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 execute_algo
from gemseo import execute_post
from gemseo.problems.multiobjective_optimization.fonseca_fleming import FonsecaFleming
from gemseo.settings.opt import MNBI_Settings
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 - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize FonsecaFleming
INFO - 16:21:08: with respect to x
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: Solving optimization problem with algorithm MNBI:
INFO - 16:21:08: Searching for the individual optimum of each objective
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize f_0
INFO - 16:21:08: with respect to x
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: 1%| | 6/1000 [00:00<00:00, 1183.16 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 16:21:08: 1%| | 7/1000 [00:00<00:00, 1185.12 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 16:21:08: 1%| | 8/1000 [00:00<00:00, 1194.32 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]]
INFO - 16:21:08: 1%| | 9/1000 [00:00<00:00, 1199.82 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]]
INFO - 16:21:08: 1%| | 10/1000 [00:00<00:00, 1219.98 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]]
INFO - 16:21:08: 1%| | 11/1000 [00:00<00:00, 1219.63 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]]
INFO - 16:21:08: 1%| | 12/1000 [00:00<00:00, 1221.64 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:21:08: 1%|▏ | 13/1000 [00:00<00:00, 1225.55 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: Objective: 0.0
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.5773502690103198 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.5773502690115331 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.5773502690114345 | 4 | float |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize f_1
INFO - 16:21:08: with respect to x
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: 1%|▏ | 14/1000 [00:00<00:00, 1038.25 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:21:08: 2%|▏ | 15/1000 [00:00<00:00, 1061.04 it/sec, feas=True, obj=[1. 1.]]
INFO - 16:21:08: 2%|▏ | 16/1000 [00:00<00:00, 1077.45 it/sec, feas=True, obj=[0.99999998 0.9931056 ]]
INFO - 16:21:08: 2%|▏ | 17/1000 [00:00<00:00, 1085.23 it/sec, feas=True, obj=[0.99688636 0.14955784]]
INFO - 16:21:08: 2%|▏ | 18/1000 [00:00<00:00, 1092.57 it/sec, feas=True, obj=[0.9492493 0.07206897]]
INFO - 16:21:08: 2%|▏ | 19/1000 [00:00<00:00, 1100.18 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 16:21:08: 2%|▏ | 20/1000 [00:00<00:00, 1105.50 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 16:21:08: 2%|▏ | 21/1000 [00:00<00:00, 1111.80 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]]
INFO - 16:21:08: 2%|▏ | 22/1000 [00:00<00:00, 1119.05 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]]
INFO - 16:21:08: 2%|▏ | 23/1000 [00:00<00:00, 1130.62 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]]
INFO - 16:21:08: 2%|▏ | 24/1000 [00:00<00:00, 1133.76 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]]
INFO - 16:21:08: 2%|▎ | 25/1000 [00:00<00:00, 1137.56 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:21:08: 3%|▎ | 26/1000 [00:00<00:00, 1142.79 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: Objective: 0.0
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.5773502690171886 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.5773502690183139 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.5773502690182495 | 4 | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: | t | -inf | 0 | inf | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: 3%|▎ | 27/1000 [00:00<00:00, 1011.54 it/sec, feas=True, obj=[0.98168436 0. ]]
ERROR - 16:21:08: 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 - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.1439142599025487
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [ 4.99600361e-16 -1.33226763e-15]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+------------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+------------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1439142599025487 | inf | float |
INFO - 16:21:08: +------+-------------+------------------------+-------------+-------+
INFO - 16:21:08: 3%|▎ | 28/1000 [00:00<00:01, 716.09 it/sec, feas=True, obj=[0.63212056 0.63212056]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: None
INFO - 16:21:08: Solution:
INFO - 16:21:08: Objective: 0.8939534673502063
INFO - 16:21:08: Pareto efficient solutions:
INFO - 16:21:08: Pareto optimal points : 8 / 28
INFO - 16:21:08: Utopia point : [0. 0.]
INFO - 16:21:08: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 16:21:08: Distance from utopia : 0.8939534673502063
INFO - 16:21:08: Objective values:
INFO - 16:21:08: +------+----------+----------+----------+
INFO - 16:21:08: | name | 1 | 2 | 3 |
INFO - 16:21:08: +------+----------+----------+----------+
INFO - 16:21:08: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 16:21:08: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 16:21:08: +------+----------+----------+----------+
INFO - 16:21:08: Design space:
INFO - 16:21:08: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:21:08: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 16:21:08: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:21:08: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:21:08: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:21:08: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:21:08: +-------+-------------+---------+----------+---+-------------+-------+
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 0x7c2f8fcfcda0>
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 - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize FonsecaFleming
INFO - 16:21:08: with respect to x
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: Solving optimization problem with algorithm MNBI:
INFO - 16:21:08: Searching for the individual optimum of each objective
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize f_0
INFO - 16:21:08: with respect to x
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: 1%| | 6/1000 [00:00<00:00, 1259.30 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 16:21:08: 1%| | 7/1000 [00:00<00:00, 1252.73 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 16:21:08: 1%| | 8/1000 [00:00<00:00, 1255.50 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]]
INFO - 16:21:08: 1%| | 9/1000 [00:00<00:00, 1252.74 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]]
INFO - 16:21:08: 1%| | 10/1000 [00:00<00:00, 1268.08 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]]
INFO - 16:21:08: 1%| | 11/1000 [00:00<00:00, 1262.38 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]]
INFO - 16:21:08: 1%| | 12/1000 [00:00<00:00, 1260.18 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:21:08: 1%|▏ | 13/1000 [00:00<00:00, 1262.41 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: Objective: 0.0
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.5773502690103198 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.5773502690115331 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.5773502690114345 | 4 | float |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize f_1
INFO - 16:21:08: with respect to x
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: 1%|▏ | 14/1000 [00:00<00:00, 1041.67 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:21:08: 2%|▏ | 15/1000 [00:00<00:00, 1065.17 it/sec, feas=True, obj=[1. 1.]]
INFO - 16:21:08: 2%|▏ | 16/1000 [00:00<00:00, 1080.69 it/sec, feas=True, obj=[0.99999998 0.9931056 ]]
INFO - 16:21:08: 2%|▏ | 17/1000 [00:00<00:00, 1085.99 it/sec, feas=True, obj=[0.99688636 0.14955784]]
INFO - 16:21:08: 2%|▏ | 18/1000 [00:00<00:00, 1092.69 it/sec, feas=True, obj=[0.9492493 0.07206897]]
INFO - 16:21:08: 2%|▏ | 19/1000 [00:00<00:00, 1100.91 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 16:21:08: 2%|▏ | 20/1000 [00:00<00:00, 1107.13 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 16:21:08: 2%|▏ | 21/1000 [00:00<00:00, 1112.77 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]]
INFO - 16:21:08: 2%|▏ | 22/1000 [00:00<00:00, 1117.74 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]]
INFO - 16:21:08: 2%|▏ | 23/1000 [00:00<00:00, 1128.98 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]]
INFO - 16:21:08: 2%|▏ | 24/1000 [00:00<00:00, 1132.22 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]]
INFO - 16:21:08: 2%|▎ | 25/1000 [00:00<00:00, 1137.05 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:21:08: 3%|▎ | 26/1000 [00:00<00:00, 1141.50 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: Objective: 0.0
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.5773502690171886 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.5773502690183139 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.5773502690182495 | 4 | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0 | 4 | float |
INFO - 16:21:08: | t | -inf | 0 | inf | float |
INFO - 16:21:08: +------+-------------+-------+-------------+-------+
INFO - 16:21:08: 3%|▎ | 27/1000 [00:00<00:00, 1016.15 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:21:08: 3%|▎ | 28/1000 [00:00<00:00, 1021.91 it/sec, feas=True, obj=[0.90043834 0.20664322]]
INFO - 16:21:08: 3%|▎ | 29/1000 [00:00<00:00, 1018.28 it/sec, feas=True, obj=[0.91873293 0.15869784]]
INFO - 16:21:08: 3%|▎ | 30/1000 [00:00<00:00, 1017.38 it/sec, feas=True, obj=[0.91966962 0.15614908]]
INFO - 16:21:08: 3%|▎ | 31/1000 [00:00<00:00, 1016.31 it/sec, feas=True, obj=[0.91967277 0.15614049]]
INFO - 16:21:08: 3%|▎ | 32/1000 [00:00<00:00, 1015.72 it/sec, feas=True, obj=[0.91967277 0.15614049]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.04794255052713356
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [ 2.02608763e-13 -3.60156349e-13]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.3394642615047618 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.3394642612459058 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.3394642612538421 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.04794255052713356 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.3394642615047618 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.3394642612459058 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.3394642612538421 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.04794255052713356 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: 3%|▎ | 33/1000 [00:00<00:01, 926.18 it/sec, feas=True, obj=[0.91967277 0.15614049]]
INFO - 16:21:08: 3%|▎ | 34/1000 [00:00<00:01, 931.87 it/sec, feas=True, obj=[0.84203912 0.33739501]]
INFO - 16:21:08: 4%|▎ | 35/1000 [00:00<00:01, 937.44 it/sec, feas=True, obj=[0.85527677 0.31046303]]
INFO - 16:21:08: 4%|▎ | 36/1000 [00:00<00:01, 937.71 it/sec, feas=True, obj=[0.85546004 0.31007996]]
INFO - 16:21:08: 4%|▎ | 37/1000 [00:00<00:01, 940.27 it/sec, feas=True, obj=[0.85546007 0.31008016]]
INFO - 16:21:08: 4%|▍ | 38/1000 [00:00<00:01, 946.47 it/sec, feas=True, obj=[0.85546004 0.31007996]]
INFO - 16:21:08: 4%|▍ | 39/1000 [00:00<00:01, 945.36 it/sec, feas=True, obj=[0.85546004 0.31007996]]
INFO - 16:21:08: 4%|▍ | 40/1000 [00:00<00:01, 946.54 it/sec, feas=True, obj=[0.85546005 0.31007993]]
INFO - 16:21:08: 4%|▍ | 41/1000 [00:00<00:01, 947.90 it/sec, feas=True, obj=[0.85546009 0.31007985]]
INFO - 16:21:08: 4%|▍ | 42/1000 [00:00<00:01, 950.26 it/sec, feas=True, obj=[0.85546012 0.31007978]]
INFO - 16:21:08: 4%|▍ | 43/1000 [00:00<00:01, 955.82 it/sec, feas=True, obj=[0.8554601 0.31007982]]
INFO - 16:21:08: 4%|▍ | 44/1000 [00:00<00:00, 961.46 it/sec, feas=True, obj=[0.85546009 0.31007984]]
INFO - 16:21:08: 4%|▍ | 45/1000 [00:00<00:00, 967.15 it/sec, feas=True, obj=[0.85546009 0.31007985]]
INFO - 16:21:08: 5%|▍ | 46/1000 [00:00<00:00, 973.05 it/sec, feas=True, obj=[0.85546009 0.31007985]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.09364288152510496
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [ 8.90168644e-08 -5.43837472e-08]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.2256025800102535 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.2256025813833293 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.225602581344992 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.09364288152510496 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.2256025800102535 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.2256025813833293 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.225602581344992 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.09364288152510496 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: 5%|▍ | 47/1000 [00:00<00:01, 919.44 it/sec, feas=True, obj=[0.85546009 0.31007985]]
INFO - 16:21:08: 5%|▍ | 48/1000 [00:00<00:01, 923.39 it/sec, feas=True, obj=[0.77161691 0.45984452]]
INFO - 16:21:08: 5%|▍ | 49/1000 [00:00<00:01, 923.69 it/sec, feas=True, obj=[0.77767797 0.45048948]]
INFO - 16:21:08: 5%|▌ | 50/1000 [00:00<00:01, 924.47 it/sec, feas=True, obj=[0.77769345 0.45046534]]
INFO - 16:21:08: 5%|▌ | 51/1000 [00:00<00:01, 925.78 it/sec, feas=True, obj=[0.77769345 0.45046534]]
INFO - 16:21:08: 5%|▌ | 52/1000 [00:00<00:01, 928.03 it/sec, feas=True, obj=[0.77769345 0.45046533]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.1255364919707028
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [-4.93896729e-11 3.78963430e-09]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.130635251180903 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.1306236158744216 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.1306239407408536 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1255364919707028 | inf | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.130635251180903 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.1306236158744216 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.1306239407408536 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1255364919707028 | inf | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: 5%|▌ | 53/1000 [00:00<00:01, 862.60 it/sec, feas=True, obj=[0.77769345 0.45046533]]
INFO - 16:21:08: 5%|▌ | 54/1000 [00:00<00:01, 866.95 it/sec, feas=True, obj=[0.68170379 0.57895302]]
INFO - 16:21:08: 6%|▌ | 55/1000 [00:00<00:01, 868.45 it/sec, feas=True, obj=[0.68474464 0.57570928]]
INFO - 16:21:08: 6%|▌ | 56/1000 [00:00<00:01, 870.11 it/sec, feas=True, obj=[0.68462383 0.57558142]]
INFO - 16:21:08: 6%|▌ | 57/1000 [00:00<00:01, 871.55 it/sec, feas=True, obj=[0.68463908 0.57556312]]
INFO - 16:21:08: 6%|▌ | 58/1000 [00:00<00:01, 872.85 it/sec, feas=True, obj=[0.68463912 0.57556308]]
INFO - 16:21:08: 6%|▌ | 59/1000 [00:00<00:01, 874.79 it/sec, feas=True, obj=[0.68463912 0.57556308]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.14185683491615905
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [2.43262084e-07 3.27480598e-07]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.04287461308631135 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.04287494223710642 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.04287493304700618 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1418568349161591 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | -0.04287461308631135 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | -0.04287494223710642 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | -0.04287493304700618 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1418568349161591 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: 6%|▌ | 60/1000 [00:00<00:01, 840.60 it/sec, feas=True, obj=[0.68463912 0.57556308]]
INFO - 16:21:08: 6%|▌ | 61/1000 [00:00<00:01, 844.56 it/sec, feas=True, obj=[0.57513103 0.68501143]]
INFO - 16:21:08: 6%|▌ | 62/1000 [00:00<00:01, 846.21 it/sec, feas=True, obj=[0.57556323 0.6846392 ]]
INFO - 16:21:08: 6%|▋ | 63/1000 [00:00<00:01, 848.89 it/sec, feas=True, obj=[0.57572435 0.68475688]]
INFO - 16:21:08: 6%|▋ | 64/1000 [00:00<00:01, 853.35 it/sec, feas=True, obj=[0.5755641 0.68463965]]
INFO - 16:21:08: 6%|▋ | 65/1000 [00:00<00:01, 853.47 it/sec, feas=True, obj=[0.57556313 0.68463907]]
INFO - 16:21:08: 7%|▋ | 66/1000 [00:00<00:01, 855.20 it/sec, feas=True, obj=[0.57556308 0.68463912]]
INFO - 16:21:08: 7%|▋ | 67/1000 [00:00<00:01, 857.73 it/sec, feas=True, obj=[0.57556308 0.68463912]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.1418563998953318
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [1.73495133e-06 1.23800550e-06]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.04169925261518337 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.04348747161026356 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.04343754339469275 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1418563998953318 | inf | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.04169925261518337 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.04348747161026356 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.04343754339469275 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.1418563998953318 | inf | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: 7%|▋ | 68/1000 [00:00<00:01, 826.99 it/sec, feas=True, obj=[0.57556308 0.68463912]]
INFO - 16:21:08: 7%|▋ | 69/1000 [00:00<00:01, 830.56 it/sec, feas=True, obj=[0.45538924 0.77708466]]
INFO - 16:21:08: 7%|▋ | 70/1000 [00:00<00:01, 832.68 it/sec, feas=True, obj=[0.63252142 0.83907792]]
INFO - 16:21:08: 7%|▋ | 71/1000 [00:00<00:01, 833.28 it/sec, feas=True, obj=[0.45487133 0.7750112 ]]
INFO - 16:21:08: 7%|▋ | 72/1000 [00:00<00:01, 836.57 it/sec, feas=True, obj=[0.45051277 0.77766464]]
INFO - 16:21:08: 7%|▋ | 73/1000 [00:00<00:01, 838.05 it/sec, feas=True, obj=[0.45046575 0.77769322]]
INFO - 16:21:08: 7%|▋ | 74/1000 [00:00<00:01, 839.61 it/sec, feas=True, obj=[0.45046535 0.77769344]]
INFO - 16:21:08: 8%|▊ | 75/1000 [00:00<00:01, 841.32 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:21:08: 8%|▊ | 76/1000 [00:00<00:01, 843.59 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.125535809547323
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [1.09187899e-06 4.40780275e-07]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.1304145607706708 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.1307382545134637 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.1307292167773948 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.125535809547323 | inf | float |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.1304145607706708 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.1307382545134637 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.1307292167773948 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.125535809547323 | inf | float |
INFO - 16:21:08: +------+-------------+--------------------+-------------+-------+
INFO - 16:21:08: 8%|▊ | 77/1000 [00:00<00:01, 815.37 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:21:08: 8%|▊ | 78/1000 [00:00<00:01, 818.73 it/sec, feas=True, obj=[0.31706447 0.85215876]]
INFO - 16:21:08: 8%|▊ | 79/1000 [00:00<00:01, 820.57 it/sec, feas=True, obj=[0.44069654 0.88070624]]
INFO - 16:21:08: 8%|▊ | 80/1000 [00:00<00:01, 820.96 it/sec, feas=True, obj=[0.31749875 0.85247189]]
INFO - 16:21:08: 8%|▊ | 81/1000 [00:00<00:01, 823.94 it/sec, feas=True, obj=[0.31049571 0.85526244]]
INFO - 16:21:08: 8%|▊ | 82/1000 [00:00<00:01, 825.40 it/sec, feas=True, obj=[0.31008062 0.85545979]]
INFO - 16:21:08: 8%|▊ | 83/1000 [00:00<00:01, 826.83 it/sec, feas=True, obj=[0.31007991 0.85546006]]
INFO - 16:21:08: 8%|▊ | 84/1000 [00:00<00:01, 828.45 it/sec, feas=True, obj=[0.31007988 0.85546007]]
INFO - 16:21:08: 8%|▊ | 85/1000 [00:00<00:01, 830.03 it/sec, feas=True, obj=[0.31007988 0.85546008]]
INFO - 16:21:08: 9%|▊ | 86/1000 [00:00<00:01, 831.51 it/sec, feas=True, obj=[0.31007988 0.85546008]]
ERROR - 16:21:08: 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 - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.09364249860428303
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [1.16135075e-06 1.35331413e-07]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.2252840082297061 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.2257678647994927 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.2257543552148791 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.09364249860428303 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832]
INFO - 16:21:08: Optimization problem:
INFO - 16:21:08: minimize -t_extraction
INFO - 16:21:08: with respect to t, x
INFO - 16:21:08: under the inequality constraints
INFO - 16:21:08: beta_sub_optim_constraint <= 0.0
INFO - 16:21:08: over the design space:
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.2252840082297061 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.2257678647994927 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.2257543552148791 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.09364249860428303 | inf | float |
INFO - 16:21:08: +------+-------------+----------------------+-------------+-------+
INFO - 16:21:08: 9%|▊ | 87/1000 [00:00<00:01, 807.80 it/sec, feas=True, obj=[0.31007988 0.85546008]]
INFO - 16:21:08: 9%|▉ | 88/1000 [00:00<00:01, 810.60 it/sec, feas=True, obj=[0.17166205 0.91400962]]
INFO - 16:21:08: 9%|▉ | 89/1000 [00:00<00:01, 813.89 it/sec, feas=True, obj=[0.31290173 0.93170725]]
INFO - 16:21:08: 9%|▉ | 90/1000 [00:00<00:01, 815.67 it/sec, feas=True, obj=[0.17159576 0.91440627]]
INFO - 16:21:08: 9%|▉ | 91/1000 [00:00<00:01, 818.32 it/sec, feas=True, obj=[0.15690892 0.9193933 ]]
INFO - 16:21:08: 9%|▉ | 92/1000 [00:00<00:01, 819.65 it/sec, feas=True, obj=[0.15614425 0.91967142]]
INFO - 16:21:08: 9%|▉ | 93/1000 [00:00<00:01, 821.23 it/sec, feas=True, obj=[0.15614052 0.91967276]]
INFO - 16:21:08: 9%|▉ | 94/1000 [00:00<00:01, 822.80 it/sec, feas=True, obj=[0.15614049 0.91967277]]
INFO - 16:21:08: 10%|▉ | 95/1000 [00:00<00:01, 824.35 it/sec, feas=True, obj=[0.15614049 0.91967277]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:21:08: Solution:
INFO - 16:21:08: The solution is feasible.
INFO - 16:21:08: Objective: 0.0479411260233733
INFO - 16:21:08: Standardized constraints:
INFO - 16:21:08: beta_sub_optim_constraint = [5.15990506e-06 4.55681550e-08]
INFO - 16:21:08: Design space:
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: | x[0] | -4 | 0.3392459389454796 | 4 | float |
INFO - 16:21:08: | x[1] | -4 | 0.3395733823668694 | 4 | float |
INFO - 16:21:08: | x[2] | -4 | 0.3395642399370322 | 4 | float |
INFO - 16:21:08: | t | -inf | -0.0479411260233733 | inf | float |
INFO - 16:21:08: +------+-------------+---------------------+-------------+-------+
INFO - 16:21:08: 10%|▉ | 96/1000 [00:00<00:01, 726.37 it/sec, feas=True, obj=[0.15614049 0.91967277]]
INFO - 16:21:08: Optimization result:
INFO - 16:21:08: Optimizer info:
INFO - 16:21:08: Status: None
INFO - 16:21:08: Message: None
INFO - 16:21:08: Solution:
INFO - 16:21:08: Objective: 0.8939534673502063
INFO - 16:21:08: Pareto efficient solutions:
INFO - 16:21:08: Pareto optimal points : 63 / 96
INFO - 16:21:08: Utopia point : [0. 0.]
INFO - 16:21:08: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 16:21:08: Distance from utopia : 0.8939534673502063
INFO - 16:21:08: Objective values:
INFO - 16:21:08: +------+----------+----------+----------+
INFO - 16:21:08: | name | 1 | 2 | 3 |
INFO - 16:21:08: +------+----------+----------+----------+
INFO - 16:21:08: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 16:21:08: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 16:21:08: +------+----------+----------+----------+
INFO - 16:21:08: Design space:
INFO - 16:21:08: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:21:08: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 16:21:08: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:21:08: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:21:08: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:21:08: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:21:08: +-------+-------------+---------+----------+---+-------------+-------+
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 0x7c2f8f717f50>
Total running time of the script: (0 minutes 0.391 seconds)