# 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 - 08:37:39:
INFO - 08:37:39: *** Start MDOScenario execution ***
INFO - 08:37:39: MDOScenario
INFO - 08:37:39:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
INFO - 08:37:39:    MDO formulation: MDF
INFO - 08:37:39: Optimization problem:
INFO - 08:37:39:    minimize f(x_0, x_1, x_2)
INFO - 08:37:39:    with respect to x_0, x_1, x_2
INFO - 08:37:39:    subject to constraints:
INFO - 08:37:39:       c_1(x_0, x_1, x_2) <= 0.0
INFO - 08:37:39:       c_2(x_0, x_1, x_2) <= 0.0
INFO - 08:37:39:    over the design space:
INFO - 08:37:39:    |                             Parameter space                             |
INFO - 08:37:39:    +------+-------------+-------+-------------+-------+----------------------+
INFO - 08:37:39:    | name | lower_bound | value | upper_bound | type  | Initial distribution |
INFO - 08:37:39:    +------+-------------+-------+-------------+-------+----------------------+
INFO - 08:37:39:    | x_0  |      0      |  0.5  |      1      | float |                      |
INFO - 08:37:39:    | x_1  |      0      |  0.5  |      1      | float |                      |
INFO - 08:37:39:    | x_2  |      0      |  0.5  |      1      | float |                      |
INFO - 08:37:39:    | x_2  |      0      |  0.5  |      1      | float |                      |
INFO - 08:37:39:    | x_2  |      0      |  0.5  |      1      | float |                      |
INFO - 08:37:39:    +------+-------------+-------+-------------+-------+----------------------+
INFO - 08:37:39: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 08:37:39: ...   0%|          | 0/100 [00:00<?, ?it]
INFO - 08:37:39: ...   1%|          | 1/100 [00:00<00:04, 22.38 it/sec, obj=1]
INFO - 08:37:39: ...   2%|▏         | 2/100 [00:00<00:08, 10.94 it/sec, obj=0.921]
INFO - 08:37:39: ...   3%|▎         | 3/100 [00:00<00:05, 16.37 it/sec, obj=0.513]
INFO - 08:37:39: ...   4%|▍         | 4/100 [00:00<00:08, 11.17 it/sec, obj=0.438]
INFO - 08:37:39: ...   5%|▌         | 5/100 [00:00<00:08, 11.74 it/sec, obj=0.418]
INFO - 08:37:39: ...   6%|▌         | 6/100 [00:00<00:07, 12.16 it/sec, obj=0.416]
INFO - 08:37:39: ...   7%|▋         | 7/100 [00:00<00:07, 12.48 it/sec, obj=0.415]
INFO - 08:37:39: ...   8%|▊         | 8/100 [00:00<00:07, 12.75 it/sec, obj=0.415]
INFO - 08:37:39: ...   9%|▉         | 9/100 [00:00<00:07, 12.99 it/sec, obj=0.415]
INFO - 08:37:39: ...  10%|█         | 10/100 [00:00<00:06, 13.19 it/sec, obj=0.415]
INFO - 08:37:39: ...  11%|█         | 11/100 [00:00<00:06, 13.36 it/sec, obj=0.415]
INFO - 08:37:39: ...  12%|█▏        | 12/100 [00:00<00:06, 14.15 it/sec, obj=0.415]
INFO - 08:37:39: ...  13%|█▎        | 13/100 [00:00<00:05, 15.33 it/sec, obj=0.415]
INFO - 08:37:39: Optimization result:
INFO - 08:37:39:    Optimizer info:
INFO - 08:37:39:       Status: None
INFO - 08:37:39:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 08:37:39:       Number of calls to the objective function by the optimizer: 15
INFO - 08:37:39:    Solution:
INFO - 08:37:39:       The solution is feasible.
INFO - 08:37:39:       Objective: 0.4147215357836146
INFO - 08:37:39:       Standardized constraints:
INFO - 08:37:39:          c_1 = [-0.32430628 -0.43254422]
INFO - 08:37:39:          c_2 = [ 9.31144051e-13 -2.51296986e-01 -2.35380042e-01 -4.99967955e-01]
INFO - 08:37:39:       +---------------------------------------------------------------------------------------+
INFO - 08:37:39:       |                                    Parameter space                                    |
INFO - 08:37:39:       +------+-------------+---------------------+-------------+-------+----------------------+
INFO - 08:37:39:       | name | lower_bound |        value        | upper_bound | type  | Initial distribution |
INFO - 08:37:39:       +------+-------------+---------------------+-------------+-------+----------------------+
INFO - 08:37:39:       | x_0  |      0      |  0.4836327506555587 |      1      | float |                      |
INFO - 08:37:39:       | x_1  |      0      |          1          |      1      | float |                      |
INFO - 08:37:39:       | x_2  |      0      | 0.08671670660039867 |      1      | float |                      |
INFO - 08:37:39:       | x_2  |      0      |  0.9085357960727601 |      1      | float |                      |
INFO - 08:37:39:       | x_2  |      0      |  0.2480176667988829 |      1      | float |                      |
INFO - 08:37:39:       +------+-------------+---------------------+-------------+-------+----------------------+
INFO - 08:37:39: *** End MDOScenario execution (time: 0:00:00.865961) ***

{'max_iter': 100, 'algo': 'NLOPT_SLSQP'}


## Post-process the results¶

scenario.post_process("OptHistoryView", save=False, show=True)

/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/genson/schema/strategies/base.py:42: UserWarning: Schema incompatible. Keyword 'description' has conflicting values ('The width and height of the figure in inches, e.g. (w, h).\nIf None, use the :attr:.OptPostProcessor.DEFAULT_FIG_SIZE\nof the post-processor.' vs. 'The width and height of the figure in inches, e.g. (w, h).\nIf None, use the :attr:.OptPostProcessor.DEFAULT_FIG_SIZE\nof the post-processor.'). Using 'The width and height of the figure in inches, e.g. (w, h).\nIf None, use the :attr:.OptPostProcessor.DEFAULT_FIG_SIZE\nof the post-processor.'
warn(('Schema incompatible. Keyword {0!r} has conflicting '

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f873a933460>


## Solve the associated quadratic programming problem¶

problem = problem.create_quadratic_programming_problem()
execute_algo(problem, algo_name="NLOPT_SLSQP", max_iter=100)

    INFO - 08:37:41: Optimization problem:
INFO - 08:37:41:    minimize f = 0.5x'Qx + c'x + d
INFO - 08:37:41:    with respect to x
INFO - 08:37:41:    subject to constraints:
INFO - 08:37:41:       g: Ax-b <= 0 <= 0.0
INFO - 08:37:41:    over the design space:
INFO - 08:37:41:    +------+-------------+-------+-------------+-------+
INFO - 08:37:41:    | name | lower_bound | value | upper_bound | type  |
INFO - 08:37:41:    +------+-------------+-------+-------------+-------+
INFO - 08:37:41:    | x[0] |      0      |  0.5  |      1      | float |
INFO - 08:37:41:    | x[1] |      0      |  0.5  |      1      | float |
INFO - 08:37:41:    | x[2] |      0      |  0.5  |      1      | float |
INFO - 08:37:41:    | x[3] |      0      |  0.5  |      1      | float |
INFO - 08:37:41:    | x[4] |      0      |  0.5  |      1      | float |
INFO - 08:37:41:    +------+-------------+-------+-------------+-------+
INFO - 08:37:41: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 08:37:41: ...   0%|          | 0/100 [00:00<?, ?it]
INFO - 08:37:41: ...   1%|          | 1/100 [00:00<00:00, 2280.75 it/sec, obj=1]
INFO - 08:37:41: ...   2%|▏         | 2/100 [00:00<00:00, 581.21 it/sec, obj=0.921]
INFO - 08:37:41: ...   3%|▎         | 3/100 [00:00<00:00, 808.67 it/sec, obj=0.513]
INFO - 08:37:41: ...   4%|▍         | 4/100 [00:00<00:00, 512.34 it/sec, obj=0.438]
INFO - 08:37:41: ...   5%|▌         | 5/100 [00:00<00:00, 517.98 it/sec, obj=0.418]
INFO - 08:37:41: ...   6%|▌         | 6/100 [00:00<00:00, 502.47 it/sec, obj=0.416]
INFO - 08:37:41: ...   7%|▋         | 7/100 [00:00<00:00, 495.53 it/sec, obj=0.415]
INFO - 08:37:41: ...   8%|▊         | 8/100 [00:00<00:00, 502.12 it/sec, obj=0.415]
INFO - 08:37:41: ...   9%|▉         | 9/100 [00:00<00:00, 508.45 it/sec, obj=0.415]
INFO - 08:37:41: ...  10%|█         | 10/100 [00:00<00:00, 513.08 it/sec, obj=0.415]
INFO - 08:37:41: ...  11%|█         | 11/100 [00:00<00:00, 516.03 it/sec, obj=0.415]
INFO - 08:37:41: ...  12%|█▏        | 12/100 [00:00<00:00, 516.06 it/sec, obj=0.415]
INFO - 08:37:41: ...  13%|█▎        | 13/100 [00:00<00:00, 552.98 it/sec, obj=0.415]
INFO - 08:37:41: Optimization result:
INFO - 08:37:41:    Optimizer info:
INFO - 08:37:41:       Status: None
INFO - 08:37:41:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 08:37:41:       Number of calls to the objective function by the optimizer: 15
INFO - 08:37:41:    Solution:
INFO - 08:37:41:       The solution is feasible.
INFO - 08:37:41:       Objective: 0.414721553468123
INFO - 08:37:41:       Standardized constraints:
INFO - 08:37:41:          g = [-3.24306238e-01 -4.32544172e-01 -4.44089210e-16 -2.51297007e-01
INFO - 08:37:41:  -2.35380057e-01 -4.99968031e-01]
INFO - 08:37:41:       Design space:
INFO - 08:37:41:       +------+-------------+---------------------+-------------+-------+
INFO - 08:37:41:       | name | lower_bound |        value        | upper_bound | type  |
INFO - 08:37:41:       +------+-------------+---------------------+-------------+-------+
INFO - 08:37:41:       | x[0] |      0      |  0.4836327595359132 |      1      | float |
INFO - 08:37:41:       | x[1] |      0      |  0.9999999999999998 |      1      | float |
INFO - 08:37:41:       | x[2] |      0      | 0.08671677713547089 |      1      | float |
INFO - 08:37:41:       | x[3] |      0      |  0.9085357909356101 |      1      | float |
INFO - 08:37:41:       | x[4] |      0      |  0.2480176979962943 |      1      | float |
INFO - 08:37:41:       +------+-------------+---------------------+-------------+-------+

Optimization result:
Design variables: [0.48363276 1.         0.08671678 0.90853579 0.2480177 ]
Objective function: 0.414721553468123
Feasible solution: True


## Post-process the results¶

execute_post(problem, "OptHistoryView", save=False, show=True)

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f873a9f3190>


Total running time of the script: ( 0 minutes 3.916 seconds)

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