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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.mdo.scalable.parametric.core.scalable_discipline_settings import (
    ScalableDisciplineSettings,
)
from gemseo.problems.mdo.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)
plot scalable param mdf

Solve the MDO using an MDF formulation#

scenario = problem.create_scenario()
scenario.execute(algo_name="NLOPT_SLSQP", max_iter=100)

   INFO - 08:36:47:
   INFO - 08:36:47: *** Start MDOScenario execution ***
   INFO - 08:36:47: MDOScenario
   INFO - 08:36:47:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
   INFO - 08:36:47:    MDO formulation: MDF
   INFO - 08:36:47: Optimization problem:
   INFO - 08:36:47:    minimize f(x_0, x_1, x_2)
   INFO - 08:36:47:    with respect to x_0, x_1, x_2
   INFO - 08:36:47:    subject to constraints:
   INFO - 08:36:47:       c_1(x_0, x_1, x_2) <= 0
   INFO - 08:36:47:       c_2(x_0, x_1, x_2) <= 0
   INFO - 08:36:47:    over the design space:
   INFO - 08:36:47:       +--------+-------------+-------+-------------+-------+
   INFO - 08:36:47:       | Name   | Lower bound | Value | Upper bound | Type  |
   INFO - 08:36:47:       +--------+-------------+-------+-------------+-------+
   INFO - 08:36:47:       | x_0    |      0      |  0.5  |      1      | float |
   INFO - 08:36:47:       | x_1    |      0      |  0.5  |      1      | float |
   INFO - 08:36:47:       | x_2[0] |      0      |  0.5  |      1      | float |
   INFO - 08:36:47:       | x_2[1] |      0      |  0.5  |      1      | float |
   INFO - 08:36:47:       | x_2[2] |      0      |  0.5  |      1      | float |
   INFO - 08:36:47:       +--------+-------------+-------+-------------+-------+
   INFO - 08:36:47: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 08:36:47:      1%|          | 1/100 [00:00<00:03, 31.82 it/sec, obj=3.07]
WARNING - 08:36:47: MDAJacobi has reached its maximum number of iterations but the normed residual 2.7151398445206794e-06 is still above the tolerance 1e-06.
   INFO - 08:36:47:      2%|▏         | 2/100 [00:00<00:06, 16.23 it/sec, obj=1.21]
   INFO - 08:36:47:      3%|▎         | 3/100 [00:00<00:05, 18.22 it/sec, obj=0.991]
   INFO - 08:36:47:      4%|▍         | 4/100 [00:00<00:04, 19.64 it/sec, obj=0.986]
   INFO - 08:36:47:      5%|▌         | 5/100 [00:00<00:04, 20.65 it/sec, obj=0.982]
   INFO - 08:36:47:      6%|▌         | 6/100 [00:00<00:04, 21.40 it/sec, obj=0.971]
WARNING - 08:36:47: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427901203368072e-06 is still above the tolerance 1e-06.
   INFO - 08:36:47:      7%|▋         | 7/100 [00:00<00:04, 21.87 it/sec, obj=0.97]
WARNING - 08:36:47: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427840078240745e-06 is still above the tolerance 1e-06.
   INFO - 08:36:47:      8%|▊         | 8/100 [00:00<00:04, 22.17 it/sec, obj=0.969]
WARNING - 08:36:47: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427840073629847e-06 is still above the tolerance 1e-06.
   INFO - 08:36:47:      9%|▉         | 9/100 [00:00<00:04, 22.43 it/sec, obj=0.969]
WARNING - 08:36:47: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427840071115847e-06 is still above the tolerance 1e-06.
   INFO - 08:36:47:     10%|█         | 10/100 [00:00<00:03, 22.66 it/sec, obj=0.969]
   INFO - 08:36:47:     11%|█         | 11/100 [00:00<00:03, 24.86 it/sec, obj=Not evaluated]
   INFO - 08:36:47: Optimization result:
   INFO - 08:36:47:    Optimizer info:
   INFO - 08:36:47:       Status: None
   INFO - 08:36:47:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
   INFO - 08:36:47:       Number of calls to the objective function by the optimizer: 11
   INFO - 08:36:47:    Solution:
   INFO - 08:36:47:       The solution is feasible.
   INFO - 08:36:47:       Objective: 0.9692147822181947
   INFO - 08:36:47:       Standardized constraints:
   INFO - 08:36:47:          c_1 = [-0.68663938 -0.21340355]
   INFO - 08:36:47:          c_2 = [-7.31227901e-01 -1.68967318e-01 -2.32696422e-01  7.82707232e-15]
   INFO - 08:36:47:       Design space:
   INFO - 08:36:47:          +--------+-------------+--------------------+-------------+-------+
   INFO - 08:36:47:          | Name   | Lower bound |       Value        | Upper bound | Type  |
   INFO - 08:36:47:          +--------+-------------+--------------------+-------------+-------+
   INFO - 08:36:47:          | x_0    |      0      | 0.7071335797308679 |      1      | float |
   INFO - 08:36:47:          | x_1    |      0      |         1          |      1      | float |
   INFO - 08:36:47:          | x_2[0] |      0      |         0          |      1      | float |
   INFO - 08:36:47:          | x_2[1] |      0      | 0.5233182522437052 |      1      | float |
   INFO - 08:36:47:          | x_2[2] |      0      |         0          |      1      | float |
   INFO - 08:36:47:          +--------+-------------+--------------------+-------------+-------+
   INFO - 08:36:47: *** End MDOScenario execution (time: 0:00:00.449574) ***

Post-process the results#

scenario.post_process(post_name="OptHistoryView", save=False, show=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Evolution of the distance to the optimum
  • Evolution of the inequality constraints
<gemseo.post.opt_history_view.OptHistoryView object at 0x7f2514a242b0>

Solve the associated quadratic programming problem#

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

    INFO - 08:36:48: Optimization problem:
    INFO - 08:36:48:    minimize f = 0.5x'Qx + c'x + d
    INFO - 08:36:48:    with respect to x
    INFO - 08:36:48:    subject to constraints:
    INFO - 08:36:48:       g: Ax-b <= 0 <= 0.0
    INFO - 08:36:48:    over the design space:
    INFO - 08:36:48:       +------+-------------+-------+-------------+-------+
    INFO - 08:36:48:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:48:       +------+-------------+-------+-------------+-------+
    INFO - 08:36:48:       | x[0] |      0      |  0.5  |      1      | float |
    INFO - 08:36:48:       | x[1] |      0      |  0.5  |      1      | float |
    INFO - 08:36:48:       | x[2] |      0      |  0.5  |      1      | float |
    INFO - 08:36:48:       | x[3] |      0      |  0.5  |      1      | float |
    INFO - 08:36:48:       | x[4] |      0      |  0.5  |      1      | float |
    INFO - 08:36:48:       +------+-------------+-------+-------------+-------+
    INFO - 08:36:48: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:48:      1%|          | 1/100 [00:00<00:00, 2396.75 it/sec, obj=3.07]
    INFO - 08:36:48:      2%|▏         | 2/100 [00:00<00:00, 588.92 it/sec, obj=1.21]
    INFO - 08:36:48:      3%|▎         | 3/100 [00:00<00:00, 591.75 it/sec, obj=0.991]
    INFO - 08:36:48:      4%|▍         | 4/100 [00:00<00:00, 593.23 it/sec, obj=0.986]
    INFO - 08:36:48:      5%|▌         | 5/100 [00:00<00:00, 599.22 it/sec, obj=0.982]
    INFO - 08:36:48:      6%|▌         | 6/100 [00:00<00:00, 599.50 it/sec, obj=0.971]
    INFO - 08:36:48:      7%|▋         | 7/100 [00:00<00:00, 602.70 it/sec, obj=0.97]
   ERROR - 08:36:48: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:48:      8%|▊         | 8/100 [00:00<00:00, 576.62 it/sec, obj=0.969]
    INFO - 08:36:48: Optimization result:
    INFO - 08:36:48:    Optimizer info:
    INFO - 08:36:48:       Status: None
    INFO - 08:36:48:       Message: GEMSEO stopped the driver.
    INFO - 08:36:48:       Number of calls to the objective function by the optimizer: 9
    INFO - 08:36:48:    Solution:
    INFO - 08:36:48:       The solution is feasible.
    INFO - 08:36:48:       Objective: 0.9692176254005034
    INFO - 08:36:48:       Standardized constraints:
    INFO - 08:36:48:          g = [-6.86640980e-01 -2.13404451e-01 -7.31227677e-01 -1.68967471e-01
    INFO - 08:36:48:  -2.32695870e-01 -2.22044605e-15]
    INFO - 08:36:48:       Design space:
    INFO - 08:36:48:          +------+-------------+--------------------+-------------+-------+
    INFO - 08:36:48:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 08:36:48:          +------+-------------+--------------------+-------------+-------+
    INFO - 08:36:48:          | x[0] |      0      | 0.7071348743877915 |      1      | float |
    INFO - 08:36:48:          | x[1] |      0      |         1          |      1      | float |
    INFO - 08:36:48:          | x[2] |      0      |         0          |      1      | float |
    INFO - 08:36:48:          | x[3] |      0      | 0.5233180438726639 |      1      | float |
    INFO - 08:36:48:          | x[4] |      0      |         0          |      1      | float |
    INFO - 08:36:48:          +------+-------------+--------------------+-------------+-------+
Optimization result:
  • Design variables: [0.70713487 1. 0. 0.52331804 0. ]
  • Objective function: 0.9692176254005034
  • Feasible solution: True


Post-process the results#

execute_post(problem, post_name="OptHistoryView", save=False, show=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Evolution of the distance to the optimum
  • Evolution of the inequality constraints
<gemseo.post.opt_history_view.OptHistoryView object at 0x7f24f40d8c10>

Total running time of the script: (0 minutes 3.305 seconds)

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