390e-16 -1.83880688e-15]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.339464261305511 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.3394642613042733 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.3394642613061056 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.04794255057360056 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.339464261305511 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.3394642613042733 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.3394642613061056 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.04794255057360056 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: 3%|▎ | 32/1000 [00:00<00:02, 473.14 it/sec, obj=[0.91967277 0.15614049]]
INFO - 08:36:10: 3%|▎ | 33/1000 [00:00<00:02, 476.55 it/sec, obj=[0.84203912 0.33739501]]
INFO - 08:36:10: 3%|▎ | 34/1000 [00:00<00:02, 479.90 it/sec, obj=[0.85527677 0.31046303]]
INFO - 08:36:10: 4%|▎ | 35/1000 [00:00<00:02, 481.41 it/sec, obj=[0.85546004 0.31007996]]
INFO - 08:36:10: 4%|▎ | 36/1000 [00:00<00:01, 483.62 it/sec, obj=[0.85546004 0.31007995]]
INFO - 08:36:10: 4%|▎ | 37/1000 [00:00<00:01, 485.14 it/sec, obj=[0.85546009 0.31007984]]
INFO - 08:36:10: 4%|▍ | 38/1000 [00:00<00:01, 486.87 it/sec, obj=[0.8554601 0.31007982]]
INFO - 08:36:10: 4%|▍ | 39/1000 [00:00<00:01, 497.44 it/sec, obj=[0.8554601 0.31007983]]
INFO - 08:36:10: 4%|▍ | 40/1000 [00:00<00:01, 499.86 it/sec, obj=[0.8554601 0.31007983]]
INFO - 08:36:10: 4%|▍ | 41/1000 [00:00<00:01, 501.89 it/sec, obj=[0.85546009 0.31007984]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 12
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.09364289795630283
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [ 5.50654545e-08 -3.31157324e-08]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.2256025551311831 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.2256025557747829 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.2256025548218257 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.09364289795630283 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.2256025551311831 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.2256025557747829 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.2256025548218257 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.09364289795630283 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: 4%|▍ | 42/1000 [00:00<00:02, 459.56 it/sec, obj=[0.77161691 0.45984452]]
INFO - 08:36:10: 4%|▍ | 43/1000 [00:00<00:02, 461.27 it/sec, obj=[0.77767797 0.45048948]]
INFO - 08:36:10: 4%|▍ | 44/1000 [00:00<00:02, 463.21 it/sec, obj=[0.77769345 0.45046534]]
INFO - 08:36:10: 4%|▍ | 45/1000 [00:00<00:02, 464.71 it/sec, obj=[0.77769475 0.45046867]]
INFO - 08:36:10: 5%|▍ | 46/1000 [00:00<00:02, 473.32 it/sec, obj=[0.77769346 0.45046536]]
INFO - 08:36:10: 5%|▍ | 47/1000 [00:00<00:02, 475.74 it/sec, obj=[0.77769345 0.45046534]]
INFO - 08:36:10: 5%|▍ | 48/1000 [00:00<00:02, 468.73 it/sec, obj=[0.77769345 0.45046533]]
ERROR - 08:36:10: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
nlopt_problem.optimize(x_0.real)
File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 11
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.1255363970177465
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [1.38732549e-06 3.42942337e-06]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.1302316085444764 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.1325189233805686 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.1291321707661721 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.1255363970177465 | inf | float |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.1302316085444764 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.1325189233805686 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.1291321707661721 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.1255363970177465 | inf | float |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: 5%|▍ | 49/1000 [00:00<00:02, 443.17 it/sec, obj=[0.77769345 0.45046533]]
INFO - 08:36:10: 5%|▌ | 50/1000 [00:00<00:02, 445.59 it/sec, obj=[0.68555698 0.58426668]]
INFO - 08:36:10: 5%|▌ | 51/1000 [00:00<00:02, 448.16 it/sec, obj=[0.68399938 0.57650637]]
INFO - 08:36:10: 5%|▌ | 52/1000 [00:00<00:02, 450.74 it/sec, obj=[0.68462482 0.57558952]]
INFO - 08:36:10: 5%|▌ | 53/1000 [00:00<00:02, 452.11 it/sec, obj=[0.68463858 0.57556374]]
INFO - 08:36:10: 5%|▌ | 54/1000 [00:00<00:02, 453.95 it/sec, obj=[0.68463912 0.57556308]]
INFO - 08:36:10: 6%|▌ | 55/1000 [00:00<00:02, 455.43 it/sec, obj=[0.68463912 0.57556308]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 10
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.14185306201349607
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [3.45183683e-06 4.64490810e-06]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.04291047733084286 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.04270203738455658 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.04301066762956651 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.1418530620134961 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | -0.04291047733084286 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | -0.04270203738455658 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | -0.04301066762956651 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.1418530620134961 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: 6%|▌ | 56/1000 [00:00<00:02, 433.69 it/sec, obj=[0.68463912 0.57556308]]
INFO - 08:36:10: 6%|▌ | 57/1000 [00:00<00:02, 435.39 it/sec, obj=[0.57517744 0.68504627]]
INFO - 08:36:10: 6%|▌ | 58/1000 [00:00<00:02, 436.97 it/sec, obj=[0.64468964 0.73529265]]
INFO - 08:36:10: 6%|▌ | 59/1000 [00:00<00:02, 443.33 it/sec, obj=[0.57567735 0.68526336]]
INFO - 08:36:10: 6%|▌ | 60/1000 [00:00<00:02, 438.68 it/sec, obj=[0.57562684 0.68458418]]
INFO - 08:36:10: 6%|▌ | 61/1000 [00:00<00:02, 440.30 it/sec, obj=[0.57556309 0.68463912]]
INFO - 08:36:10: 6%|▌ | 62/1000 [00:00<00:02, 441.84 it/sec, obj=[0.57556308 0.68463912]]
INFO - 08:36:10: 6%|▋ | 63/1000 [00:00<00:02, 443.47 it/sec, obj=[0.57556308 0.68463912]]
INFO - 08:36:10: 6%|▋ | 64/1000 [00:00<00:02, 445.06 it/sec, obj=[0.57556308 0.68463912]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 13
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.141857085596892
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [4.92134715e-08 3.53502475e-08]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.04285487868216808 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.04297029133272012 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.04279940357728407 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.141857085596892 | inf | float |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.04285487868216808 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.04297029133272012 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.04279940357728407 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.141857085596892 | inf | float |
INFO - 08:36:10: +------+-------------+---------------------+-------------+-------+
INFO - 08:36:10: 6%|▋ | 65/1000 [00:00<00:02, 423.76 it/sec, obj=[0.57556308 0.68463912]]
INFO - 08:36:10: 7%|▋ | 66/1000 [00:00<00:02, 425.07 it/sec, obj=[0.45296521 0.77610508]]
INFO - 08:36:10: 7%|▋ | 67/1000 [00:00<00:02, 426.37 it/sec, obj=[0.4857272 0.79138788]]
INFO - 08:36:10: 7%|▋ | 68/1000 [00:00<00:02, 431.76 it/sec, obj=[0.45359005 0.77673074]]
INFO - 08:36:10: 7%|▋ | 69/1000 [00:00<00:02, 428.30 it/sec, obj=[0.45080811 0.77747394]]
INFO - 08:36:10: 7%|▋ | 70/1000 [00:00<00:02, 429.75 it/sec, obj=[0.45046544 0.77769341]]
INFO - 08:36:10: 7%|▋ | 71/1000 [00:00<00:02, 431.00 it/sec, obj=[0.45046534 0.77769345]]
INFO - 08:36:10: 7%|▋ | 72/1000 [00:00<00:02, 432.42 it/sec, obj=[0.45046533 0.77769345]]
INFO - 08:36:10: 7%|▋ | 73/1000 [00:00<00:02, 433.77 it/sec, obj=[0.45046533 0.77769345]]
INFO - 08:36:10: 7%|▋ | 74/1000 [00:00<00:02, 435.18 it/sec, obj=[0.45046533 0.77769345]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 14
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.12553645235059005
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [ 1.49882953e-07 -4.26679669e-09]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.1305933450637484 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.130790914197771 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.1304983800119963 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.12553645235059 | inf | float |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.1305933450637484 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.130790914197771 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.1304983800119963 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.12553645235059 | inf | float |
INFO - 08:36:10: +------+-------------+--------------------+-------------+-------+
INFO - 08:36:10: 8%|▊ | 75/1000 [00:00<00:02, 420.87 it/sec, obj=[0.45046533 0.77769345]]
INFO - 08:36:10: 8%|▊ | 76/1000 [00:00<00:02, 422.21 it/sec, obj=[0.31703362 0.85215238]]
INFO - 08:36:10: 8%|▊ | 77/1000 [00:00<00:02, 423.51 it/sec, obj=[0.40288985 0.87338417]]
INFO - 08:36:10: 8%|▊ | 78/1000 [00:00<00:02, 428.17 it/sec, obj=[0.31715667 0.85249332]]
INFO - 08:36:10: 8%|▊ | 79/1000 [00:00<00:02, 426.11 it/sec, obj=[0.31040011 0.85530776]]
INFO - 08:36:10: 8%|▊ | 80/1000 [00:00<00:02, 426.68 it/sec, obj=[0.31008035 0.85545991]]
INFO - 08:36:10: 8%|▊ | 81/1000 [00:00<00:02, 427.88 it/sec, obj=[0.3100799 0.85546007]]
INFO - 08:36:10: 8%|▊ | 82/1000 [00:00<00:02, 429.20 it/sec, obj=[0.31007988 0.85546007]]
INFO - 08:36:10: 8%|▊ | 83/1000 [00:00<00:02, 430.40 it/sec, obj=[0.31007988 0.85546008]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 13
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.09364266739626721
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [7.23490535e-07 8.72958074e-08]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.2255448712436445 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.2258763306714222 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.2253855494856154 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.09364266739626721 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832]
INFO - 08:36:10: Optimization problem:
INFO - 08:36:10: minimize -t_extraction
INFO - 08:36:10: with respect to t, x
INFO - 08:36:10: subject to constraints:
INFO - 08:36:10: beta_sub_optim_constraint <= 0.0
INFO - 08:36:10: over the design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.2255448712436445 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.2258763306714222 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.2253855494856154 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.09364266739626721 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: 8%|▊ | 84/1000 [00:00<00:02, 417.68 it/sec, obj=[0.31007988 0.85546008]]
INFO - 08:36:10: 8%|▊ | 85/1000 [00:00<00:02, 419.31 it/sec, obj=[0.17162737 0.91400636]]
INFO - 08:36:10: 9%|▊ | 86/1000 [00:00<00:02, 421.20 it/sec, obj=[0.29857451 0.93068206]]
INFO - 08:36:10: 9%|▊ | 87/1000 [00:00<00:02, 425.35 it/sec, obj=[0.17152252 0.91447953]]
INFO - 08:36:10: 9%|▉ | 88/1000 [00:00<00:02, 423.54 it/sec, obj=[0.15696325 0.91937307]]
INFO - 08:36:10: 9%|▉ | 89/1000 [00:00<00:02, 424.60 it/sec, obj=[0.15614412 0.91967146]]
INFO - 08:36:10: 9%|▉ | 90/1000 [00:00<00:02, 425.74 it/sec, obj=[0.15614051 0.91967277]]
INFO - 08:36:10: 9%|▉ | 91/1000 [00:00<00:02, 426.24 it/sec, obj=[0.15614049 0.91967277]]
INFO - 08:36:10: 9%|▉ | 92/1000 [00:00<00:02, 427.38 it/sec, obj=[0.15614049 0.91967277]]
INFO - 08:36:10: 9%|▉ | 93/1000 [00:00<00:02, 428.38 it/sec, obj=[0.15614049 0.91967277]]
INFO - 08:36:10: 9%|▉ | 94/1000 [00:00<00:02, 429.54 it/sec, obj=[0.15614049 0.91967277]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 15
INFO - 08:36:10: Solution:
INFO - 08:36:10: The solution is feasible.
INFO - 08:36:10: Objective: 0.047941264984527124
INFO - 08:36:10: Standardized constraints:
INFO - 08:36:10: beta_sub_optim_constraint = [ 4.88540472e-06 -4.82444740e-08]
INFO - 08:36:10: Design space:
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: | x[0] | -4 | 0.3394255200896286 | 4 | float |
INFO - 08:36:10: | x[1] | -4 | 0.3396321336864006 | 4 | float |
INFO - 08:36:10: | x[2] | -4 | 0.3393262076587185 | 4 | float |
INFO - 08:36:10: | t | -inf | -0.04794126498452712 | inf | float |
INFO - 08:36:10: +------+-------------+----------------------+-------------+-------+
INFO - 08:36:10: 10%|▉ | 95/1000 [00:00<00:02, 386.95 it/sec, obj=[0.15614049 0.91967277]]
INFO - 08:36:10: Optimization result:
INFO - 08:36:10: Optimizer info:
INFO - 08:36:10: Status: None
INFO - 08:36:10: Message: None
INFO - 08:36:10: Number of calls to the objective function by the optimizer: 123
INFO - 08:36:10: Solution:
INFO - 08:36:10: Objective: 0.8939534673502061
INFO - 08:36:10: Pareto efficient solutions:
INFO - 08:36:10: Pareto optimal points : 61 / 95
INFO - 08:36:10: Utopia point : [0. 0.]
INFO - 08:36:10: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 08:36:10: Distance from utopia : 0.8939534673502061
INFO - 08:36:10: Objective values:
INFO - 08:36:10: +------+----------+----------+----------+
INFO - 08:36:10: | name | 1 | 2 | 3 |
INFO - 08:36:10: +------+----------+----------+----------+
INFO - 08:36:10: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 08:36:10: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 08:36:10: +------+----------+----------+----------+
INFO - 08:36:10: Design space:
INFO - 08:36:10: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 08:36:10: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 08:36:10: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 08:36:10: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 08:36:10: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 08:36:10: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 08:36:10: +-------+-------------+---------+----------+---+-------------+-------+
Display the Pareto front#
We can clearly see the effect of the refinement.
execute_post(opt_problem, post_name="ParetoFront", save=False, show=True)
<gemseo.post.pareto_front.ParetoFront object at 0x7f2522aaf850>
Total running time of the script: (0 minutes 0.874 seconds)