Note
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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]:
We also show how the Pareto front can be refined.
from __future__ import annotations
from gemseo import configure_logger
from gemseo import execute_algo
from gemseo import execute_post
from gemseo.algos.opt.mnbi.settings.mnbi_settings import MNBI_Settings
from gemseo.problems.multiobjective_optimization.fonseca_fleming import FonsecaFleming
configure_logger()
<RootLogger root (INFO)>
Solve the Fonseca-Fleming optimization problem#
The 3 sub-optimization problems of mNBI are solved with SLSQP, a gradient-based optimization algorithm from the NLOPT library, with a maximum of 100 iterations. The analytic gradients are provided.
opt_problem = FonsecaFleming()
mnbi_settings = MNBI_Settings(
max_iter=1000,
sub_optim_max_iter=100,
n_sub_optim=3,
sub_optim_algo="NLOPT_SLSQP",
)
result = execute_algo(opt_problem, settings_model=mnbi_settings)
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize FonsecaFleming
INFO - 00:09:54: with respect to x
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: Solving optimization problem with algorithm MNBI:
INFO - 00:09:54: Searching for the individual optimum of each objective
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize f_0
INFO - 00:09:54: with respect to x
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: 1%| | 6/1000 [00:00<00:00, 1185.56 it/sec, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 00:09:54: 1%| | 7/1000 [00:00<00:00, 1217.15 it/sec, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 00:09:54: 1%| | 8/1000 [00:00<00:00, 1249.79 it/sec, obj=[9.01501096e-14 9.81684376e-01]]
INFO - 00:09:54: 1%| | 9/1000 [00:00<00:00, 1282.79 it/sec, obj=[8.15628010e-10 9.81684362e-01]]
INFO - 00:09:54: 1%| | 10/1000 [00:00<00:00, 1390.27 it/sec, obj=[7.07334191e-12 9.81684374e-01]]
INFO - 00:09:54: 1%| | 11/1000 [00:00<00:00, 1395.78 it/sec, obj=[4.27435864e-14 9.81684376e-01]]
INFO - 00:09:54: 1%| | 12/1000 [00:00<00:00, 1313.80 it/sec, obj=[0. 0.98168436]]
INFO - 00:09:54: 1%|▏ | 13/1000 [00:00<00:00, 1329.06 it/sec, obj=[0. 0.98168436]]
INFO - 00:09:54: 1%|▏ | 14/1000 [00:00<00:00, 1405.30 it/sec, obj=[0. 0.98168436]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 17
INFO - 00:09:54: Solution:
INFO - 00:09:54: Objective: 0.0
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.5773502684895009 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.5773502684994094 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.5773502684993135 | 4 | float |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize f_1
INFO - 00:09:54: with respect to x
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: 2%|▏ | 15/1000 [00:00<00:00, 1156.16 it/sec, obj=[1. 1.]]
INFO - 00:09:54: 2%|▏ | 16/1000 [00:00<00:00, 1214.75 it/sec, obj=[0.99999998 0.9931056 ]]
INFO - 00:09:54: 2%|▏ | 17/1000 [00:00<00:00, 1223.14 it/sec, obj=[0.99688636 0.14955784]]
INFO - 00:09:54: 2%|▏ | 18/1000 [00:00<00:00, 1186.82 it/sec, obj=[0.9492493 0.07206897]]
INFO - 00:09:54: 2%|▏ | 19/1000 [00:00<00:00, 1200.76 it/sec, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 00:09:54: 2%|▏ | 20/1000 [00:00<00:00, 1214.67 it/sec, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 00:09:54: 2%|▏ | 21/1000 [00:00<00:00, 1229.35 it/sec, obj=[9.81684376e-01 9.24815780e-14]]
INFO - 00:09:54: 2%|▏ | 22/1000 [00:00<00:00, 1241.20 it/sec, obj=[9.81684362e-01 8.52572346e-10]]
INFO - 00:09:54: 2%|▏ | 23/1000 [00:00<00:00, 1284.56 it/sec, obj=[9.81684374e-01 7.39219796e-12]]
INFO - 00:09:54: 2%|▏ | 24/1000 [00:00<00:00, 1290.60 it/sec, obj=[9.81684376e-01 4.29656311e-14]]
INFO - 00:09:54: 2%|▎ | 25/1000 [00:00<00:00, 1258.78 it/sec, obj=[0.98168436 0. ]]
INFO - 00:09:54: 3%|▎ | 26/1000 [00:00<00:00, 1267.87 it/sec, obj=[0.98168436 0. ]]
INFO - 00:09:54: 3%|▎ | 27/1000 [00:00<00:00, 1305.18 it/sec, obj=[0.98168436 0. ]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 17
INFO - 00:09:54: Solution:
INFO - 00:09:54: Objective: 0.0
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.5773502685200489 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.5773502685300462 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.5773502685281993 | 4 | float |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.49084218 0.49084218]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: | t | -inf | 0 | inf | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: 3%|▎ | 28/1000 [00:00<00:00, 1120.12 it/sec, obj=[0.63212056 0.63212056]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 4
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.14391425994444806
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [ 8.16013923e-15 -4.96824804e-15]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+------------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+------------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -9.676703882632864e-13 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -9.676703882632864e-13 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -9.676703882632864e-13 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.1439142599444481 | inf | float |
INFO - 00:09:54: +------+-------------+------------------------+-------------+-------+
INFO - 00:09:54: 3%|▎ | 29/1000 [00:00<00:01, 787.88 it/sec, obj=[0.63212056 0.63212056]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: None
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 36
INFO - 00:09:54: Solution:
INFO - 00:09:54: Objective: 0.8939534673502061
INFO - 00:09:54: Pareto efficient solutions:
INFO - 00:09:54: Pareto optimal points : 9 / 29
INFO - 00:09:54: Utopia point : [0. 0.]
INFO - 00:09:54: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 00:09:54: Distance from utopia : 0.8939534673502061
INFO - 00:09:54: Objective values:
INFO - 00:09:54: +------+----------+----------+----------+
INFO - 00:09:54: | name | 1 | 2 | 3 |
INFO - 00:09:54: +------+----------+----------+----------+
INFO - 00:09:54: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 00:09:54: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 00:09:54: +------+----------+----------+----------+
INFO - 00:09:54: Design space:
INFO - 00:09:54: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 00:09:54: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 00:09:54: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 00:09:54: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 00:09:54: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 00:09:54: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 00:09:54: +-------+-------------+---------+----------+---+-------------+-------+
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 0x7573a0e849b0>
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 - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize FonsecaFleming
INFO - 00:09:54: with respect to x
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: Solving optimization problem with algorithm MNBI:
INFO - 00:09:54: Searching for the individual optimum of each objective
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize f_0
INFO - 00:09:54: with respect to x
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: 1%| | 6/1000 [00:00<00:00, 1230.42 it/sec, obj=[2.04753293e-04 9.82706845e-01]]
INFO - 00:09:54: 1%| | 7/1000 [00:00<00:00, 1260.25 it/sec, obj=[1.10060811e-06 9.81607360e-01]]
INFO - 00:09:54: 1%| | 8/1000 [00:00<00:00, 1290.16 it/sec, obj=[9.01501096e-14 9.81684376e-01]]
INFO - 00:09:54: 1%| | 9/1000 [00:00<00:00, 1319.98 it/sec, obj=[8.15628010e-10 9.81684362e-01]]
INFO - 00:09:54: 1%| | 10/1000 [00:00<00:00, 1425.28 it/sec, obj=[7.07334191e-12 9.81684374e-01]]
INFO - 00:09:54: 1%| | 11/1000 [00:00<00:00, 1429.46 it/sec, obj=[4.27435864e-14 9.81684376e-01]]
INFO - 00:09:54: 1%| | 12/1000 [00:00<00:00, 1337.58 it/sec, obj=[0. 0.98168436]]
INFO - 00:09:54: 1%|▏ | 13/1000 [00:00<00:00, 1355.25 it/sec, obj=[0. 0.98168436]]
INFO - 00:09:54: 1%|▏ | 14/1000 [00:00<00:00, 1433.01 it/sec, obj=[0. 0.98168436]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 17
INFO - 00:09:54: Solution:
INFO - 00:09:54: Objective: 0.0
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.5773502684895009 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.5773502684994094 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.5773502684993135 | 4 | float |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize f_1
INFO - 00:09:54: with respect to x
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: 2%|▏ | 15/1000 [00:00<00:00, 1179.94 it/sec, obj=[1. 1.]]
INFO - 00:09:54: 2%|▏ | 16/1000 [00:00<00:00, 1239.11 it/sec, obj=[0.99999998 0.9931056 ]]
INFO - 00:09:54: 2%|▏ | 17/1000 [00:00<00:00, 1246.71 it/sec, obj=[0.99688636 0.14955784]]
INFO - 00:09:54: 2%|▏ | 18/1000 [00:00<00:00, 1206.22 it/sec, obj=[0.9492493 0.07206897]]
INFO - 00:09:54: 2%|▏ | 19/1000 [00:00<00:00, 1219.01 it/sec, obj=[9.82706845e-01 2.04753293e-04]]
INFO - 00:09:54: 2%|▏ | 20/1000 [00:00<00:00, 1232.31 it/sec, obj=[9.81607360e-01 1.10060811e-06]]
INFO - 00:09:54: 2%|▏ | 21/1000 [00:00<00:00, 1246.64 it/sec, obj=[9.81684376e-01 9.24815780e-14]]
INFO - 00:09:54: 2%|▏ | 22/1000 [00:00<00:00, 1259.36 it/sec, obj=[9.81684362e-01 8.52572346e-10]]
INFO - 00:09:54: 2%|▏ | 23/1000 [00:00<00:00, 1303.35 it/sec, obj=[9.81684374e-01 7.39219796e-12]]
INFO - 00:09:54: 2%|▏ | 24/1000 [00:00<00:00, 1308.62 it/sec, obj=[9.81684376e-01 4.29656311e-14]]
INFO - 00:09:54: 2%|▎ | 25/1000 [00:00<00:00, 1275.56 it/sec, obj=[0.98168436 0. ]]
INFO - 00:09:54: 3%|▎ | 26/1000 [00:00<00:00, 1285.07 it/sec, obj=[0.98168436 0. ]]
INFO - 00:09:54: 3%|▎ | 27/1000 [00:00<00:00, 1323.03 it/sec, obj=[0.98168436 0. ]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 17
INFO - 00:09:54: Solution:
INFO - 00:09:54: Objective: 0.0
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.5773502685200489 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.5773502685300462 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.5773502685281993 | 4 | float |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.87260832 0.10907604]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0 | 4 | float |
INFO - 00:09:54: | t | -inf | 0 | inf | float |
INFO - 00:09:54: +------+-------------+-------+-------------+-------+
INFO - 00:09:54: 3%|▎ | 28/1000 [00:00<00:00, 1135.45 it/sec, obj=[0.90043834 0.20664322]]
INFO - 00:09:54: 3%|▎ | 29/1000 [00:00<00:00, 1134.00 it/sec, obj=[0.91873293 0.15869784]]
INFO - 00:09:54: 3%|▎ | 30/1000 [00:00<00:00, 1133.01 it/sec, obj=[0.91966962 0.15614908]]
INFO - 00:09:54: 3%|▎ | 31/1000 [00:00<00:00, 1133.08 it/sec, obj=[0.91967277 0.15614049]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 7
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.047942550573600556
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [ 6.93889390e-16 -1.83880688e-15]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.339464261305511 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.3394642613042733 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.3394642613061056 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.04794255057360056 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.76353228 0.21815208]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.339464261305511 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.3394642613042733 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.3394642613061056 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.04794255057360056 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: 3%|▎ | 32/1000 [00:00<00:00, 1025.02 it/sec, obj=[0.91967277 0.15614049]]
INFO - 00:09:54: 3%|▎ | 33/1000 [00:00<00:00, 1029.16 it/sec, obj=[0.84203912 0.33739501]]
INFO - 00:09:54: 3%|▎ | 34/1000 [00:00<00:00, 1035.41 it/sec, obj=[0.85527677 0.31046303]]
INFO - 00:09:54: 4%|▎ | 35/1000 [00:00<00:00, 1037.57 it/sec, obj=[0.85546004 0.31007996]]
INFO - 00:09:54: 4%|▎ | 36/1000 [00:00<00:00, 1040.15 it/sec, obj=[0.85546004 0.31007995]]
INFO - 00:09:54: 4%|▎ | 37/1000 [00:00<00:00, 1042.69 it/sec, obj=[0.85546009 0.31007984]]
INFO - 00:09:54: 4%|▍ | 38/1000 [00:00<00:00, 1044.77 it/sec, obj=[0.8554601 0.31007982]]
INFO - 00:09:54: 4%|▍ | 39/1000 [00:00<00:00, 1066.93 it/sec, obj=[0.8554601 0.31007983]]
INFO - 00:09:54: 4%|▍ | 40/1000 [00:00<00:00, 1071.10 it/sec, obj=[0.8554601 0.31007983]]
INFO - 00:09:54: 4%|▍ | 41/1000 [00:00<00:00, 1075.29 it/sec, obj=[0.85546009 0.31007984]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 12
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.09364289795630283
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [ 5.50654545e-08 -3.31157324e-08]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.2256025551311831 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.2256025557747829 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.2256025548218257 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.09364289795630283 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.65445624 0.32722812]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.2256025551311831 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.2256025557747829 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.2256025548218257 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.09364289795630283 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: 4%|▍ | 42/1000 [00:00<00:00, 993.85 it/sec, obj=[0.77161691 0.45984452]]
INFO - 00:09:54: 4%|▍ | 43/1000 [00:00<00:00, 995.50 it/sec, obj=[0.77767797 0.45048948]]
INFO - 00:09:54: 4%|▍ | 44/1000 [00:00<00:00, 998.15 it/sec, obj=[0.77769345 0.45046534]]
INFO - 00:09:54: 4%|▍ | 45/1000 [00:00<00:00, 1001.04 it/sec, obj=[0.77769475 0.45046867]]
INFO - 00:09:54: 5%|▍ | 46/1000 [00:00<00:00, 1018.97 it/sec, obj=[0.77769346 0.45046536]]
INFO - 00:09:54: 5%|▍ | 47/1000 [00:00<00:00, 1023.67 it/sec, obj=[0.77769345 0.45046534]]
INFO - 00:09:54: 5%|▍ | 48/1000 [00:00<00:00, 1007.22 it/sec, obj=[0.77769345 0.45046533]]
ERROR - 00:09:54: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
nlopt.RoundoffLimited: NLopt roundoff-limited
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 11
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.1255363970177465
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [1.38732549e-06 3.42942337e-06]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.1302316085444764 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.1325189233805686 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.1291321707661721 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.1255363970177465 | inf | float |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.5453802 0.43630416]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.1302316085444764 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.1325189233805686 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.1291321707661721 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.1255363970177465 | inf | float |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: 5%|▍ | 49/1000 [00:00<00:00, 956.85 it/sec, obj=[0.77769345 0.45046533]]
INFO - 00:09:54: 5%|▌ | 50/1000 [00:00<00:00, 960.74 it/sec, obj=[0.68555698 0.58426668]]
INFO - 00:09:54: 5%|▌ | 51/1000 [00:00<00:00, 965.42 it/sec, obj=[0.68399938 0.57650637]]
INFO - 00:09:54: 5%|▌ | 52/1000 [00:00<00:00, 969.91 it/sec, obj=[0.68462482 0.57558952]]
INFO - 00:09:54: 5%|▌ | 53/1000 [00:00<00:00, 972.30 it/sec, obj=[0.68463858 0.57556374]]
INFO - 00:09:54: 5%|▌ | 54/1000 [00:00<00:00, 975.18 it/sec, obj=[0.68463912 0.57556308]]
INFO - 00:09:54: 6%|▌ | 55/1000 [00:00<00:00, 978.05 it/sec, obj=[0.68463912 0.57556308]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 10
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.14185306201349607
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [3.45183683e-06 4.64490810e-06]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.04291047733084286 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.04270203738455658 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.04301066762956651 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.1418530620134961 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.43630416 0.5453802 ]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | -0.04291047733084286 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | -0.04270203738455658 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | -0.04301066762956651 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.1418530620134961 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: 6%|▌ | 56/1000 [00:00<00:01, 933.48 it/sec, obj=[0.68463912 0.57556308]]
INFO - 00:09:54: 6%|▌ | 57/1000 [00:00<00:01, 935.12 it/sec, obj=[0.57517744 0.68504627]]
INFO - 00:09:54: 6%|▌ | 58/1000 [00:00<00:01, 937.83 it/sec, obj=[0.64468964 0.73529265]]
INFO - 00:09:54: 6%|▌ | 59/1000 [00:00<00:00, 950.41 it/sec, obj=[0.57567735 0.68526336]]
INFO - 00:09:54: 6%|▌ | 60/1000 [00:00<00:01, 939.96 it/sec, obj=[0.57562684 0.68458418]]
INFO - 00:09:54: 6%|▌ | 61/1000 [00:00<00:00, 942.42 it/sec, obj=[0.57556309 0.68463912]]
INFO - 00:09:54: 6%|▌ | 62/1000 [00:00<00:00, 945.32 it/sec, obj=[0.57556308 0.68463912]]
INFO - 00:09:54: 6%|▋ | 63/1000 [00:00<00:00, 947.98 it/sec, obj=[0.57556308 0.68463912]]
INFO - 00:09:54: 6%|▋ | 64/1000 [00:00<00:00, 950.62 it/sec, obj=[0.57556308 0.68463912]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 13
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.141857085596892
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [4.92134715e-08 3.53502475e-08]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.04285487868216808 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.04297029133272012 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.04279940357728407 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.141857085596892 | inf | float |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.32722812 0.65445624]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.04285487868216808 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.04297029133272012 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.04279940357728407 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.141857085596892 | inf | float |
INFO - 00:09:54: +------+-------------+---------------------+-------------+-------+
INFO - 00:09:54: 6%|▋ | 65/1000 [00:00<00:01, 916.86 it/sec, obj=[0.57556308 0.68463912]]
INFO - 00:09:54: 7%|▋ | 66/1000 [00:00<00:01, 918.82 it/sec, obj=[0.45296521 0.77610508]]
INFO - 00:09:54: 7%|▋ | 67/1000 [00:00<00:01, 921.21 it/sec, obj=[0.4857272 0.79138788]]
INFO - 00:09:54: 7%|▋ | 68/1000 [00:00<00:00, 932.59 it/sec, obj=[0.45359005 0.77673074]]
INFO - 00:09:54: 7%|▋ | 69/1000 [00:00<00:01, 923.90 it/sec, obj=[0.45080811 0.77747394]]
INFO - 00:09:54: 7%|▋ | 70/1000 [00:00<00:01, 926.22 it/sec, obj=[0.45046544 0.77769341]]
INFO - 00:09:54: 7%|▋ | 71/1000 [00:00<00:01, 928.81 it/sec, obj=[0.45046534 0.77769345]]
INFO - 00:09:54: 7%|▋ | 72/1000 [00:00<00:00, 931.39 it/sec, obj=[0.45046533 0.77769345]]
INFO - 00:09:54: 7%|▋ | 73/1000 [00:00<00:00, 934.09 it/sec, obj=[0.45046533 0.77769345]]
INFO - 00:09:54: 7%|▋ | 74/1000 [00:00<00:00, 936.57 it/sec, obj=[0.45046533 0.77769345]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 14
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.12553645235059005
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [ 1.49882953e-07 -4.26679669e-09]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.1305933450637484 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.130790914197771 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.1304983800119963 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.12553645235059 | inf | float |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.21815208 0.76353228]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.1305933450637484 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.130790914197771 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.1304983800119963 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.12553645235059 | inf | float |
INFO - 00:09:54: +------+-------------+--------------------+-------------+-------+
INFO - 00:09:54: 8%|▊ | 75/1000 [00:00<00:01, 908.26 it/sec, obj=[0.45046533 0.77769345]]
INFO - 00:09:54: 8%|▊ | 76/1000 [00:00<00:01, 910.09 it/sec, obj=[0.31703362 0.85215238]]
INFO - 00:09:54: 8%|▊ | 77/1000 [00:00<00:01, 912.40 it/sec, obj=[0.40288985 0.87338417]]
INFO - 00:09:54: 8%|▊ | 78/1000 [00:00<00:00, 922.24 it/sec, obj=[0.31715667 0.85249332]]
INFO - 00:09:54: 8%|▊ | 79/1000 [00:00<00:01, 917.03 it/sec, obj=[0.31040011 0.85530776]]
INFO - 00:09:54: 8%|▊ | 80/1000 [00:00<00:01, 918.85 it/sec, obj=[0.31008035 0.85545991]]
INFO - 00:09:54: 8%|▊ | 81/1000 [00:00<00:00, 921.44 it/sec, obj=[0.3100799 0.85546007]]
INFO - 00:09:54: 8%|▊ | 82/1000 [00:00<00:00, 923.76 it/sec, obj=[0.31007988 0.85546007]]
INFO - 00:09:54: 8%|▊ | 83/1000 [00:00<00:00, 926.01 it/sec, obj=[0.31007988 0.85546008]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 13
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.09364266739626721
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [7.23490535e-07 8.72958074e-08]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.2255448712436445 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.2258763306714222 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.2253855494856154 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.09364266739626721 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: Solving mNBI sub-problem for phi_beta = [0.10907604 0.87260832]
INFO - 00:09:54: Optimization problem:
INFO - 00:09:54: minimize -t_extraction
INFO - 00:09:54: with respect to t, x
INFO - 00:09:54: subject to constraints:
INFO - 00:09:54: beta_sub_optim_constraint <= 0.0
INFO - 00:09:54: over the design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.2255448712436445 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.2258763306714222 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.2253855494856154 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.09364266739626721 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: 8%|▊ | 84/1000 [00:00<00:01, 901.05 it/sec, obj=[0.31007988 0.85546008]]
INFO - 00:09:54: 8%|▊ | 85/1000 [00:00<00:01, 903.61 it/sec, obj=[0.17162737 0.91400636]]
INFO - 00:09:54: 9%|▊ | 86/1000 [00:00<00:01, 907.42 it/sec, obj=[0.29857451 0.93068206]]
INFO - 00:09:54: 9%|▊ | 87/1000 [00:00<00:00, 916.05 it/sec, obj=[0.17152252 0.91447953]]
INFO - 00:09:54: 9%|▉ | 88/1000 [00:00<00:01, 911.37 it/sec, obj=[0.15696325 0.91937307]]
INFO - 00:09:54: 9%|▉ | 89/1000 [00:00<00:00, 913.33 it/sec, obj=[0.15614412 0.91967146]]
INFO - 00:09:54: 9%|▉ | 90/1000 [00:00<00:00, 915.36 it/sec, obj=[0.15614051 0.91967277]]
INFO - 00:09:54: 9%|▉ | 91/1000 [00:00<00:00, 917.45 it/sec, obj=[0.15614049 0.91967277]]
INFO - 00:09:54: 9%|▉ | 92/1000 [00:00<00:00, 919.49 it/sec, obj=[0.15614049 0.91967277]]
INFO - 00:09:54: 9%|▉ | 93/1000 [00:00<00:00, 921.66 it/sec, obj=[0.15614049 0.91967277]]
INFO - 00:09:54: 9%|▉ | 94/1000 [00:00<00:00, 923.68 it/sec, obj=[0.15614049 0.91967277]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 15
INFO - 00:09:54: Solution:
INFO - 00:09:54: The solution is feasible.
INFO - 00:09:54: Objective: 0.047941264984527124
INFO - 00:09:54: Standardized constraints:
INFO - 00:09:54: beta_sub_optim_constraint = [ 4.88540472e-06 -4.82444740e-08]
INFO - 00:09:54: Design space:
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | Name | Lower bound | Value | Upper bound | Type |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: | x[0] | -4 | 0.3394255200896286 | 4 | float |
INFO - 00:09:54: | x[1] | -4 | 0.3396321336864006 | 4 | float |
INFO - 00:09:54: | x[2] | -4 | 0.3393262076587185 | 4 | float |
INFO - 00:09:54: | t | -inf | -0.04794126498452712 | inf | float |
INFO - 00:09:54: +------+-------------+----------------------+-------------+-------+
INFO - 00:09:54: 10%|▉ | 95/1000 [00:00<00:01, 814.96 it/sec, obj=[0.15614049 0.91967277]]
INFO - 00:09:54: Optimization result:
INFO - 00:09:54: Optimizer info:
INFO - 00:09:54: Status: None
INFO - 00:09:54: Message: None
INFO - 00:09:54: Number of calls to the objective function by the optimizer: 123
INFO - 00:09:54: Solution:
INFO - 00:09:54: Objective: 0.8939534673502061
INFO - 00:09:54: Pareto efficient solutions:
INFO - 00:09:54: Pareto optimal points : 61 / 95
INFO - 00:09:54: Utopia point : [0. 0.]
INFO - 00:09:54: Compromise solution (closest to utopia) : [[0.63212056 0.63212056]]
INFO - 00:09:54: Distance from utopia : 0.8939534673502061
INFO - 00:09:54: Objective values:
INFO - 00:09:54: +------+----------+----------+----------+
INFO - 00:09:54: | name | 1 | 2 | 3 |
INFO - 00:09:54: +------+----------+----------+----------+
INFO - 00:09:54: | 1 | 0 | 0.981684 | 0.632121 |
INFO - 00:09:54: | 2 | 0.981684 | 0 | 0.632121 |
INFO - 00:09:54: +------+----------+----------+----------+
INFO - 00:09:54: Design space:
INFO - 00:09:54: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 00:09:54: | name | lower_bound | 1 | 2 | 3 | upper_bound | type |
INFO - 00:09:54: +-------+-------------+---------+----------+---+-------------+-------+
INFO - 00:09:54: | x (1) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 00:09:54: | x (2) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 00:09:54: | x (3) | -4 | 0.57735 | -0.57735 | 0 | 4 | float |
INFO - 00:09:54: +-------+-------------+---------+----------+---+-------------+-------+
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 0x75739be3a1e0>
Total running time of the script: (0 minutes 0.374 seconds)