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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.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 - 13:53:46:
    INFO - 13:53:46: *** Start MDOScenario execution ***
    INFO - 13:53:46: MDOScenario
    INFO - 13:53:46:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
    INFO - 13:53:46:    MDO formulation: MDF
    INFO - 13:53:46: Optimization problem:
    INFO - 13:53:46:    minimize f(x_0, x_1, x_2)
    INFO - 13:53:46:    with respect to x_0, x_1, x_2
    INFO - 13:53:46:    subject to constraints:
    INFO - 13:53:46:       c_1(x_0, x_1, x_2) <= 0.0
    INFO - 13:53:46:       c_2(x_0, x_1, x_2) <= 0.0
    INFO - 13:53:46:    over the design space:
    INFO - 13:53:46:       +--------+-------------+-------+-------------+-------+
    INFO - 13:53:46:       | Name   | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:46:       +--------+-------------+-------+-------------+-------+
    INFO - 13:53:46:       | x_0    |      0      |  0.5  |      1      | float |
    INFO - 13:53:46:       | x_1    |      0      |  0.5  |      1      | float |
    INFO - 13:53:46:       | x_2[0] |      0      |  0.5  |      1      | float |
    INFO - 13:53:46:       | x_2[1] |      0      |  0.5  |      1      | float |
    INFO - 13:53:46:       | x_2[2] |      0      |  0.5  |      1      | float |
    INFO - 13:53:46:       +--------+-------------+-------+-------------+-------+
    INFO - 13:53:46: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 13:53:46:      1%|          | 1/100 [00:00<00:04, 19.85 it/sec, obj=3.07]
 WARNING - 13:53:46: MDAJacobi has reached its maximum number of iterations but the normed residual 2.1168696144554684e-06 is still above the tolerance 1e-06.
    INFO - 13:53:46:      2%|▏         | 2/100 [00:00<00:12,  8.01 it/sec, obj=1.21]
    INFO - 13:53:46:      3%|▎         | 3/100 [00:00<00:10,  9.15 it/sec, obj=0.991]
    INFO - 13:53:47:      4%|▍         | 4/100 [00:00<00:09,  9.90 it/sec, obj=0.986]
    INFO - 13:53:47:      5%|▌         | 5/100 [00:00<00:09, 10.41 it/sec, obj=0.982]
    INFO - 13:53:47:      6%|▌         | 6/100 [00:00<00:08, 10.79 it/sec, obj=0.971]
    INFO - 13:53:47:      7%|▋         | 7/100 [00:00<00:08, 11.04 it/sec, obj=0.97]
    INFO - 13:53:47:      8%|▊         | 8/100 [00:00<00:08, 11.25 it/sec, obj=0.969]
    INFO - 13:53:47:      9%|▉         | 9/100 [00:00<00:07, 11.41 it/sec, obj=0.969]
    INFO - 13:53:47:     10%|█         | 10/100 [00:00<00:07, 11.54 it/sec, obj=0.969]
    INFO - 13:53:47:     11%|█         | 11/100 [00:00<00:07, 12.68 it/sec, obj=Not evaluated]
    INFO - 13:53:47: Optimization result:
    INFO - 13:53:47:    Optimizer info:
    INFO - 13:53:47:       Status: None
    INFO - 13:53:47:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
    INFO - 13:53:47:       Number of calls to the objective function by the optimizer: 11
    INFO - 13:53:47:    Solution:
    INFO - 13:53:47:       The solution is feasible.
    INFO - 13:53:47:       Objective: 0.9692177673322224
    INFO - 13:53:47:       Standardized constraints:
    INFO - 13:53:47:          c_1 = [-0.68664086 -0.21340455]
    INFO - 13:53:47:          c_2 = [-7.31227816e-01 -1.68967484e-01 -2.32695971e-01  1.19487753e-12]
    INFO - 13:53:47:       Design space:
    INFO - 13:53:47:          +--------+-------------+-----------------------+-------------+-------+
    INFO - 13:53:47:          | Name   | Lower bound |         Value         | Upper bound | Type  |
    INFO - 13:53:47:          +--------+-------------+-----------------------+-------------+-------+
    INFO - 13:53:47:          | x_0    |      0      |   0.7071349698120538  |      1      | float |
    INFO - 13:53:47:          | x_1    |      0      |   0.9999999999999997  |      1      | float |
    INFO - 13:53:47:          | x_2[0] |      0      | 2.906542539477308e-16 |      1      | float |
    INFO - 13:53:47:          | x_2[1] |      0      |   0.5233175560073929  |      1      | float |
    INFO - 13:53:47:          | x_2[2] |      0      | 6.286235338479938e-31 |      1      | float |
    INFO - 13:53:47:          +--------+-------------+-----------------------+-------------+-------+
    INFO - 13:53:47: *** End MDOScenario execution (time: 0:00:00.884565) ***

{'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 0x7f2d1c04bcd0>

Solve the associated quadratic programming problem

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

    INFO - 13:53:48: Optimization problem:
    INFO - 13:53:48:    minimize f = 0.5x'Qx + c'x + d
    INFO - 13:53:48:    with respect to x
    INFO - 13:53:48:    subject to constraints:
    INFO - 13:53:48:       g: Ax-b <= 0 <= 0.0
    INFO - 13:53:48:    over the design space:
    INFO - 13:53:48:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:48:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:48:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:48:       | x[0] |      0      |  0.5  |      1      | float |
    INFO - 13:53:48:       | x[1] |      0      |  0.5  |      1      | float |
    INFO - 13:53:48:       | x[2] |      0      |  0.5  |      1      | float |
    INFO - 13:53:48:       | x[3] |      0      |  0.5  |      1      | float |
    INFO - 13:53:48:       | x[4] |      0      |  0.5  |      1      | float |
    INFO - 13:53:48:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:48: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 13:53:48:      1%|          | 1/100 [00:00<00:00, 2167.60 it/sec, obj=3.07]
    INFO - 13:53:48:      2%|▏         | 2/100 [00:00<00:00, 614.51 it/sec, obj=1.21]
    INFO - 13:53:48:      3%|▎         | 3/100 [00:00<00:00, 610.02 it/sec, obj=0.991]
    INFO - 13:53:48:      4%|▍         | 4/100 [00:00<00:00, 606.92 it/sec, obj=0.986]
    INFO - 13:53:48:      5%|▌         | 5/100 [00:00<00:00, 603.08 it/sec, obj=0.982]
    INFO - 13:53:48:      6%|▌         | 6/100 [00:00<00:00, 604.76 it/sec, obj=0.971]
    INFO - 13:53:48:      7%|▋         | 7/100 [00:00<00:00, 603.06 it/sec, obj=0.97]
   ERROR - 13:53:48: 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/lib_nlopt.py", line 498, 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 - 13:53:48:      8%|▊         | 8/100 [00:00<00:00, 579.47 it/sec, obj=0.969]
    INFO - 13:53:48: Optimization result:
    INFO - 13:53:48:    Optimizer info:
    INFO - 13:53:48:       Status: None
    INFO - 13:53:48:       Message:  GEMSEO Stopped the driver
    INFO - 13:53:48:       Number of calls to the objective function by the optimizer: 9
    INFO - 13:53:48:    Solution:
    INFO - 13:53:48:       The solution is feasible.
    INFO - 13:53:48:       Objective: 0.9692176254005034
    INFO - 13:53:48:       Standardized constraints:
    INFO - 13:53:48:          g = [-6.86640980e-01 -2.13404451e-01 -7.31227677e-01 -1.68967471e-01
    INFO - 13:53:48:  -2.32695870e-01 -2.22044605e-15]
    INFO - 13:53:48:       Design space:
    INFO - 13:53:48:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:48:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:48:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:48:          | x[0] |      0      | 0.7071348743877915 |      1      | float |
    INFO - 13:53:48:          | x[1] |      0      |         1          |      1      | float |
    INFO - 13:53:48:          | x[2] |      0      |         0          |      1      | float |
    INFO - 13:53:48:          | x[3] |      0      | 0.5233180438726639 |      1      | float |
    INFO - 13:53:48:          | x[4] |      0      |         0          |      1      | float |
    INFO - 13:53:48:          +------+-------------+--------------------+-------------+-------+
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, "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 0x7f2d1be49700>

Total running time of the script: (0 minutes 3.791 seconds)

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