Note
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Parametric scalable MDO problem - MDF¶
We define a scalable problem based on two strongly coupled disciplines and a weakly one, with the following properties:
3 shared design parameters,
2 local design parameters for the first strongly coupled discipline,
2 coupling variables for the first strongly coupled discipline,
4 local design parameters for the second strongly coupled discipline,
3 coupling variables for the second strongly coupled discipline.
We would like to solve this MDO problem by means of an MDF formulation.
from gemseo.api import configure_logger
from gemseo.api import create_scenario
from gemseo.api import generate_n2_plot
from gemseo.problems.scalable.parametric.problem import TMScalableProblem
from matplotlib import pyplot as plt
configure_logger()
Out:
<RootLogger root (INFO)>
Instantiation of the scalable problem¶
n_shared = 3
n_local = [2, 4]
n_coupling = [2, 3]
problem = TMScalableProblem(n_shared, n_local, n_coupling)
Display the coupling structure¶
generate_n2_plot(problem.disciplines, save=False, show=True)
Solve the MDO using an MDF formulation¶
scenario = create_scenario(problem.disciplines, "MDF", "obj", problem.design_space)
scenario.add_constraint("cstr_0", "ineq")
scenario.add_constraint("cstr_1", "ineq")
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})
Out:
INFO - 10:03:52:
INFO - 10:03:52: *** Start MDOScenario execution ***
INFO - 10:03:52: MDOScenario
INFO - 10:03:52: Disciplines: MainModel SubModel_0 SubModel_1
INFO - 10:03:52: MDO formulation: MDF
INFO - 10:03:52: Optimization problem:
INFO - 10:03:52: minimize obj(x_local_0, x_local_1, x_shared)
INFO - 10:03:52: with respect to x_local_0, x_local_1, x_shared
INFO - 10:03:52: subject to constraints:
INFO - 10:03:52: cstr_0(x_local_0, x_local_1, x_shared) <= 0.0
INFO - 10:03:52: cstr_1(x_local_0, x_local_1, x_shared) <= 0.0
INFO - 10:03:52: over the design space:
INFO - 10:03:52: | Parameter space |
INFO - 10:03:52: +-----------+-------------+-------+-------------+-------+----------------------+
INFO - 10:03:52: | name | lower_bound | value | upper_bound | type | Initial distribution |
INFO - 10:03:52: +-----------+-------------+-------+-------------+-------+----------------------+
INFO - 10:03:52: | x_local_0 | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_local_0 | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_local_1 | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_local_1 | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_local_1 | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_local_1 | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_shared | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_shared | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: | x_shared | 0 | 0.5 | 1 | float | |
INFO - 10:03:52: +-----------+-------------+-------+-------------+-------+----------------------+
INFO - 10:03:52: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 10:03:52: ... 0%| | 0/100 [00:00<?, ?it]
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 628.5348041278223 is still above the tolerance 1e-06.
INFO - 10:03:52: ... 2%|▏ | 2/100 [00:00<00:00, 672.50 it/sec]
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 855.939250180759 is still above the tolerance 1e-06.
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1222.112924405924 is still above the tolerance 1e-06.
INFO - 10:03:52: ... 4%|▍ | 4/100 [00:00<00:00, 320.49 it/sec]
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1385.5049620986567 is still above the tolerance 1e-06.
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1733.2178166635606 is still above the tolerance 1e-06.
INFO - 10:03:52: ... 6%|▌ | 6/100 [00:00<00:00, 210.04 it/sec]
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1809.1058564937541 is still above the tolerance 1e-06.
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1810.0817661089236 is still above the tolerance 1e-06.
INFO - 10:03:52: ... 8%|▊ | 8/100 [00:00<00:00, 156.70 it/sec]
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1804.117512802312 is still above the tolerance 1e-06.
WARNING - 10:03:52: MDAJacobi has reached its maximum number of iterations but the normed residual 1781.4230266840048 is still above the tolerance 1e-06.
INFO - 10:03:53: ... 10%|█ | 10/100 [00:00<00:00, 124.50 it/sec]
WARNING - 10:03:53: MDAJacobi has reached its maximum number of iterations but the normed residual 1646.1968290578134 is still above the tolerance 1e-06.
WARNING - 10:03:53: MDAJacobi has reached its maximum number of iterations but the normed residual 909.2480409657202 is still above the tolerance 1e-06.
INFO - 10:03:53: ... 12%|█▏ | 12/100 [00:00<00:00, 103.18 it/sec]
WARNING - 10:03:53: MDAJacobi has reached its maximum number of iterations but the normed residual 725.9807159973328 is still above the tolerance 1e-06.
WARNING - 10:03:53: MDAJacobi has reached its maximum number of iterations but the normed residual 724.9413769402323 is still above the tolerance 1e-06.
INFO - 10:03:53: ... 14%|█▍ | 14/100 [00:01<00:00, 88.18 it/sec]
WARNING - 10:03:53: MDAJacobi has reached its maximum number of iterations but the normed residual 726.784699893992 is still above the tolerance 1e-06.
INFO - 10:03:53: ... 15%|█▌ | 15/100 [00:01<00:01, 82.23 it/sec]
INFO - 10:03:53: Optimization result:
INFO - 10:03:53: Optimizer info:
INFO - 10:03:53: Status: None
INFO - 10:03:53: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 10:03:53: Number of calls to the objective function by the optimizer: 15
INFO - 10:03:53: Solution:
INFO - 10:03:53: The solution is feasible.
INFO - 10:03:53: Objective: 0.670463878639397
INFO - 10:03:53: Standardized constraints:
INFO - 10:03:53: cstr_0 = [-0.01693211 -5.62972098]
INFO - 10:03:53: cstr_1 = [-1.05472950e+00 2.22044605e-16 -1.81142650e+00]
INFO - 10:03:53: +----------------------------------------------------------------------------------------------+
INFO - 10:03:53: | Parameter space |
INFO - 10:03:53: +-----------+-------------+-----------------------+-------------+-------+----------------------+
INFO - 10:03:53: | name | lower_bound | value | upper_bound | type | Initial distribution |
INFO - 10:03:53: +-----------+-------------+-----------------------+-------------+-------+----------------------+
INFO - 10:03:53: | x_local_0 | 0 | 0.5931064439648591 | 1 | float | |
INFO - 10:03:53: | x_local_0 | 0 | 1 | 1 | float | |
INFO - 10:03:53: | x_local_1 | 0 | 0 | 1 | float | |
INFO - 10:03:53: | x_local_1 | 0 | 0.9546530639347032 | 1 | float | |
INFO - 10:03:53: | x_local_1 | 0 | 0 | 1 | float | |
INFO - 10:03:53: | x_local_1 | 0 | 4.985109760672119e-16 | 1 | float | |
INFO - 10:03:53: | x_shared | 0 | 5.297941653541373e-17 | 1 | float | |
INFO - 10:03:53: | x_shared | 0 | 0 | 1 | float | |
INFO - 10:03:53: | x_shared | 0 | 2.001779104424825e-16 | 1 | float | |
INFO - 10:03:53: +-----------+-------------+-----------------------+-------------+-------+----------------------+
INFO - 10:03:53: *** End MDOScenario execution (time: 0:00:01.231608) ***
{'max_iter': 100, 'algo': 'NLOPT_SLSQP'}
Post-process the results¶
scenario.post_process("OptHistoryView", save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Total running time of the script: ( 0 minutes 2.497 seconds)