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 - 16:17:17: Optimization problem:
INFO - 16:17:17: minimize FonsecaFleming
INFO - 16:17:17: with respect to x
INFO - 16:17:17: over the design space:
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: Solving optimization problem with algorithm MNBI:
INFO - 16:17:17: Searching for the individual optimum of each objective
INFO - 16:17:17: Optimization problem:
INFO - 16:17:17: minimize f_0
INFO - 16:17:17: with respect to x
INFO - 16:17:17: over the design space:
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: 1%| | 6/1000 [00:00<00:01, 801.15 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 16:17:17: 1%| | 7/1000 [00:00<00:01, 791.02 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 16:17:17: 1%| | 8/1000 [00:00<00:01, 786.00 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]]
INFO - 16:17:17: 1%| | 9/1000 [00:00<00:01, 780.61 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]]
INFO - 16:17:17: 1%| | 10/1000 [00:00<00:01, 787.83 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]]
INFO - 16:17:17: 1%| | 11/1000 [00:00<00:01, 782.98 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]]
INFO - 16:17:17: 1%| | 12/1000 [00:00<00:01, 778.63 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:17:17: 1%|▏ | 13/1000 [00:00<00:01, 777.54 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:17:17: Optimization result:
INFO - 16:17:17: Optimizer info:
INFO - 16:17:17: Status: None
INFO - 16:17:17: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:17: Solution:
INFO - 16:17:17: Objective: 0.0
INFO - 16:17:17: Design space:
INFO - 16:17:17: +------+-------------+--------------------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+--------------------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | 0.5773502690103198 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | 0.5773502690115331 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | 0.5773502690114345 | 4 | float |
INFO - 16:17:17: +------+-------------+--------------------+-------------+-------+
INFO - 16:17:17: Optimization problem:
INFO - 16:17:17: minimize f_1
INFO - 16:17:17: with respect to x
INFO - 16:17:17: over the design space:
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: 1%|▏ | 14/1000 [00:00<00:01, 650.20 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:17:17: 2%|▏ | 15/1000 [00:00<00:01, 664.88 it/sec, feas=True, obj=[1. 1.]]
INFO - 16:17:17: 2%|▏ | 16/1000 [00:00<00:01, 672.87 it/sec, feas=True, obj=[0.99999998 0.9931056 ]]
INFO - 16:17:17: 2%|▏ | 17/1000 [00:00<00:01, 675.89 it/sec, feas=True, obj=[0.99688636 0.14955784]]
INFO - 16:17:17: 2%|▏ | 18/1000 [00:00<00:01, 679.15 it/sec, feas=True, obj=[0.9492493 0.07206897]]
INFO - 16:17:17: 2%|▏ | 19/1000 [00:00<00:01, 681.81 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 16:17:17: 2%|▏ | 20/1000 [00:00<00:01, 684.12 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 16:17:17: 2%|▏ | 21/1000 [00:00<00:01, 686.67 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]]
INFO - 16:17:17: 2%|▏ | 22/1000 [00:00<00:01, 689.41 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]]
INFO - 16:17:17: 2%|▏ | 23/1000 [00:00<00:01, 690.56 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]]
INFO - 16:17:17: 2%|▏ | 24/1000 [00:00<00:01, 691.67 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]]
INFO - 16:17:17: 2%|▎ | 25/1000 [00:00<00:01, 693.73 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:17:17: 3%|▎ | 26/1000 [00:00<00:01, 695.22 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:17:17: Optimization result:
INFO - 16:17:17: Optimizer info:
INFO - 16:17:17: Status: None
INFO - 16:17:17: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:17: Solution:
INFO - 16:17:17: Objective: 0.0
INFO - 16:17:17: Design space:
INFO - 16:17:17: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | -0.5773502690171886 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | -0.5773502690183139 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | -0.5773502690182495 | 4 | float |
INFO - 16:17:17: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:17: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218]
INFO - 16:17:17: Optimization problem:
INFO - 16:17:17: minimize -t_extraction
INFO - 16:17:17: with respect to t, x
INFO - 16:17:17: under the inequality constraints
INFO - 16:17:17: beta_sub_optim_constraint <= 0.0
INFO - 16:17:17: over the design space:
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:17: | t | -inf | 0 | inf | float |
INFO - 16:17:17: +------+-------------+-------+-------------+-------+
INFO - 16:17:17: 3%|▎ | 27/1000 [00:00<00:01, 613.89 it/sec, feas=True, obj=[0.98168436 0. ]]
ERROR - 16:17:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.3.3/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/6.3.3/lib/python3.12/site-packages/nlopt/nlopt.py", line 454, in optimize
return _nlopt.opt_optimize(self, *args)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nlopt.RoundoffLimited: NLopt roundoff-limited
INFO - 16:17:17: Optimization result:
INFO - 16:17:17: Optimizer info:
INFO - 16:17:17: Status: None
INFO - 16:17:17: Message: GEMSEO stopped the driver.
INFO - 16:17:17: Solution:
INFO - 16:17:17: The solution is feasible.
INFO - 16:17:17: Objective: 0.1439142599025487
INFO - 16:17:17: Standardized constraints:
INFO - 16:17:17: beta_sub_optim_constraint = [ 4.99600361e-16 -1.33226763e-15]
INFO - 16:17:17: Design space:
INFO - 16:17:17: +------+-------------+------------------------+-------------+-------+
INFO - 16:17:17: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:17: +------+-------------+------------------------+-------------+-------+
INFO - 16:17:17: | x[0] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 16:17:17: | x[1] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 16:17:17: | x[2] | -4 | -2.193800696659309e-13 | 4 | float |
INFO - 16:17:17: | t | -inf | -0.1439142599025487 | inf | float |
INFO - 16:17:17: +------+-------------+------------------------+-------------+-------+
INFO - 16:17:18: 3%|▎ | 28/1000 [00:00<00:02, 452.42 it/sec, feas=True, obj=[0.63212056 0.63212056]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: None
INFO - 16:17:18: Solution:
INFO - 16:17:18: Objective: 0.8939534673502063
INFO - 16:17:18: Pareto efficient solutions:
INFO - 16:17:18: Pareto optimal points : 8 / 28
INFO - 16:17:18: Utopia point : [0. 0.]
INFO - 16:17:18: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 16:17:18: Distance from utopia : 0.8939534673502063
INFO - 16:17:18: Objective values:
INFO - 16:17:18: +------+----------+----------+----------+
INFO - 16:17:18: | name | 1 | 2 | 3 |
INFO - 16:17:18: +------+----------+----------+----------+
INFO - 16:17:18: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 16:17:18: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 16:17:18: +------+----------+----------+----------+
INFO - 16:17:18: Design space:
INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:17:18: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:17:18: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:17:18: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:17:18: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+
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 0x7b1d50d764b0>
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 - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize FonsecaFleming
INFO - 16:17:18: with respect to x
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: Solving optimization problem with algorithm MNBI:
INFO - 16:17:18: Searching for the individual optimum of each objective
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize f_0
INFO - 16:17:18: with respect to x
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: 1%| | 6/1000 [00:00<00:01, 812.43 it/sec, feas=True, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 16:17:18: 1%| | 7/1000 [00:00<00:01, 801.09 it/sec, feas=True, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 16:17:18: 1%| | 8/1000 [00:00<00:01, 793.85 it/sec, feas=True, obj=[2.36699549e-13 9.81684376e-01]]
INFO - 16:17:18: 1%| | 9/1000 [00:00<00:01, 787.96 it/sec, feas=True, obj=[3.17715032e-09 9.81684363e-01]]
INFO - 16:17:18: 1%| | 10/1000 [00:00<00:01, 792.20 it/sec, feas=True, obj=[2.74601453e-11 9.81684374e-01]]
INFO - 16:17:18: 1%| | 11/1000 [00:00<00:01, 786.98 it/sec, feas=True, obj=[5.44009282e-14 9.81684376e-01]]
INFO - 16:17:18: 1%| | 12/1000 [00:00<00:01, 781.37 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:17:18: 1%|▏ | 13/1000 [00:00<00:01, 779.74 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: Objective: 0.0
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+--------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+--------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.5773502690103198 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.5773502690115331 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.5773502690114345 | 4 | float |
INFO - 16:17:18: +------+-------------+--------------------+-------------+-------+
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize f_1
INFO - 16:17:18: with respect to x
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: 1%|▏ | 14/1000 [00:00<00:01, 646.39 it/sec, feas=True, obj=[0. 0.98168436]]
INFO - 16:17:18: 2%|▏ | 15/1000 [00:00<00:01, 660.49 it/sec, feas=True, obj=[1. 1.]]
INFO - 16:17:18: 2%|▏ | 16/1000 [00:00<00:01, 669.40 it/sec, feas=True, obj=[0.99999998 0.9931056 ]]
INFO - 16:17:18: 2%|▏ | 17/1000 [00:00<00:01, 672.60 it/sec, feas=True, obj=[0.99688636 0.14955784]]
INFO - 16:17:18: 2%|▏ | 18/1000 [00:00<00:01, 676.37 it/sec, feas=True, obj=[0.9492493 0.07206897]]
INFO - 16:17:18: 2%|▏ | 19/1000 [00:00<00:01, 679.38 it/sec, feas=True, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 16:17:18: 2%|▏ | 20/1000 [00:00<00:01, 681.90 it/sec, feas=True, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 16:17:18: 2%|▏ | 21/1000 [00:00<00:01, 684.46 it/sec, feas=True, obj=[9.81684376e-01 2.44582132e-13]]
INFO - 16:17:18: 2%|▏ | 22/1000 [00:00<00:01, 687.54 it/sec, feas=True, obj=[9.81684363e-01 3.30383776e-09]]
INFO - 16:17:18: 2%|▏ | 23/1000 [00:00<00:01, 693.38 it/sec, feas=True, obj=[9.81684374e-01 2.85538260e-11]]
INFO - 16:17:18: 2%|▏ | 24/1000 [00:00<00:01, 693.79 it/sec, feas=True, obj=[9.81684376e-01 5.49560397e-14]]
INFO - 16:17:18: 2%|▎ | 25/1000 [00:00<00:01, 695.80 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:17:18: 3%|▎ | 26/1000 [00:00<00:01, 698.13 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: Objective: 0.0
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.5773502690171886 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.5773502690183139 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.5773502690182495 | 4 | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0 | 4 | float |
INFO - 16:17:18: | t | -inf | 0 | inf | float |
INFO - 16:17:18: +------+-------------+-------+-------------+-------+
INFO - 16:17:18: 3%|▎ | 27/1000 [00:00<00:01, 616.92 it/sec, feas=True, obj=[0.98168436 0. ]]
INFO - 16:17:18: 3%|▎ | 28/1000 [00:00<00:01, 621.06 it/sec, feas=True, obj=[0.90043834 0.20664322]]
INFO - 16:17:18: 3%|▎ | 29/1000 [00:00<00:01, 619.89 it/sec, feas=True, obj=[0.91873293 0.15869784]]
INFO - 16:17:18: 3%|▎ | 30/1000 [00:00<00:01, 619.39 it/sec, feas=True, obj=[0.91966962 0.15614908]]
INFO - 16:17:18: 3%|▎ | 31/1000 [00:00<00:01, 619.05 it/sec, feas=True, obj=[0.91967277 0.15614049]]
INFO - 16:17:18: 3%|▎ | 32/1000 [00:00<00:01, 618.82 it/sec, feas=True, obj=[0.91967277 0.15614049]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.04794255052713356
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [ 2.02608763e-13 -3.60156349e-13]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.3394642615047618 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.3394642612459058 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.3394642612538421 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.04794255052713356 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.3394642615047618 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.3394642612459058 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.3394642612538421 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.04794255052713356 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: 3%|▎ | 33/1000 [00:00<00:01, 559.90 it/sec, feas=True, obj=[0.91967277 0.15614049]]
INFO - 16:17:18: 3%|▎ | 34/1000 [00:00<00:01, 564.13 it/sec, feas=True, obj=[0.84203912 0.33739501]]
INFO - 16:17:18: 4%|▎ | 35/1000 [00:00<00:01, 564.23 it/sec, feas=True, obj=[0.85527677 0.31046303]]
INFO - 16:17:18: 4%|▎ | 36/1000 [00:00<00:01, 564.73 it/sec, feas=True, obj=[0.85546004 0.31007996]]
INFO - 16:17:18: 4%|▎ | 37/1000 [00:00<00:01, 565.41 it/sec, feas=True, obj=[0.85546007 0.31008016]]
INFO - 16:17:18: 4%|▍ | 38/1000 [00:00<00:01, 569.30 it/sec, feas=True, obj=[0.85546004 0.31007996]]
INFO - 16:17:18: 4%|▍ | 39/1000 [00:00<00:01, 568.86 it/sec, feas=True, obj=[0.85546004 0.31007996]]
INFO - 16:17:18: 4%|▍ | 40/1000 [00:00<00:01, 570.17 it/sec, feas=True, obj=[0.85546007 0.3100799 ]]
INFO - 16:17:18: 4%|▍ | 41/1000 [00:00<00:01, 571.13 it/sec, feas=True, obj=[0.85546007 0.31007989]]
INFO - 16:17:18: 4%|▍ | 42/1000 [00:00<00:01, 572.78 it/sec, feas=True, obj=[0.855474 0.31005075]]
INFO - 16:17:18: 4%|▍ | 43/1000 [00:00<00:01, 576.11 it/sec, feas=True, obj=[0.85546477 0.31007007]]
INFO - 16:17:18: 4%|▍ | 44/1000 [00:00<00:01, 579.59 it/sec, feas=True, obj=[0.85546165 0.31007657]]
INFO - 16:17:18: 4%|▍ | 45/1000 [00:00<00:01, 582.91 it/sec, feas=True, obj=[0.85546061 0.31007877]]
INFO - 16:17:18: 5%|▍ | 46/1000 [00:00<00:01, 585.54 it/sec, feas=True, obj=[0.85546025 0.3100795 ]]
INFO - 16:17:18: 5%|▍ | 47/1000 [00:00<00:01, 588.63 it/sec, feas=True, obj=[0.85546013 0.31007975]]
INFO - 16:17:18: 5%|▍ | 48/1000 [00:00<00:01, 591.61 it/sec, feas=True, obj=[0.85546009 0.31007984]]
INFO - 16:17:18: 5%|▍ | 49/1000 [00:00<00:01, 590.59 it/sec, feas=True, obj=[0.85546008 0.31007986]]
INFO - 16:17:18: 5%|▌ | 50/1000 [00:00<00:01, 590.86 it/sec, feas=True, obj=[0.85546008 0.31007988]]
INFO - 16:17:18: 5%|▌ | 51/1000 [00:00<00:01, 591.45 it/sec, feas=True, obj=[0.85546008 0.31007988]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.09363100822564815
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [ 2.56270122e-05 -1.74268465e-05]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.2256188538769552 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.225624434684276 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.2256242629358214 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.09363100822564815 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.2256188538769552 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.225624434684276 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.2256242629358214 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.09363100822564815 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: 5%|▌ | 52/1000 [00:00<00:01, 557.22 it/sec, feas=True, obj=[0.85546008 0.31007988]]
INFO - 16:17:18: 5%|▌ | 53/1000 [00:00<00:01, 559.93 it/sec, feas=True, obj=[0.77161371 0.45984945]]
INFO - 16:17:18: 5%|▌ | 54/1000 [00:00<00:01, 560.44 it/sec, feas=True, obj=[0.77769164 0.45052483]]
INFO - 16:17:18: 6%|▌ | 55/1000 [00:00<00:01, 561.28 it/sec, feas=True, obj=[0.77768304 0.45048318]]
INFO - 16:17:18: 6%|▌ | 56/1000 [00:00<00:01, 562.08 it/sec, feas=True, obj=[0.77769323 0.45046567]]
INFO - 16:17:18: 6%|▌ | 57/1000 [00:00<00:01, 563.41 it/sec, feas=True, obj=[0.77769366 0.45046587]]
INFO - 16:17:18: 6%|▌ | 58/1000 [00:00<00:01, 565.71 it/sec, feas=True, obj=[0.77769326 0.45046564]]
INFO - 16:17:18: 6%|▌ | 59/1000 [00:00<00:01, 565.49 it/sec, feas=True, obj=[0.77769324 0.45046566]]
INFO - 16:17:18: 6%|▌ | 60/1000 [00:00<00:01, 566.31 it/sec, feas=True, obj=[0.77769345 0.45046533]]
INFO - 16:17:18: 6%|▌ | 61/1000 [00:00<00:01, 567.01 it/sec, feas=True, obj=[0.77769345 0.45046533]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.12550633340841144
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [1.91969087e-05 4.74588828e-05]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.1317111882954194 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.1300429705285642 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.1300943096640808 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1255063334084114 | inf | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.1317111882954194 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.1300429705285642 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.1300943096640808 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1255063334084114 | inf | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: 6%|▌ | 62/1000 [00:00<00:01, 533.98 it/sec, feas=True, obj=[0.77769345 0.45046533]]
INFO - 16:17:18: 6%|▋ | 63/1000 [00:00<00:01, 536.28 it/sec, feas=True, obj=[0.68287184 0.58056149]]
INFO - 16:17:18: 6%|▋ | 64/1000 [00:00<00:01, 537.42 it/sec, feas=True, obj=[0.71551876 0.62183493]]
INFO - 16:17:18: 6%|▋ | 65/1000 [00:00<00:01, 537.65 it/sec, feas=True, obj=[0.6822982 0.57927725]]
INFO - 16:17:18: 7%|▋ | 66/1000 [00:00<00:01, 539.63 it/sec, feas=True, obj=[0.68457659 0.57570624]]
INFO - 16:17:18: 7%|▋ | 67/1000 [00:00<00:01, 540.39 it/sec, feas=True, obj=[0.68463465 0.57556826]]
INFO - 16:17:18: 7%|▋ | 68/1000 [00:00<00:01, 541.24 it/sec, feas=True, obj=[0.68463912 0.57556308]]
INFO - 16:17:18: 7%|▋ | 69/1000 [00:00<00:01, 542.16 it/sec, feas=True, obj=[0.68463912 0.57556308]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.14182402977147854
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [2.80166348e-05 3.76715222e-05]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.04284533444766803 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.04288451608870236 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.04288331028044423 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1418240297714785 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | -0.04284533444766803 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | -0.04288451608870236 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | -0.04288331028044423 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1418240297714785 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: 7%|▋ | 70/1000 [00:00<00:01, 523.07 it/sec, feas=True, obj=[0.68463912 0.57556308]]
INFO - 16:17:18: 7%|▋ | 71/1000 [00:00<00:01, 525.27 it/sec, feas=True, obj=[0.57513208 0.68501203]]
INFO - 16:17:18: 7%|▋ | 72/1000 [00:00<00:01, 526.02 it/sec, feas=True, obj=[0.57742427 0.68600327]]
INFO - 16:17:18: 7%|▋ | 73/1000 [00:00<00:01, 527.02 it/sec, feas=True, obj=[0.57581454 0.68442239]]
INFO - 16:17:18: 7%|▋ | 74/1000 [00:00<00:01, 527.72 it/sec, feas=True, obj=[0.5755631 0.6846391]]
INFO - 16:17:18: 8%|▊ | 75/1000 [00:00<00:01, 528.59 it/sec, feas=True, obj=[0.57556308 0.68463912]]
INFO - 16:17:18: 8%|▊ | 76/1000 [00:00<00:01, 529.91 it/sec, feas=True, obj=[0.57556312 0.68463915]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.1418570827634196
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [5.72929534e-08 2.36021925e-08]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.04289632102515561 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.04286361028511543 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.04286461695199684 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1418570827634196 | inf | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.04289632102515561 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.04286361028511543 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.04286461695199684 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1418570827634196 | inf | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: 8%|▊ | 77/1000 [00:00<00:01, 514.01 it/sec, feas=True, obj=[0.57556308 0.68463912]]
INFO - 16:17:18: 8%|▊ | 78/1000 [00:00<00:01, 516.15 it/sec, feas=True, obj=[0.45294809 0.77609816]]
INFO - 16:17:18: 8%|▊ | 79/1000 [00:00<00:01, 516.95 it/sec, feas=True, obj=[0.45218303 0.77835848]]
INFO - 16:17:18: 8%|▊ | 80/1000 [00:00<00:01, 517.96 it/sec, feas=True, obj=[0.45106502 0.77730893]]
INFO - 16:17:18: 8%|▊ | 81/1000 [00:00<00:01, 518.77 it/sec, feas=True, obj=[0.4504655 0.77769335]]
INFO - 16:17:18: 8%|▊ | 82/1000 [00:00<00:01, 519.45 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:17:18: 8%|▊ | 83/1000 [00:00<00:01, 520.69 it/sec, feas=True, obj=[0.45046544 0.77769349]]
INFO - 16:17:18: 8%|▊ | 84/1000 [00:00<00:01, 522.63 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:17:18: 8%|▊ | 85/1000 [00:00<00:01, 522.14 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.1255364904575047
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [1.05241364e-07 4.25739157e-08]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.1302782435029721 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.1308104725924997 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.1307940930583973 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1255364904575047 | inf | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.1302782435029721 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.1308104725924997 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.1307940930583973 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.1255364904575047 | inf | float |
INFO - 16:17:18: +------+-------------+---------------------+-------------+-------+
INFO - 16:17:18: 9%|▊ | 86/1000 [00:00<00:01, 507.22 it/sec, feas=True, obj=[0.45046533 0.77769345]]
INFO - 16:17:18: 9%|▊ | 87/1000 [00:00<00:01, 509.13 it/sec, feas=True, obj=[0.31721618 0.85219022]]
INFO - 16:17:18: 9%|▉ | 88/1000 [00:00<00:01, 510.27 it/sec, feas=True, obj=[0.55958733 0.90369381]]
INFO - 16:17:18: 9%|▉ | 89/1000 [00:00<00:01, 510.48 it/sec, feas=True, obj=[0.31884168 0.85239351]]
INFO - 16:17:18: 9%|▉ | 90/1000 [00:00<00:01, 512.08 it/sec, feas=True, obj=[0.31084099 0.85510192]]
INFO - 16:17:18: 9%|▉ | 91/1000 [00:00<00:01, 512.85 it/sec, feas=True, obj=[0.31008381 0.85545831]]
INFO - 16:17:18: 9%|▉ | 92/1000 [00:00<00:01, 513.65 it/sec, feas=True, obj=[0.31007993 0.85546005]]
INFO - 16:17:18: 9%|▉ | 93/1000 [00:00<00:01, 514.55 it/sec, feas=True, obj=[0.31007988 0.85546007]]
INFO - 16:17:18: 9%|▉ | 94/1000 [00:00<00:01, 515.44 it/sec, feas=True, obj=[0.31007988 0.85546008]]
INFO - 16:17:18: 10%|▉ | 95/1000 [00:00<00:01, 516.35 it/sec, feas=True, obj=[0.31007988 0.85546008]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.09364002856425353
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [6.77503844e-06 1.07286382e-06]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.2252072104370182 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.2258054864979764 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.2257870743455523 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.09364002856425353 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832]
INFO - 16:17:18: Optimization problem:
INFO - 16:17:18: minimize -t_extraction
INFO - 16:17:18: with respect to t, x
INFO - 16:17:18: under the inequality constraints
INFO - 16:17:18: beta_sub_optim_constraint <= 0.0
INFO - 16:17:18: over the design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.2252072104370182 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.2258054864979764 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.2257870743455523 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.09364002856425353 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: 10%|▉ | 96/1000 [00:00<00:01, 502.72 it/sec, feas=True, obj=[0.31007988 0.85546008]]
INFO - 16:17:18: 10%|▉ | 97/1000 [00:00<00:01, 504.08 it/sec, feas=True, obj=[0.17176674 0.91401932]]
INFO - 16:17:18: 10%|▉ | 98/1000 [00:00<00:01, 505.77 it/sec, feas=True, obj=[0.33992347 0.9334342 ]]
INFO - 16:17:18: 10%|▉ | 99/1000 [00:00<00:01, 506.75 it/sec, feas=True, obj=[0.1717712 0.91427008]]
INFO - 16:17:18: 10%|█ | 100/1000 [00:00<00:01, 508.19 it/sec, feas=True, obj=[0.15682461 0.91942509]]
INFO - 16:17:18: 10%|█ | 101/1000 [00:00<00:01, 508.83 it/sec, feas=True, obj=[0.15614481 0.91967125]]
INFO - 16:17:18: 10%|█ | 102/1000 [00:00<00:01, 509.64 it/sec, feas=True, obj=[0.15614056 0.91967275]]
INFO - 16:17:18: 10%|█ | 103/1000 [00:00<00:01, 510.45 it/sec, feas=True, obj=[0.15614049 0.91967277]]
INFO - 16:17:18: 10%|█ | 104/1000 [00:00<00:01, 511.51 it/sec, feas=True, obj=[0.15614049 0.91967277]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:17:18: Solution:
INFO - 16:17:18: The solution is feasible.
INFO - 16:17:18: Objective: 0.04794076312252382
INFO - 16:17:18: Standardized constraints:
INFO - 16:17:18: beta_sub_optim_constraint = [6.07230357e-06 2.29674000e-07]
INFO - 16:17:18: Design space:
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: | x[0] | -4 | 0.3391432958311196 | 4 | float |
INFO - 16:17:18: | x[1] | -4 | 0.3396269686354314 | 4 | float |
INFO - 16:17:18: | x[2] | -4 | 0.3396120834377401 | 4 | float |
INFO - 16:17:18: | t | -inf | -0.04794076312252382 | inf | float |
INFO - 16:17:18: +------+-------------+----------------------+-------------+-------+
INFO - 16:17:18: 10%|█ | 105/1000 [00:00<00:01, 459.49 it/sec, feas=True, obj=[0.15614049 0.91967277]]
INFO - 16:17:18: Optimization result:
INFO - 16:17:18: Optimizer info:
INFO - 16:17:18: Status: None
INFO - 16:17:18: Message: None
INFO - 16:17:18: Solution:
INFO - 16:17:18: Objective: 0.8939534673502063
INFO - 16:17:18: Pareto efficient solutions:
INFO - 16:17:18: Pareto optimal points : 66 / 105
INFO - 16:17:18: Utopia point : [0. 0.]
INFO - 16:17:18: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 16:17:18: Distance from utopia : 0.8939534673502063
INFO - 16:17:18: Objective values:
INFO - 16:17:18: +------+----------+----------+----------+
INFO - 16:17:18: | name | 1 | 2 | 3 |
INFO - 16:17:18: +------+----------+----------+----------+
INFO - 16:17:18: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 16:17:18: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 16:17:18: +------+----------+----------+----------+
INFO - 16:17:18: Design space:
INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:17:18: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 16:17:18: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:17:18: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:17:18: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 16:17:18: +-------+-------------+---------+----------+---+-------------+-------+
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 0x7b1d31a40b00>
Total running time of the script: (0 minutes 0.588 seconds)