Note
Click here to download the full example code
Variables influence¶
In this example, we illustrate the use of the VariableInfluence
plot
on the Sobieski’s SSBJ problem.
from gemseo.api import configure_logger
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.problems.sobieski.core.problem import SobieskiProblem
from matplotlib import pyplot as plt
Import¶
The first step is to import some functions from the API and a method to get the design space.
configure_logger()
Out:
<RootLogger root (INFO)>
Description¶
The VariableInfluence post-processing performs first-order variable influence analysis.
The method computes \(\frac{d f}{d x_i} \cdot \left(x_{i_*} - x_{initial_design}\right)\), where \(x_{initial_design}\) is the initial value of the variable and \(x_{i_*}\) is the optimal value of the variable.
Create disciplines¶
At this point, we instantiate the disciplines of Sobieski’s SSBJ problem: Propulsion, Aerodynamics, Structure and Mission
disciplines = create_discipline(
[
"SobieskiPropulsion",
"SobieskiAerodynamics",
"SobieskiStructure",
"SobieskiMission",
]
)
Create design space¶
We also read the design space from the SobieskiProblem
.
design_space = SobieskiProblem().design_space
Create and execute scenario¶
The next step is to build an MDO scenario in order to maximize the range, encoded ‘y_4’, with respect to the design parameters, while satisfying the inequality constraints ‘g_1’, ‘g_2’ and ‘g_3’. We can use the MDF formulation, the SLSQP optimization algorithm and a maximum number of iterations equal to 100.
scenario = create_scenario(
disciplines,
formulation="MDF",
objective_name="y_4",
maximize_objective=True,
design_space=design_space,
)
scenario.set_differentiation_method("user")
for constraint in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
Out:
INFO - 07:15:15:
INFO - 07:15:15: *** Start MDOScenario execution ***
INFO - 07:15:15: MDOScenario
INFO - 07:15:15: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 07:15:15: MDO formulation: MDF
INFO - 07:15:15: Optimization problem:
INFO - 07:15:15: minimize -y_4(x_shared, x_1, x_2, x_3)
INFO - 07:15:15: with respect to x_1, x_2, x_3, x_shared
INFO - 07:15:15: subject to constraints:
INFO - 07:15:15: g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 07:15:15: g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 07:15:15: g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 07:15:15: over the design space:
INFO - 07:15:15: +----------+-------------+-------+-------------+-------+
INFO - 07:15:15: | name | lower_bound | value | upper_bound | type |
INFO - 07:15:15: +----------+-------------+-------+-------------+-------+
INFO - 07:15:15: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 07:15:15: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 07:15:15: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 07:15:15: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 07:15:15: | x_shared | 40 | 55 | 70 | float |
INFO - 07:15:15: | x_shared | 500 | 1000 | 1500 | float |
INFO - 07:15:15: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 07:15:15: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 07:15:15: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 07:15:15: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 07:15:15: +----------+-------------+-------+-------------+-------+
INFO - 07:15:15: Solving optimization problem with algorithm SLSQP:
INFO - 07:15:15: ... 0%| | 0/10 [00:00<?, ?it]
INFO - 07:15:15: ... 20%|██ | 2/10 [00:00<00:00, 41.68 it/sec, obj=-2.12e+3]
WARNING - 07:15:16: MDAJacobi has reached its maximum number of iterations but the normed residual 1.0259352902248124e-06 is still above the tolerance 1e-06.
INFO - 07:15:16: ... 30%|███ | 3/10 [00:00<00:00, 23.75 it/sec, obj=-3.8e+3]
INFO - 07:15:16: ... 40%|████ | 4/10 [00:00<00:00, 17.12 it/sec, obj=-3.96e+3]
INFO - 07:15:16: ... 50%|█████ | 5/10 [00:00<00:00, 13.39 it/sec, obj=-3.96e+3]
INFO - 07:15:16: ... 60%|██████ | 6/10 [00:00<00:00, 10.98 it/sec, obj=-3.96e+3]
INFO - 07:15:16: ... 70%|███████ | 7/10 [00:01<00:00, 9.48 it/sec, obj=-4.81e+3]
INFO - 07:15:16: ... 90%|█████████ | 9/10 [00:01<00:00, 7.89 it/sec, obj=-3.87e+3]
INFO - 07:15:16: ... 100%|██████████| 10/10 [00:01<00:00, 7.50 it/sec, obj=-4.64e+3]
INFO - 07:15:16: Optimization result:
INFO - 07:15:16: Optimizer info:
INFO - 07:15:16: Status: None
INFO - 07:15:16: Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 07:15:16: Number of calls to the objective function by the optimizer: 12
INFO - 07:15:16: Solution:
INFO - 07:15:16: The solution is feasible.
INFO - 07:15:16: Objective: -3963.5118239326903
INFO - 07:15:16: Standardized constraints:
INFO - 07:15:16: g_1 = [-0.01808064 -0.03336052 -0.04426042 -0.05184355 -0.05733364 -0.13720861
INFO - 07:15:16: -0.10279139]
INFO - 07:15:16: g_2 = 9.785920617177979e-06
INFO - 07:15:16: g_3 = [-7.67233630e-01 -2.32766370e-01 8.55509121e-05 -1.83255000e-01]
INFO - 07:15:16: Design space:
INFO - 07:15:16: +----------+-------------+---------------------+-------------+-------+
INFO - 07:15:16: | name | lower_bound | value | upper_bound | type |
INFO - 07:15:16: +----------+-------------+---------------------+-------------+-------+
INFO - 07:15:16: | x_shared | 0.01 | 0.06000244648015432 | 0.09 | float |
INFO - 07:15:16: | x_shared | 30000 | 60000 | 60000 | float |
INFO - 07:15:16: | x_shared | 1.4 | 1.4 | 1.8 | float |
INFO - 07:15:16: | x_shared | 2.5 | 2.5 | 8.5 | float |
INFO - 07:15:16: | x_shared | 40 | 70 | 70 | float |
INFO - 07:15:16: | x_shared | 500 | 1500 | 1500 | float |
INFO - 07:15:16: | x_1 | 0.1 | 0.3999997783130735 | 0.4 | float |
INFO - 07:15:16: | x_1 | 0.75 | 0.75 | 1.25 | float |
INFO - 07:15:16: | x_2 | 0.75 | 0.75 | 1.25 | float |
INFO - 07:15:16: | x_3 | 0.1 | 0.1562581125267868 | 1 | float |
INFO - 07:15:16: +----------+-------------+---------------------+-------------+-------+
INFO - 07:15:16: *** End MDOScenario execution (time: 0:00:01.347202) ***
{'max_iter': 10, 'algo': 'SLSQP'}
Post-process scenario¶
Lastly, we post-process the scenario by means of the BasicHistory
plot.
Tip
Each post-processing method requires different inputs and offers a variety
of customization options. Use the API function
get_post_processing_options_schema()
to print a table with
the options for any post-processing algorithm.
Or refer to our dedicated page:
Post-processing algorithms.
scenario.post_process("VariableInfluence", save=False, show=False, fig_size=(15, 12))
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Out:
INFO - 07:15:17: VariableInfluence for function -y_4
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [1 4 3 2 5 9 7 8 0]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.0/lib/python3.9/site-packages/gemseo/post/variable_influence.py:234: UserWarning: FixedFormatter should only be used together with FixedLocator
axe.set_xticklabels(x_labels, fontsize=font_size, rotation=rotation)
INFO - 07:15:17: VariableInfluence for function g_1_0
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [0 7 3 5 6]
INFO - 07:15:17: VariableInfluence for function g_1_1
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [7 0 3 5 6]
INFO - 07:15:17: VariableInfluence for function g_1_2
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [7 0 3 5 6]
INFO - 07:15:17: VariableInfluence for function g_1_3
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [7 0 3 5 6]
INFO - 07:15:17: VariableInfluence for function g_1_4
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [7 0 3 5 6]
INFO - 07:15:17: VariableInfluence for function g_1_5
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [3 7 5 6]
INFO - 07:15:17: VariableInfluence for function g_1_6
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [3 7 5 6]
INFO - 07:15:17: VariableInfluence for function g_2
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [0]
INFO - 07:15:17: VariableInfluence for function g_3_0
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [1 9 5 2 4 0 8]
INFO - 07:15:17: VariableInfluence for function g_3_1
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [1 9 5 2 4 0 8]
INFO - 07:15:17: VariableInfluence for function g_3_2
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [1 9 2]
INFO - 07:15:17: VariableInfluence for function g_3_3
INFO - 07:15:17: Most influential variables indices to explain % of the function variation: 99
INFO - 07:15:17: [9 1 2]
Total running time of the script: ( 0 minutes 2.462 seconds)