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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 - 13:51:39:
    INFO - 13:51:39: *** Start MDOScenario execution ***
    INFO - 13:51:39: MDOScenario
    INFO - 13:51:39:    Disciplines: MainDiscipline ScalableDiscipline[1] ScalableDiscipline[2]
    INFO - 13:51:39:    MDO formulation: MDF
    INFO - 13:51:39: Optimization problem:
    INFO - 13:51:39:    minimize f(x_0, x_1, x_2)
    INFO - 13:51:39:    with respect to x_0, x_1, x_2
    INFO - 13:51:39:    subject to constraints:
    INFO - 13:51:39:       c_1(x_0, x_1, x_2) <= 0.0
    INFO - 13:51:39:       c_2(x_0, x_1, x_2) <= 0.0
    INFO - 13:51:39:    over the design space:
    INFO - 13:51:39:    +--------+-------------+-------+-------------+-------+----------------------+
    INFO - 13:51:39:    | name   | lower_bound | value | upper_bound | type  | Initial distribution |
    INFO - 13:51:39:    +--------+-------------+-------+-------------+-------+----------------------+
    INFO - 13:51:39:    | x_0    |      0      |  0.5  |      1      | float |                      |
    INFO - 13:51:39:    | x_1    |      0      |  0.5  |      1      | float |                      |
    INFO - 13:51:39:    | x_2[0] |      0      |  0.5  |      1      | float |                      |
    INFO - 13:51:39:    | x_2[1] |      0      |  0.5  |      1      | float |                      |
    INFO - 13:51:39:    | x_2[2] |      0      |  0.5  |      1      | float |                      |
    INFO - 13:51:39:    +--------+-------------+-------+-------------+-------+----------------------+
    INFO - 13:51:39: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 13:51:39: ...   0%|          | 0/100 [00:00<?, ?it]
    INFO - 13:51:40: ...   1%|          | 1/100 [00:00<00:04, 20.92 it/sec, obj=1]
    INFO - 13:51:40: ...   2%|▏         | 2/100 [00:00<00:10,  9.56 it/sec, obj=0.921]
    INFO - 13:51:40: ...   3%|▎         | 3/100 [00:00<00:06, 14.31 it/sec, obj=0.513]
    INFO - 13:51:40: ...   4%|▍         | 4/100 [00:00<00:09,  9.82 it/sec, obj=0.438]
    INFO - 13:51:40: ...   5%|▌         | 5/100 [00:00<00:09, 10.36 it/sec, obj=0.418]
    INFO - 13:51:40: ...   6%|▌         | 6/100 [00:00<00:08, 10.77 it/sec, obj=0.416]
    INFO - 13:51:40: ...   7%|▋         | 7/100 [00:00<00:08, 11.05 it/sec, obj=0.415]
    INFO - 13:51:40: ...   8%|▊         | 8/100 [00:00<00:08, 11.28 it/sec, obj=0.415]
    INFO - 13:51:40: ...   9%|▉         | 9/100 [00:00<00:07, 11.47 it/sec, obj=0.415]
    INFO - 13:51:40: ...  10%|█         | 10/100 [00:00<00:07, 11.62 it/sec, obj=0.415]
    INFO - 13:51:40: ...  11%|█         | 11/100 [00:00<00:07, 11.74 it/sec, obj=0.415]
    INFO - 13:51:40: ...  12%|█▏        | 12/100 [00:00<00:07, 12.45 it/sec, obj=0.415]
    INFO - 13:51:40: ...  13%|█▎        | 13/100 [00:00<00:06, 13.48 it/sec, obj=0.415]
    INFO - 13:51:40: Optimization result:
    INFO - 13:51:40:    Optimizer info:
    INFO - 13:51:40:       Status: None
    INFO - 13:51:40:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 13:51:40:       Number of calls to the objective function by the optimizer: 15
    INFO - 13:51:40:    Solution:
    INFO - 13:51:40:       The solution is feasible.
    INFO - 13:51:40:       Objective: 0.4147214093889784
    INFO - 13:51:40:       Standardized constraints:
    INFO - 13:51:40:          c_1 = [-0.32430622 -0.43254409]
    INFO - 13:51:40:          c_2 = [ 2.44645415e-11 -2.51297060e-01 -2.35380107e-01 -4.99968067e-01]
    INFO - 13:51:40:       Scalable design space:
    INFO - 13:51:40:       +--------+-------------+---------------------+-------------+-------+----------------------+
    INFO - 13:51:40:       | name   | lower_bound |        value        | upper_bound | type  | Initial distribution |
    INFO - 13:51:40:       +--------+-------------+---------------------+-------------+-------+----------------------+
    INFO - 13:51:40:       | x_0    |      0      |  0.4836326345734573 |      1      | float |                      |
    INFO - 13:51:40:       | x_1    |      0      |  0.9999999999999998 |      1      | float |                      |
    INFO - 13:51:40:       | x_2[0] |      0      | 0.08671679318925574 |      1      | float |                      |
    INFO - 13:51:40:       | x_2[1] |      0      |  0.9085357497327241 |      1      | float |                      |
    INFO - 13:51:40:       | x_2[2] |      0      |  0.2480176751996585 |      1      | float |                      |
    INFO - 13:51:40:       +--------+-------------+---------------------+-------------+-------+----------------------+
    INFO - 13:51:40: *** End MDOScenario execution (time: 0:00:00.982792) ***

{'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 0x7f0078a77ac0>

Solve the associated quadratic programming problem

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

INFO - 13:51:42: Optimization problem:
INFO - 13:51:42:    minimize f = 0.5x'Qx + c'x + d
INFO - 13:51:42:    with respect to x
INFO - 13:51:42:    subject to constraints:
INFO - 13:51:42:       g: Ax-b <= 0 <= 0.0
INFO - 13:51:42:    over the design space:
INFO - 13:51:42:    +------+-------------+-------+-------------+-------+
INFO - 13:51:42:    | name | lower_bound | value | upper_bound | type  |
INFO - 13:51:42:    +------+-------------+-------+-------------+-------+
INFO - 13:51:42:    | x[0] |      0      |  0.5  |      1      | float |
INFO - 13:51:42:    | x[1] |      0      |  0.5  |      1      | float |
INFO - 13:51:42:    | x[2] |      0      |  0.5  |      1      | float |
INFO - 13:51:42:    | x[3] |      0      |  0.5  |      1      | float |
INFO - 13:51:42:    | x[4] |      0      |  0.5  |      1      | float |
INFO - 13:51:42:    +------+-------------+-------+-------------+-------+
INFO - 13:51:42: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 13:51:42: ...   0%|          | 0/100 [00:00<?, ?it]
INFO - 13:51:42: ...   1%|          | 1/100 [00:00<00:00, 1800.13 it/sec, obj=1]
INFO - 13:51:42: ...   2%|▏         | 2/100 [00:00<00:00, 493.13 it/sec, obj=0.921]
INFO - 13:51:42: ...   3%|▎         | 3/100 [00:00<00:00, 679.06 it/sec, obj=0.513]
INFO - 13:51:42: ...   4%|▍         | 4/100 [00:00<00:00, 478.91 it/sec, obj=0.438]
INFO - 13:51:42: ...   5%|▌         | 5/100 [00:00<00:00, 449.69 it/sec, obj=0.418]
INFO - 13:51:42: ...   6%|▌         | 6/100 [00:00<00:00, 458.08 it/sec, obj=0.416]
INFO - 13:51:42: ...   7%|▋         | 7/100 [00:00<00:00, 466.54 it/sec, obj=0.415]
INFO - 13:51:42: ...   8%|▊         | 8/100 [00:00<00:00, 462.15 it/sec, obj=0.415]
INFO - 13:51:42: ...   9%|▉         | 9/100 [00:00<00:00, 458.53 it/sec, obj=0.415]
INFO - 13:51:42: ...  10%|█         | 10/100 [00:00<00:00, 464.31 it/sec, obj=0.415]
INFO - 13:51:42: ...  11%|█         | 11/100 [00:00<00:00, 468.14 it/sec, obj=0.415]
INFO - 13:51:42: ...  12%|█▏        | 12/100 [00:00<00:00, 472.87 it/sec, obj=0.415]
INFO - 13:51:42: ...  13%|█▎        | 13/100 [00:00<00:00, 505.74 it/sec, obj=0.415]
INFO - 13:51:42: Optimization result:
INFO - 13:51:42:    Optimizer info:
INFO - 13:51:42:       Status: None
INFO - 13:51:42:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 13:51:42:       Number of calls to the objective function by the optimizer: 15
INFO - 13:51:42:    Solution:
INFO - 13:51:42:       The solution is feasible.
INFO - 13:51:42:       Objective: 0.414721553468123
INFO - 13:51:42:       Standardized constraints:
INFO - 13:51:42:          g = [-3.24306238e-01 -4.32544172e-01 -4.44089210e-16 -2.51297007e-01
INFO - 13:51:42:  -2.35380057e-01 -4.99968031e-01]
INFO - 13:51:42:       Design space:
INFO - 13:51:42:       +------+-------------+---------------------+-------------+-------+
INFO - 13:51:42:       | name | lower_bound |        value        | upper_bound | type  |
INFO - 13:51:42:       +------+-------------+---------------------+-------------+-------+
INFO - 13:51:42:       | x[0] |      0      |  0.4836327595359132 |      1      | float |
INFO - 13:51:42:       | x[1] |      0      |  0.9999999999999998 |      1      | float |
INFO - 13:51:42:       | x[2] |      0      | 0.08671677713547089 |      1      | float |
INFO - 13:51:42:       | x[3] |      0      |  0.9085357909356101 |      1      | float |
INFO - 13:51:42:       | x[4] |      0      |  0.2480176979962943 |      1      | float |
INFO - 13:51:42:       +------+-------------+---------------------+-------------+-------+
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)
  • 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 0x7f0078c39fd0>

Total running time of the script: (0 minutes 4.003 seconds)

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