Note
Go to the end to download the full example code
Parametric scalable MDO problem - MDF¶
We define
a ScalableProblem
with a shared design variable of size 1
and 2 strongly coupled disciplines.
The first one has a local design variable of size 1
and a coupling variable of size 2
while the second one has a local design variable of size 3
and a coupling variable of size 4.
We would like to solve this MDO problem by means of an MDF formulation.
from __future__ import annotations
from gemseo import configure_logger
from gemseo import execute_algo
from gemseo import execute_post
from gemseo import generate_n2_plot
from gemseo.problems.scalable.parametric.core.scalable_discipline_settings import (
ScalableDisciplineSettings,
)
from gemseo.problems.scalable.parametric.scalable_problem import ScalableProblem
configure_logger()
<RootLogger root (INFO)>
Instantiation of the scalable problem¶
problem = ScalableProblem(
[ScalableDisciplineSettings(1, 2), ScalableDisciplineSettings(3, 4)], 1
)
Display the coupling structure¶
generate_n2_plot(problem.disciplines, save=False, show=True)
Solve the MDO using an MDF formulation¶
scenario = problem.create_scenario()
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})
INFO - 08:23:28:
INFO - 08:23:28: *** Start MDOScenario execution ***
INFO - 08:23:28: MDOScenario
INFO - 08:23:28: Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
INFO - 08:23:28: MDO formulation: MDF
INFO - 08:23:28: Optimization problem:
INFO - 08:23:28: minimize f(x_0, x_1, x_2)
INFO - 08:23:28: with respect to x_0, x_1, x_2
INFO - 08:23:28: subject to constraints:
INFO - 08:23:28: c_1(x_0, x_1, x_2) <= 0.0
INFO - 08:23:28: c_2(x_0, x_1, x_2) <= 0.0
INFO - 08:23:28: over the design space:
INFO - 08:23:28: +--------+-------------+-------+-------------+-------+----------------------+
INFO - 08:23:28: | name | lower_bound | value | upper_bound | type | Initial distribution |
INFO - 08:23:28: +--------+-------------+-------+-------------+-------+----------------------+
INFO - 08:23:28: | x_0 | 0 | 0.5 | 1 | float | |
INFO - 08:23:28: | x_1 | 0 | 0.5 | 1 | float | |
INFO - 08:23:28: | x_2[0] | 0 | 0.5 | 1 | float | |
INFO - 08:23:28: | x_2[1] | 0 | 0.5 | 1 | float | |
INFO - 08:23:28: | x_2[2] | 0 | 0.5 | 1 | float | |
INFO - 08:23:28: +--------+-------------+-------+-------------+-------+----------------------+
INFO - 08:23:28: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 08:23:28: ... 0%| | 0/100 [00:00<?, ?it]
INFO - 08:23:28: ... 1%| | 1/100 [00:00<00:04, 21.76 it/sec, obj=1]
INFO - 08:23:28: ... 2%|▏ | 2/100 [00:00<00:09, 10.13 it/sec, obj=0.921]
INFO - 08:23:28: ... 3%|▎ | 3/100 [00:00<00:06, 15.17 it/sec, obj=0.513]
INFO - 08:23:28: ... 4%|▍ | 4/100 [00:00<00:09, 10.40 it/sec, obj=0.438]
INFO - 08:23:29: ... 5%|▌ | 5/100 [00:00<00:08, 10.97 it/sec, obj=0.418]
INFO - 08:23:29: ... 6%|▌ | 6/100 [00:00<00:08, 11.41 it/sec, obj=0.416]
INFO - 08:23:29: ... 7%|▋ | 7/100 [00:00<00:07, 11.71 it/sec, obj=0.415]
INFO - 08:23:29: ... 8%|▊ | 8/100 [00:00<00:07, 11.99 it/sec, obj=0.415]
INFO - 08:23:29: ... 9%|▉ | 9/100 [00:00<00:07, 12.21 it/sec, obj=0.415]
INFO - 08:23:29: ... 10%|█ | 10/100 [00:00<00:07, 12.40 it/sec, obj=0.415]
INFO - 08:23:29: ... 11%|█ | 11/100 [00:00<00:07, 12.55 it/sec, obj=0.415]
INFO - 08:23:29: ... 12%|█▏ | 12/100 [00:00<00:06, 13.30 it/sec, obj=0.415]
INFO - 08:23:29: ... 13%|█▎ | 13/100 [00:00<00:06, 14.40 it/sec, obj=0.415]
INFO - 08:23:29: Optimization result:
INFO - 08:23:29: Optimizer info:
INFO - 08:23:29: Status: None
INFO - 08:23:29: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 08:23:29: Number of calls to the objective function by the optimizer: 15
INFO - 08:23:29: Solution:
INFO - 08:23:29: The solution is feasible.
INFO - 08:23:29: Objective: 0.4147214093889784
INFO - 08:23:29: Standardized constraints:
INFO - 08:23:29: c_1 = [-0.32430622 -0.43254409]
INFO - 08:23:29: c_2 = [ 2.44645415e-11 -2.51297060e-01 -2.35380107e-01 -4.99968067e-01]
INFO - 08:23:29: Scalable design space:
INFO - 08:23:29: +--------+-------------+---------------------+-------------+-------+----------------------+
INFO - 08:23:29: | name | lower_bound | value | upper_bound | type | Initial distribution |
INFO - 08:23:29: +--------+-------------+---------------------+-------------+-------+----------------------+
INFO - 08:23:29: | x_0 | 0 | 0.4836326345734573 | 1 | float | |
INFO - 08:23:29: | x_1 | 0 | 0.9999999999999998 | 1 | float | |
INFO - 08:23:29: | x_2[0] | 0 | 0.08671679318925574 | 1 | float | |
INFO - 08:23:29: | x_2[1] | 0 | 0.9085357497327241 | 1 | float | |
INFO - 08:23:29: | x_2[2] | 0 | 0.2480176751996585 | 1 | float | |
INFO - 08:23:29: +--------+-------------+---------------------+-------------+-------+----------------------+
INFO - 08:23:29: *** End MDOScenario execution (time: 0:00:00.921109) ***
{'max_iter': 100, 'algo': 'NLOPT_SLSQP'}
Post-process the results¶
scenario.post_process("OptHistoryView", save=False, show=True)
<gemseo.post.opt_history_view.OptHistoryView object at 0x7f1c96173790>
Solve the associated quadratic programming problem¶
problem = problem.create_quadratic_programming_problem()
execute_algo(problem, algo_name="NLOPT_SLSQP", max_iter=100)
INFO - 08:23:30: Optimization problem:
INFO - 08:23:30: minimize f = 0.5x'Qx + c'x + d
INFO - 08:23:30: with respect to x
INFO - 08:23:30: subject to constraints:
INFO - 08:23:30: g: Ax-b <= 0 <= 0.0
INFO - 08:23:30: over the design space:
INFO - 08:23:30: +------+-------------+-------+-------------+-------+
INFO - 08:23:30: | name | lower_bound | value | upper_bound | type |
INFO - 08:23:30: +------+-------------+-------+-------------+-------+
INFO - 08:23:30: | x[0] | 0 | 0.5 | 1 | float |
INFO - 08:23:30: | x[1] | 0 | 0.5 | 1 | float |
INFO - 08:23:30: | x[2] | 0 | 0.5 | 1 | float |
INFO - 08:23:30: | x[3] | 0 | 0.5 | 1 | float |
INFO - 08:23:30: | x[4] | 0 | 0.5 | 1 | float |
INFO - 08:23:30: +------+-------------+-------+-------------+-------+
INFO - 08:23:30: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 08:23:30: ... 0%| | 0/100 [00:00<?, ?it]
INFO - 08:23:30: ... 1%| | 1/100 [00:00<00:00, 2104.52 it/sec, obj=1]
INFO - 08:23:30: ... 2%|▏ | 2/100 [00:00<00:00, 530.05 it/sec, obj=0.921]
INFO - 08:23:30: ... 3%|▎ | 3/100 [00:00<00:00, 744.46 it/sec, obj=0.513]
INFO - 08:23:30: ... 4%|▍ | 4/100 [00:00<00:00, 524.60 it/sec, obj=0.438]
INFO - 08:23:30: ... 5%|▌ | 5/100 [00:00<00:00, 513.44 it/sec, obj=0.418]
INFO - 08:23:30: ... 6%|▌ | 6/100 [00:00<00:00, 525.20 it/sec, obj=0.416]
INFO - 08:23:30: ... 7%|▋ | 7/100 [00:00<00:00, 533.36 it/sec, obj=0.415]
INFO - 08:23:30: ... 8%|▊ | 8/100 [00:00<00:00, 541.53 it/sec, obj=0.415]
INFO - 08:23:30: ... 9%|▉ | 9/100 [00:00<00:00, 547.17 it/sec, obj=0.415]
INFO - 08:23:30: ... 10%|█ | 10/100 [00:00<00:00, 551.40 it/sec, obj=0.415]
INFO - 08:23:30: ... 11%|█ | 11/100 [00:00<00:00, 555.26 it/sec, obj=0.415]
INFO - 08:23:30: ... 12%|█▏ | 12/100 [00:00<00:00, 558.76 it/sec, obj=0.415]
INFO - 08:23:30: ... 13%|█▎ | 13/100 [00:00<00:00, 598.39 it/sec, obj=0.415]
INFO - 08:23:30: Optimization result:
INFO - 08:23:30: Optimizer info:
INFO - 08:23:30: Status: None
INFO - 08:23:30: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 08:23:30: Number of calls to the objective function by the optimizer: 15
INFO - 08:23:30: Solution:
INFO - 08:23:30: The solution is feasible.
INFO - 08:23:30: Objective: 0.414721553468123
INFO - 08:23:30: Standardized constraints:
INFO - 08:23:30: g = [-3.24306238e-01 -4.32544172e-01 -4.44089210e-16 -2.51297007e-01
INFO - 08:23:30: -2.35380057e-01 -4.99968031e-01]
INFO - 08:23:30: Design space:
INFO - 08:23:30: +------+-------------+---------------------+-------------+-------+
INFO - 08:23:30: | name | lower_bound | value | upper_bound | type |
INFO - 08:23:30: +------+-------------+---------------------+-------------+-------+
INFO - 08:23:30: | x[0] | 0 | 0.4836327595359132 | 1 | float |
INFO - 08:23:30: | x[1] | 0 | 0.9999999999999998 | 1 | float |
INFO - 08:23:30: | x[2] | 0 | 0.08671677713547089 | 1 | float |
INFO - 08:23:30: | x[3] | 0 | 0.9085357909356101 | 1 | float |
INFO - 08:23:30: | x[4] | 0 | 0.2480176979962943 | 1 | float |
INFO - 08:23:30: +------+-------------+---------------------+-------------+-------+
Post-process the results¶
execute_post(problem, "OptHistoryView", save=False, show=True)
<gemseo.post.opt_history_view.OptHistoryView object at 0x7f1c95e412b0>
Total running time of the script: (0 minutes 3.879 seconds)