# 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 __future__ import annotations

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()

<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.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})

    INFO - 14:44:43:
INFO - 14:44:43: *** Start MDOScenario execution ***
INFO - 14:44:43: MDOScenario
INFO - 14:44:43:    Disciplines: MainModel SubModel_0 SubModel_1
INFO - 14:44:43:    MDO formulation: MDF
INFO - 14:44:43: Optimization problem:
INFO - 14:44:43:    minimize obj(x_local_0, x_local_1, x_shared)
INFO - 14:44:43:    with respect to x_local_0, x_local_1, x_shared
INFO - 14:44:43:    subject to constraints:
INFO - 14:44:43:       cstr_0(x_local_0, x_local_1, x_shared) <= 0.0
INFO - 14:44:43:       cstr_1(x_local_0, x_local_1, x_shared) <= 0.0
INFO - 14:44:43:    over the design space:
INFO - 14:44:43:    |                               Parameter space                                |
INFO - 14:44:43:    +-----------+-------------+-------+-------------+-------+----------------------+
INFO - 14:44:43:    | name      | lower_bound | value | upper_bound | type  | Initial distribution |
INFO - 14:44:43:    +-----------+-------------+-------+-------------+-------+----------------------+
INFO - 14:44:43:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_local_0 |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_local_1 |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_shared  |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_shared  |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    | x_shared  |      0      |  0.5  |      1      | float |                      |
INFO - 14:44:43:    +-----------+-------------+-------+-------------+-------+----------------------+
INFO - 14:44:43: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 14:44:43: ...   0%|          | 0/100 [00:00<?, ?it]
WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 628.5348041278223 is still above the tolerance 1e-06.
INFO - 14:44:43: ...   2%|▏         | 2/100 [00:00<00:00, 631.85 it/sec, obj=0.5]
WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 855.939250180759 is still above the tolerance 1e-06.
WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 1222.112924405924 is still above the tolerance 1e-06.
INFO - 14:44:43: ...   4%|▍         | 4/100 [00:00<00:00, 306.86 it/sec, obj=0.5]
WARNING - 14:44:43: MDAJacobi has reached its maximum number of iterations but the normed residual 1385.5049620986567 is still above the tolerance 1e-06.
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1733.2178166635606 is still above the tolerance 1e-06.
INFO - 14:44:44: ...   6%|▌         | 6/100 [00:00<00:00, 202.13 it/sec, obj=0.5]
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1809.1058564937541 is still above the tolerance 1e-06.
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1810.0817661089236 is still above the tolerance 1e-06.
INFO - 14:44:44: ...   8%|▊         | 8/100 [00:00<00:00, 150.66 it/sec, obj=0.5]
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1804.117512802312 is still above the tolerance 1e-06.
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1781.4230266840048 is still above the tolerance 1e-06.
INFO - 14:44:44: ...  10%|█         | 10/100 [00:00<00:00, 120.36 it/sec, obj=0.5]
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 1646.1968290578134 is still above the tolerance 1e-06.
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 909.2480409657202 is still above the tolerance 1e-06.
INFO - 14:44:44: ...  12%|█▏        | 12/100 [00:00<00:00, 100.13 it/sec, obj=0.5]
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 725.9807159973328 is still above the tolerance 1e-06.
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 724.9413769402323 is still above the tolerance 1e-06.
INFO - 14:44:44: ...  14%|█▍        | 14/100 [00:01<00:01, 85.75 it/sec, obj=0.5]
WARNING - 14:44:44: MDAJacobi has reached its maximum number of iterations but the normed residual 726.784699893992 is still above the tolerance 1e-06.
INFO - 14:44:44: ...  15%|█▌        | 15/100 [00:01<00:01, 80.00 it/sec, obj=0.5]
INFO - 14:44:44: Optimization result:
INFO - 14:44:44:    Optimizer info:
INFO - 14:44:44:       Status: None
INFO - 14:44:44:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 14:44:44:       Number of calls to the objective function by the optimizer: 15
INFO - 14:44:44:    Solution:
INFO - 14:44:44:       The solution is feasible.
INFO - 14:44:44:       Objective: 0.670463878639397
INFO - 14:44:44:       Standardized constraints:
INFO - 14:44:44:          cstr_0 = [-0.01693211 -5.62972098]
INFO - 14:44:44:          cstr_1 = [-1.05472950e+00  2.22044605e-16 -1.81142650e+00]
INFO - 14:44:44:       +----------------------------------------------------------------------------------------------+
INFO - 14:44:44:       |                                       Parameter space                                        |
INFO - 14:44:44:       +-----------+-------------+-----------------------+-------------+-------+----------------------+
INFO - 14:44:44:       | name      | lower_bound |         value         | upper_bound | type  | Initial distribution |
INFO - 14:44:44:       +-----------+-------------+-----------------------+-------------+-------+----------------------+
INFO - 14:44:44:       | x_local_0 |      0      |   0.5931064439648591  |      1      | float |                      |
INFO - 14:44:44:       | x_local_0 |      0      |           1           |      1      | float |                      |
INFO - 14:44:44:       | x_local_1 |      0      |           0           |      1      | float |                      |
INFO - 14:44:44:       | x_local_1 |      0      |   0.9546530639347032  |      1      | float |                      |
INFO - 14:44:44:       | x_local_1 |      0      |           0           |      1      | float |                      |
INFO - 14:44:44:       | x_local_1 |      0      | 4.985109760672119e-16 |      1      | float |                      |
INFO - 14:44:44:       | x_shared  |      0      | 5.297941653541373e-17 |      1      | float |                      |
INFO - 14:44:44:       | x_shared  |      0      |           0           |      1      | float |                      |
INFO - 14:44:44:       | x_shared  |      0      | 2.001779104424825e-16 |      1      | float |                      |
INFO - 14:44:44:       +-----------+-------------+-----------------------+-------------+-------+----------------------+
INFO - 14:44:44: *** End MDOScenario execution (time: 0:00:01.268875) ***

{'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 2.605 seconds)

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