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)
plot scalable param mdf

Solve the MDO using an MDF formulation

scenario = problem.create_scenario()
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})

    INFO - 13:08:52:
    INFO - 13:08:52: *** Start MDOScenario execution ***
    INFO - 13:08:52: MDOScenario
    INFO - 13:08:52:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
    INFO - 13:08:52:    MDO formulation: MDF
    INFO - 13:08:52: Optimization problem:
    INFO - 13:08:52:    minimize f(x_0, x_1, x_2)
    INFO - 13:08:52:    with respect to x_0, x_1, x_2
    INFO - 13:08:52:    subject to constraints:
    INFO - 13:08:52:       c_1(x_0, x_1, x_2) <= 0.0
    INFO - 13:08:52:       c_2(x_0, x_1, x_2) <= 0.0
    INFO - 13:08:52:    over the design space:
    INFO - 13:08:52:       +--------+-------------+-------+-------------+-------+
    INFO - 13:08:52:       | Name   | Lower bound | Value | Upper bound | Type  |
    INFO - 13:08:52:       +--------+-------------+-------+-------------+-------+
    INFO - 13:08:52:       | x_0    |      0      |  0.5  |      1      | float |
    INFO - 13:08:52:       | x_1    |      0      |  0.5  |      1      | float |
    INFO - 13:08:52:       | x_2[0] |      0      |  0.5  |      1      | float |
    INFO - 13:08:52:       | x_2[1] |      0      |  0.5  |      1      | float |
    INFO - 13:08:52:       | x_2[2] |      0      |  0.5  |      1      | float |
    INFO - 13:08:52:       +--------+-------------+-------+-------------+-------+
    INFO - 13:08:52: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 13:08:52:      1%|          | 1/100 [00:00<00:05, 17.71 it/sec, obj=3.07]
 WARNING - 13:08:52: MDAJacobi has reached its maximum number of iterations but the normed residual 2.7151398467835046e-06 is still above the tolerance 1e-06.
    INFO - 13:08:52:      2%|▏         | 2/100 [00:00<00:14,  6.90 it/sec, obj=1.21]
    INFO - 13:08:52:      3%|▎         | 3/100 [00:00<00:12,  7.89 it/sec, obj=0.991]
    INFO - 13:08:52:      4%|▍         | 4/100 [00:00<00:11,  8.55 it/sec, obj=0.986]
    INFO - 13:08:52:      5%|▌         | 5/100 [00:00<00:10,  8.97 it/sec, obj=0.982]
    INFO - 13:08:52:      6%|▌         | 6/100 [00:00<00:10,  9.23 it/sec, obj=0.971]
 WARNING - 13:08:53: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427901205848047e-06 is still above the tolerance 1e-06.
    INFO - 13:08:53:      7%|▋         | 7/100 [00:00<00:09,  9.44 it/sec, obj=0.97]
 WARNING - 13:08:53: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427840082052262e-06 is still above the tolerance 1e-06.
    INFO - 13:08:53:      8%|▊         | 8/100 [00:00<00:09,  9.66 it/sec, obj=0.969]
 WARNING - 13:08:53: MDAJacobi has reached its maximum number of iterations but the normed residual 1.1427840072918856e-06 is still above the tolerance 1e-06.
    INFO - 13:08:53:      9%|▉         | 9/100 [00:00<00:09,  9.83 it/sec, obj=0.969]
   ERROR - 13:08:53: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.3.2/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.3.2/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 13:08:53:     10%|█         | 10/100 [00:00<00:08, 10.86 it/sec, obj=0.969]
    INFO - 13:08:53: Optimization result:
    INFO - 13:08:53:    Optimizer info:
    INFO - 13:08:53:       Status: None
    INFO - 13:08:53:       Message:  GEMSEO Stopped the driver
    INFO - 13:08:53:       Number of calls to the objective function by the optimizer: 11
    INFO - 13:08:53:    Solution:
    INFO - 13:08:53:       The solution is feasible.
    INFO - 13:08:53:       Objective: 0.969214782218196
    INFO - 13:08:53:       Standardized constraints:
    INFO - 13:08:53:          c_1 = [-0.68663938 -0.21340355]
    INFO - 13:08:53:          c_2 = [-7.31227901e-01 -1.68967318e-01 -2.32696422e-01  7.32747196e-15]
    INFO - 13:08:53:       Design space:
    INFO - 13:08:53:          +--------+-------------+--------------------+-------------+-------+
    INFO - 13:08:53:          | Name   | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:08:53:          +--------+-------------+--------------------+-------------+-------+
    INFO - 13:08:53:          | x_0    |      0      | 0.7071335797308678 |      1      | float |
    INFO - 13:08:53:          | x_1    |      0      |         1          |      1      | float |
    INFO - 13:08:53:          | x_2[0] |      0      |         0          |      1      | float |
    INFO - 13:08:53:          | x_2[1] |      0      | 0.5233182522437062 |      1      | float |
    INFO - 13:08:53:          | x_2[2] |      0      |         0          |      1      | float |
    INFO - 13:08:53:          +--------+-------------+--------------------+-------------+-------+
    INFO - 13:08:53: *** End MDOScenario execution (time: 0:00:00.940144) ***

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

Post-process the results

scenario.post_process("OptHistoryView", save=False, show=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum
  • Hessian diagonal approximation
  • Evolution of the inequality constraints
<gemseo.post.opt_history_view.OptHistoryView object at 0x7f8ba228d160>

Solve the associated quadratic programming problem

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

    INFO - 13:08:54: Optimization problem:
    INFO - 13:08:54:    minimize f = 0.5x'Qx + c'x + d
    INFO - 13:08:54:    with respect to x
    INFO - 13:08:54:    subject to constraints:
    INFO - 13:08:54:       g: Ax-b <= 0 <= 0.0
    INFO - 13:08:54:    over the design space:
    INFO - 13:08:54:       +------+-------------+-------+-------------+-------+
    INFO - 13:08:54:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:08:54:       +------+-------------+-------+-------------+-------+
    INFO - 13:08:54:       | x[0] |      0      |  0.5  |      1      | float |
    INFO - 13:08:54:       | x[1] |      0      |  0.5  |      1      | float |
    INFO - 13:08:54:       | x[2] |      0      |  0.5  |      1      | float |
    INFO - 13:08:54:       | x[3] |      0      |  0.5  |      1      | float |
    INFO - 13:08:54:       | x[4] |      0      |  0.5  |      1      | float |
    INFO - 13:08:54:       +------+-------------+-------+-------------+-------+
    INFO - 13:08:54: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 13:08:54:      1%|          | 1/100 [00:00<00:00, 1894.45 it/sec, obj=3.07]
    INFO - 13:08:54:      2%|▏         | 2/100 [00:00<00:00, 591.75 it/sec, obj=1.21]
    INFO - 13:08:54:      3%|▎         | 3/100 [00:00<00:00, 584.73 it/sec, obj=0.991]
    INFO - 13:08:54:      4%|▍         | 4/100 [00:00<00:00, 580.87 it/sec, obj=0.986]
    INFO - 13:08:54:      5%|▌         | 5/100 [00:00<00:00, 584.64 it/sec, obj=0.982]
    INFO - 13:08:54:      6%|▌         | 6/100 [00:00<00:00, 585.48 it/sec, obj=0.971]
    INFO - 13:08:54:      7%|▋         | 7/100 [00:00<00:00, 588.05 it/sec, obj=0.97]
   ERROR - 13:08:54: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.3.2/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.3.2/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 13:08:54:      8%|▊         | 8/100 [00:00<00:00, 563.88 it/sec, obj=0.969]
    INFO - 13:08:54: Optimization result:
    INFO - 13:08:54:    Optimizer info:
    INFO - 13:08:54:       Status: None
    INFO - 13:08:54:       Message:  GEMSEO Stopped the driver
    INFO - 13:08:54:       Number of calls to the objective function by the optimizer: 9
    INFO - 13:08:54:    Solution:
    INFO - 13:08:54:       The solution is feasible.
    INFO - 13:08:54:       Objective: 0.9692176254005034
    INFO - 13:08:54:       Standardized constraints:
    INFO - 13:08:54:          g = [-6.86640980e-01 -2.13404451e-01 -7.31227677e-01 -1.68967471e-01
    INFO - 13:08:54:  -2.32695870e-01 -2.22044605e-15]
    INFO - 13:08:54:       Design space:
    INFO - 13:08:54:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:08:54:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:08:54:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:08:54:          | x[0] |      0      | 0.7071348743877915 |      1      | float |
    INFO - 13:08:54:          | x[1] |      0      |         1          |      1      | float |
    INFO - 13:08:54:          | x[2] |      0      |         0          |      1      | float |
    INFO - 13:08:54:          | x[3] |      0      | 0.5233180438726639 |      1      | float |
    INFO - 13:08:54:          | x[4] |      0      |         0          |      1      | float |
    INFO - 13:08:54:          +------+-------------+--------------------+-------------+-------+
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, "OptHistoryView", save=False, show=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum
  • Hessian diagonal approximation
  • Evolution of the inequality constraints
<gemseo.post.opt_history_view.OptHistoryView object at 0x7f8ba1bd3130>

Total running time of the script: (0 minutes 4.080 seconds)

Gallery generated by Sphinx-Gallery