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.problems.multiobjective_optimization.fonseca_fleming import FonsecaFleming
from gemseo.settings.opt import MNBI_Settings
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 - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize FonsecaFleming
INFO - 20:34:35: with respect to x
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: Solving optimization problem with algorithm MNBI:
INFO - 20:34:35: Searching for the individual optimum of each objective
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize f_0
INFO - 20:34:35: with respect to x
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: 1%| | 6/1000 [00:00<00:00, 1296.41 it/sec, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 20:34:35: 1%| | 7/1000 [00:00<00:00, 1333.76 it/sec, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 20:34:35: 1%| | 8/1000 [00:00<00:00, 1364.45 it/sec, obj=[2.36699549e-13 9.81684376e-01]]
INFO - 20:34:35: 1%| | 9/1000 [00:00<00:00, 1397.79 it/sec, obj=[3.17715032e-09 9.81684363e-01]]
INFO - 20:34:35: 1%| | 10/1000 [00:00<00:00, 1506.25 it/sec, obj=[2.74601453e-11 9.81684374e-01]]
INFO - 20:34:35: 1%| | 11/1000 [00:00<00:00, 1513.99 it/sec, obj=[5.44009282e-14 9.81684376e-01]]
INFO - 20:34:35: 1%| | 12/1000 [00:00<00:00, 1420.83 it/sec, obj=[0. 0.98168436]]
INFO - 20:34:35: 1%|▏ | 13/1000 [00:00<00:00, 1433.72 it/sec, obj=[0. 0.98168436]]
INFO - 20:34:35: 1%|▏ | 14/1000 [00:00<00:00, 1514.11 it/sec, obj=[0. 0.98168436]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: Objective: 0.0
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+--------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+--------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.5773502690103198 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.5773502690115331 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.5773502690114345 | 4 | float |
INFO - 20:34:35: +------+-------------+--------------------+-------------+-------+
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize f_1
INFO - 20:34:35: with respect to x
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: 2%|▏ | 15/1000 [00:00<00:00, 1240.50 it/sec, obj=[1. 1.]]
INFO - 20:34:35: 2%|▏ | 16/1000 [00:00<00:00, 1301.52 it/sec, obj=[0.99999998 0.9931056 ]]
INFO - 20:34:35: 2%|▏ | 17/1000 [00:00<00:00, 1309.73 it/sec, obj=[0.99688636 0.14955784]]
INFO - 20:34:35: 2%|▏ | 18/1000 [00:00<00:00, 1267.86 it/sec, obj=[0.9492493 0.07206897]]
INFO - 20:34:35: 2%|▏ | 19/1000 [00:00<00:00, 1280.97 it/sec, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 20:34:35: 2%|▏ | 20/1000 [00:00<00:00, 1295.28 it/sec, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 20:34:35: 2%|▏ | 21/1000 [00:00<00:00, 1308.34 it/sec, obj=[9.81684376e-01 2.44582132e-13]]
INFO - 20:34:35: 2%|▏ | 22/1000 [00:00<00:00, 1320.02 it/sec, obj=[9.81684363e-01 3.30383776e-09]]
INFO - 20:34:35: 2%|▏ | 23/1000 [00:00<00:00, 1365.20 it/sec, obj=[9.81684374e-01 2.85538260e-11]]
INFO - 20:34:35: 2%|▏ | 24/1000 [00:00<00:00, 1373.21 it/sec, obj=[9.81684376e-01 5.49560397e-14]]
INFO - 20:34:35: 2%|▎ | 25/1000 [00:00<00:00, 1337.73 it/sec, obj=[0.98168436 0. ]]
INFO - 20:34:35: 3%|▎ | 26/1000 [00:00<00:00, 1348.42 it/sec, obj=[0.98168436 0. ]]
INFO - 20:34:35: 3%|▎ | 27/1000 [00:00<00:00, 1387.82 it/sec, obj=[0.98168436 0. ]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: Objective: 0.0
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.5773502690171886 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.5773502690183139 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.5773502690182495 | 4 | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: | t | -inf | 0 | inf | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
ERROR - 20:34:35: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 403, in _run
nlopt_problem.optimize(x_0.real)
File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.2.0/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
return _nlopt.opt_optimize(self, *args)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.1439142599025487
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [ 4.99600361e-16 -1.33226763e-15]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+------------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+------------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1439142599025487 | inf | float |
INFO - 20:34:35: +------+-------------+------------------------+-------------+-------+
INFO - 20:34:35: 3%|▎ | 28/1000 [00:00<00:01, 798.69 it/sec, obj=[0.63212056 0.63212056]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: None
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: Objective: 0.8939534673502063
INFO - 20:34:35: Pareto efficient solutions:
INFO - 20:34:35: Pareto optimal points : 8 / 28
INFO - 20:34:35: Utopia point : [0. 0.]
INFO - 20:34:35: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 20:34:35: Distance from utopia : 0.8939534673502063
INFO - 20:34:35: Objective values:
INFO - 20:34:35: +------+----------+----------+----------+
INFO - 20:34:35: | name | 1 | 2 | 3 |
INFO - 20:34:35: +------+----------+----------+----------+
INFO - 20:34:35: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 20:34:35: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 20:34:35: +------+----------+----------+----------+
INFO - 20:34:35: Design space:
INFO - 20:34:35: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 20:34:35: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 20:34:35: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 20:34:35: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 20:34:35: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 20:34:35: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 20:34:35: +-------+-------------+---------+----------+---+-------------+-------+
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 0x78592fb2bb90>
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 - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize FonsecaFleming
INFO - 20:34:35: with respect to x
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: Solving optimization problem with algorithm MNBI:
INFO - 20:34:35: Searching for the individual optimum of each objective
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize f_0
INFO - 20:34:35: with respect to x
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: 1%| | 6/1000 [00:00<00:00, 1153.87 it/sec, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 20:34:35: 1%| | 7/1000 [00:00<00:00, 1202.05 it/sec, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 20:34:35: 1%| | 8/1000 [00:00<00:00, 1239.68 it/sec, obj=[2.36699549e-13 9.81684376e-01]]
INFO - 20:34:35: 1%| | 9/1000 [00:00<00:00, 1274.91 it/sec, obj=[3.17715032e-09 9.81684363e-01]]
INFO - 20:34:35: 1%| | 10/1000 [00:00<00:00, 1381.48 it/sec, obj=[2.74601453e-11 9.81684374e-01]]
INFO - 20:34:35: 1%| | 11/1000 [00:00<00:00, 1393.79 it/sec, obj=[5.44009282e-14 9.81684376e-01]]
INFO - 20:34:35: 1%| | 12/1000 [00:00<00:00, 1320.49 it/sec, obj=[0. 0.98168436]]
INFO - 20:34:35: 1%|▏ | 13/1000 [00:00<00:00, 1343.47 it/sec, obj=[0. 0.98168436]]
INFO - 20:34:35: 1%|▏ | 14/1000 [00:00<00:00, 1417.71 it/sec, obj=[0. 0.98168436]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: Objective: 0.0
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+--------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+--------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.5773502690103198 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.5773502690115331 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.5773502690114345 | 4 | float |
INFO - 20:34:35: +------+-------------+--------------------+-------------+-------+
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize f_1
INFO - 20:34:35: with respect to x
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: 2%|▏ | 15/1000 [00:00<00:00, 1153.21 it/sec, obj=[1. 1.]]
INFO - 20:34:35: 2%|▏ | 16/1000 [00:00<00:00, 1211.22 it/sec, obj=[0.99999998 0.9931056 ]]
INFO - 20:34:35: 2%|▏ | 17/1000 [00:00<00:00, 1223.98 it/sec, obj=[0.99688636 0.14955784]]
INFO - 20:34:35: 2%|▏ | 18/1000 [00:00<00:00, 1191.58 it/sec, obj=[0.9492493 0.07206897]]
INFO - 20:34:35: 2%|▏ | 19/1000 [00:00<00:00, 1208.18 it/sec, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 20:34:35: 2%|▏ | 20/1000 [00:00<00:00, 1222.24 it/sec, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 20:34:35: 2%|▏ | 21/1000 [00:00<00:00, 1236.29 it/sec, obj=[9.81684376e-01 2.44582132e-13]]
INFO - 20:34:35: 2%|▏ | 22/1000 [00:00<00:00, 1252.32 it/sec, obj=[9.81684363e-01 3.30383776e-09]]
INFO - 20:34:35: 2%|▏ | 23/1000 [00:00<00:00, 1296.24 it/sec, obj=[9.81684374e-01 2.85538260e-11]]
INFO - 20:34:35: 2%|▏ | 24/1000 [00:00<00:00, 1305.37 it/sec, obj=[9.81684376e-01 5.49560397e-14]]
INFO - 20:34:35: 2%|▎ | 25/1000 [00:00<00:00, 1277.50 it/sec, obj=[0.98168436 0. ]]
INFO - 20:34:35: 3%|▎ | 26/1000 [00:00<00:00, 1287.36 it/sec, obj=[0.98168436 0. ]]
INFO - 20:34:35: 3%|▎ | 27/1000 [00:00<00:00, 1325.32 it/sec, obj=[0.98168436 0. ]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: Objective: 0.0
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.5773502690171886 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.5773502690183139 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.5773502690182495 | 4 | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0 | 4 | float |
INFO - 20:34:35: | t | -inf | 0 | inf | float |
INFO - 20:34:35: +------+-------------+-------+-------------+-------+
INFO - 20:34:35: 3%|▎ | 28/1000 [00:00<00:00, 1120.39 it/sec, obj=[0.90043834 0.20664322]]
INFO - 20:34:35: 3%|▎ | 29/1000 [00:00<00:00, 1121.52 it/sec, obj=[0.91873293 0.15869784]]
INFO - 20:34:35: 3%|▎ | 30/1000 [00:00<00:00, 1123.94 it/sec, obj=[0.91966962 0.15614908]]
INFO - 20:34:35: 3%|▎ | 31/1000 [00:00<00:00, 1126.43 it/sec, obj=[0.91967277 0.15614049]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.04794255052718603
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [-3.40005801e-16 1.22124533e-15]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.3394642613203538 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.3394642613418939 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.3394642613412335 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.04794255052718603 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.3394642613203538 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.3394642613418939 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.3394642613412335 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.04794255052718603 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: 3%|▎ | 32/1000 [00:00<00:00, 1028.99 it/sec, obj=[0.91967277 0.15614049]]
INFO - 20:34:35: 3%|▎ | 33/1000 [00:00<00:00, 1034.75 it/sec, obj=[0.84203912 0.33739501]]
INFO - 20:34:35: 3%|▎ | 34/1000 [00:00<00:00, 1041.82 it/sec, obj=[0.85527677 0.31046303]]
INFO - 20:34:35: 4%|▎ | 35/1000 [00:00<00:00, 1044.97 it/sec, obj=[0.85546004 0.31007996]]
INFO - 20:34:35: 4%|▎ | 36/1000 [00:00<00:00, 1048.64 it/sec, obj=[0.85546007 0.31007988]]
INFO - 20:34:35: 4%|▎ | 37/1000 [00:00<00:00, 1052.38 it/sec, obj=[0.85546011 0.31007981]]
INFO - 20:34:35: 4%|▍ | 38/1000 [00:00<00:00, 1075.27 it/sec, obj=[0.85546009 0.31007985]]
INFO - 20:34:35: 4%|▍ | 39/1000 [00:00<00:00, 1080.28 it/sec, obj=[0.85546008 0.31007987]]
INFO - 20:34:35: 4%|▍ | 40/1000 [00:00<00:00, 1060.02 it/sec, obj=[0.85546036 0.31008138]]
INFO - 20:34:35: 4%|▍ | 41/1000 [00:00<00:00, 1080.37 it/sec, obj=[0.85546008 0.31007988]]
INFO - 20:34:35: 4%|▍ | 42/1000 [00:00<00:00, 1085.66 it/sec, obj=[0.85546008 0.31007987]]
INFO - 20:34:35: 4%|▍ | 43/1000 [00:00<00:00, 1066.18 it/sec, obj=[0.85546008 0.31007988]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.0936428904369956
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [3.23069635e-07 1.54208054e-06]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.2267935871306594 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.2249791246049364 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.2250347509118633 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.0936428904369956 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.2267935871306594 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.2249791246049364 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.2250347509118633 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.0936428904369956 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: 4%|▍ | 44/1000 [00:00<00:00, 1001.30 it/sec, obj=[0.85546008 0.31007988]]
INFO - 20:34:35: 4%|▍ | 45/1000 [00:00<00:00, 1006.29 it/sec, obj=[0.77244255 0.46197037]]
INFO - 20:34:35: 5%|▍ | 46/1000 [00:00<00:00, 1013.19 it/sec, obj=[0.79066399 0.50014328]]
INFO - 20:34:35: 5%|▍ | 47/1000 [00:00<00:00, 1031.07 it/sec, obj=[0.77247321 0.46039445]]
INFO - 20:34:35: 5%|▍ | 48/1000 [00:00<00:00, 1019.74 it/sec, obj=[0.77732675 0.45120451]]
INFO - 20:34:35: 5%|▍ | 49/1000 [00:00<00:00, 1021.00 it/sec, obj=[0.77767105 0.45050041]]
INFO - 20:34:35: 5%|▌ | 50/1000 [00:00<00:00, 1021.88 it/sec, obj=[0.77769343 0.45046537]]
INFO - 20:34:35: 5%|▌ | 51/1000 [00:00<00:00, 1025.05 it/sec, obj=[0.77769345 0.45046533]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.1254738422258529
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [3.91048601e-05 9.65823903e-05]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.1302778506739593 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.1307744591161613 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.130759234500589 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1254738422258529 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.1302778506739593 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.1307744591161613 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.130759234500589 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1254738422258529 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: 5%|▌ | 52/1000 [00:00<00:00, 976.24 it/sec, obj=[0.77769345 0.45046533]]
INFO - 20:34:35: 5%|▌ | 53/1000 [00:00<00:00, 974.63 it/sec, obj=[0.68180949 0.57909344]]
INFO - 20:34:35: 5%|▌ | 54/1000 [00:00<00:00, 977.03 it/sec, obj=[0.76279322 0.68252822]]
INFO - 20:34:35: 6%|▌ | 55/1000 [00:00<00:00, 991.68 it/sec, obj=[0.68234298 0.5793074 ]]
INFO - 20:34:35: 6%|▌ | 56/1000 [00:00<00:00, 979.85 it/sec, obj=[0.68456816 0.57565254]]
INFO - 20:34:35: 6%|▌ | 57/1000 [00:00<00:00, 982.49 it/sec, obj=[0.68463865 0.57556363]]
INFO - 20:34:35: 6%|▌ | 58/1000 [00:00<00:00, 986.02 it/sec, obj=[0.68463912 0.57556308]]
INFO - 20:34:35: 6%|▌ | 59/1000 [00:00<00:00, 989.03 it/sec, obj=[0.68463912 0.57556308]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.1418536322151337
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [2.95427000e-06 3.97562998e-06]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.04283469865322287 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.04289526887534079 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.04289341196294805 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1418536322151337 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | -0.04283469865322287 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | -0.04289526887534079 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | -0.04289341196294805 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1418536322151337 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: 6%|▌ | 60/1000 [00:00<00:00, 949.88 it/sec, obj=[0.68463912 0.57556308]]
INFO - 20:34:35: 6%|▌ | 61/1000 [00:00<00:00, 952.33 it/sec, obj=[0.57513327 0.68501309]]
INFO - 20:34:35: 6%|▌ | 62/1000 [00:00<00:00, 955.52 it/sec, obj=[0.57997105 0.68786997]]
INFO - 20:34:35: 6%|▋ | 63/1000 [00:00<00:00, 960.35 it/sec, obj=[0.57615647 0.68412765]]
INFO - 20:34:35: 6%|▋ | 64/1000 [00:00<00:00, 963.39 it/sec, obj=[0.57556315 0.68463907]]
INFO - 20:34:35: 6%|▋ | 65/1000 [00:00<00:00, 966.64 it/sec, obj=[0.57556308 0.68463912]]
INFO - 20:34:35: 7%|▋ | 66/1000 [00:00<00:00, 969.46 it/sec, obj=[0.57556308 0.68463912]]
INFO - 20:34:35: 7%|▋ | 67/1000 [00:00<00:00, 972.22 it/sec, obj=[0.57556308 0.68463912]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.1418571157886582
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [7.64347430e-09 5.70086756e-09]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.0428863643568409 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.04286884211382702 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.04286937930449231 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1418571157886582 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.0428863643568409 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.04286884211382702 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.04286937930449231 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1418571157886582 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: 7%|▋ | 68/1000 [00:00<00:00, 940.27 it/sec, obj=[0.57556308 0.68463912]]
INFO - 20:34:35: 7%|▋ | 69/1000 [00:00<00:00, 942.54 it/sec, obj=[0.4529475 0.77609793]]
INFO - 20:34:35: 7%|▋ | 70/1000 [00:00<00:00, 945.37 it/sec, obj=[0.45096065 0.77788395]]
INFO - 20:34:35: 7%|▋ | 71/1000 [00:00<00:00, 949.40 it/sec, obj=[0.45063606 0.77758411]]
INFO - 20:34:35: 7%|▋ | 72/1000 [00:00<00:00, 951.99 it/sec, obj=[0.45046539 0.77769342]]
INFO - 20:34:35: 7%|▋ | 73/1000 [00:00<00:00, 954.65 it/sec, obj=[0.45046533 0.77769345]]
INFO - 20:34:35: 7%|▋ | 74/1000 [00:00<00:00, 957.52 it/sec, obj=[0.45046533 0.77769345]]
INFO - 20:34:35: 8%|▊ | 75/1000 [00:00<00:00, 960.40 it/sec, obj=[0.45046533 0.77769345]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.1255364252374492
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [1.20443868e-07 3.26237204e-08]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.130628678262207 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.1306269867059493 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.1306270385652022 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1255364252374492 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.130628678262207 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.1306269867059493 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.1306270385652022 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.1255364252374492 | inf | float |
INFO - 20:34:35: +------+-------------+---------------------+-------------+-------+
INFO - 20:34:35: 8%|▊ | 76/1000 [00:00<00:00, 931.97 it/sec, obj=[0.45046533 0.77769345]]
INFO - 20:34:35: 8%|▊ | 77/1000 [00:00<00:00, 933.96 it/sec, obj=[0.31697497 0.85214023]]
INFO - 20:34:35: 8%|▊ | 78/1000 [00:00<00:00, 936.49 it/sec, obj=[0.31011071 0.85544839]]
INFO - 20:34:35: 8%|▊ | 79/1000 [00:00<00:00, 939.16 it/sec, obj=[0.31055084 0.85552527]]
INFO - 20:34:35: 8%|▊ | 80/1000 [00:00<00:00, 948.97 it/sec, obj=[0.31010969 0.85544622]]
INFO - 20:34:35: 8%|▊ | 81/1000 [00:00<00:00, 942.36 it/sec, obj=[0.31008018 0.85545993]]
INFO - 20:34:35: 8%|▊ | 82/1000 [00:00<00:00, 945.01 it/sec, obj=[0.31007988 0.85546008]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.0936426515727078
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [5.77041547e-07 1.20798910e-07]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.2255934194588862 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.2256069512252434 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.2256065363721858 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.09364265157270781 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832]
INFO - 20:34:35: Optimization problem:
INFO - 20:34:35: minimize -t_extraction
INFO - 20:34:35: with respect to t, x
INFO - 20:34:35: under the inequality constraints
INFO - 20:34:35: beta_sub_optim_constraint <= 0.0
INFO - 20:34:35: over the design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.2255934194588862 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.2256069512252434 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.2256065363721858 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.09364265157270781 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: 8%|▊ | 83/1000 [00:00<00:01, 899.75 it/sec, obj=[0.31007987 0.85546008]]
INFO - 20:34:35: 8%|▊ | 84/1000 [00:00<00:01, 902.69 it/sec, obj=[0.17146343 0.91399085]]
INFO - 20:34:35: 8%|▊ | 85/1000 [00:00<00:01, 906.04 it/sec, obj=[0.15665503 0.91958662]]
INFO - 20:34:35: 9%|▊ | 86/1000 [00:00<00:01, 908.32 it/sec, obj=[0.15619301 0.91968459]]
INFO - 20:34:35: 9%|▊ | 87/1000 [00:00<00:01, 910.80 it/sec, obj=[0.156184 0.91965682]]
INFO - 20:34:35: 9%|▉ | 88/1000 [00:00<00:00, 913.31 it/sec, obj=[0.1561405 0.91967277]]
INFO - 20:34:35: 9%|▉ | 89/1000 [00:00<00:00, 915.83 it/sec, obj=[0.15614049 0.91967277]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: The solution is feasible.
INFO - 20:34:35: Objective: 0.04791993097249924
INFO - 20:34:35: Standardized constraints:
INFO - 20:34:35: beta_sub_optim_constraint = [6.57082378e-05 6.24935106e-06]
INFO - 20:34:35: Design space:
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | Name | Lower bound | Value | Upper bound | Type |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: | x[0] | -4 | 0.3393430625162628 | 4 | float |
INFO - 20:34:35: | x[1] | -4 | 0.3394726842127751 | 4 | float |
INFO - 20:34:35: | x[2] | -4 | 0.3394687103073935 | 4 | float |
INFO - 20:34:35: | t | -inf | -0.04791993097249924 | inf | float |
INFO - 20:34:35: +------+-------------+----------------------+-------------+-------+
INFO - 20:34:35: 9%|▉ | 90/1000 [00:00<00:01, 792.50 it/sec, obj=[0.15614049 0.91967277]]
INFO - 20:34:35: Optimization result:
INFO - 20:34:35: Optimizer info:
INFO - 20:34:35: Status: None
INFO - 20:34:35: Message: None
INFO - 20:34:35: Number of calls to the objective function by the optimizer: 0
INFO - 20:34:35: Solution:
INFO - 20:34:35: Objective: 0.8939534673502063
INFO - 20:34:35: Pareto efficient solutions:
INFO - 20:34:35: Pareto optimal points : 58 / 90
INFO - 20:34:35: Utopia point : [0. 0.]
INFO - 20:34:35: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 20:34:35: Distance from utopia : 0.8939534673502063
INFO - 20:34:35: Objective values:
INFO - 20:34:35: +------+----------+----------+----------+
INFO - 20:34:35: | name | 1 | 2 | 3 |
INFO - 20:34:35: +------+----------+----------+----------+
INFO - 20:34:35: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 20:34:35: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 20:34:35: +------+----------+----------+----------+
INFO - 20:34:35: Design space:
INFO - 20:34:35: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 20:34:35: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 20:34:35: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 20:34:35: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 20:34:35: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 20:34:35: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 20:34:35: +-------+-------------+---------+----------+---+-------------+-------+
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 0x78592f5a1d90>
Total running time of the script: (0 minutes 0.367 seconds)