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.execute({"algo": "SLSQP", "max_iter": 10})


Out:

    INFO - 10:03:14:
INFO - 10:03:14: *** Start MDOScenario execution ***
INFO - 10:03:14: MDOScenario
INFO - 10:03:14:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 10:03:14:    MDO formulation: MDF
INFO - 10:03:14: Optimization problem:
INFO - 10:03:14:    minimize -y_4(x_shared, x_1, x_2, x_3)
INFO - 10:03:14:    with respect to x_1, x_2, x_3, x_shared
INFO - 10:03:14:    subject to constraints:
INFO - 10:03:14:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 10:03:14:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 10:03:14:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 10:03:14:    over the design space:
INFO - 10:03:14:    +----------+-------------+-------+-------------+-------+
INFO - 10:03:14:    | name     | lower_bound | value | upper_bound | type  |
INFO - 10:03:14:    +----------+-------------+-------+-------------+-------+
INFO - 10:03:14:    | x_shared |     0.01    |  0.05 |     0.09    | float |
INFO - 10:03:14:    | x_shared |    30000    | 45000 |    60000    | float |
INFO - 10:03:14:    | x_shared |     1.4     |  1.6  |     1.8     | float |
INFO - 10:03:14:    | x_shared |     2.5     |  5.5  |     8.5     | float |
INFO - 10:03:14:    | x_shared |      40     |   55  |      70     | float |
INFO - 10:03:14:    | x_shared |     500     |  1000 |     1500    | float |
INFO - 10:03:14:    | x_1      |     0.1     |  0.25 |     0.4     | float |
INFO - 10:03:14:    | x_1      |     0.75    |   1   |     1.25    | float |
INFO - 10:03:14:    | x_2      |     0.75    |   1   |     1.25    | float |
INFO - 10:03:14:    | x_3      |     0.1     |  0.5  |      1      | float |
INFO - 10:03:14:    +----------+-------------+-------+-------------+-------+
INFO - 10:03:14: Solving optimization problem with algorithm SLSQP:
INFO - 10:03:14: ...   0%|          | 0/10 [00:00<?, ?it]
INFO - 10:03:14: ...  20%|██        | 2/10 [00:00<00:00, 40.73 it/sec, obj=-2.12e+3]
INFO - 10:03:14: ...  30%|███       | 3/10 [00:00<00:00, 24.52 it/sec, obj=-3.15e+3]
INFO - 10:03:14: ...  40%|████      | 4/10 [00:00<00:00, 17.51 it/sec, obj=-3.96e+3]
INFO - 10:03:14: ...  50%|█████     | 5/10 [00:00<00:00, 13.61 it/sec, obj=-3.98e+3]
INFO - 10:03:15: ...  50%|█████     | 5/10 [00:00<00:00, 12.26 it/sec, obj=-3.98e+3]
INFO - 10:03:15: Optimization result:
INFO - 10:03:15:    Optimizer info:
INFO - 10:03:15:       Status: 8
INFO - 10:03:15:       Message: Positive directional derivative for linesearch
INFO - 10:03:15:       Number of calls to the objective function by the optimizer: 6
INFO - 10:03:15:    Solution:
INFO - 10:03:15:       The solution is feasible.
INFO - 10:03:15:       Objective: -3960.1367790933214
INFO - 10:03:15:       Standardized constraints:
INFO - 10:03:15:          g_1 = [-0.01805983 -0.03334555 -0.04424879 -0.05183405 -0.05732561 -0.13720865
INFO - 10:03:15:  -0.10279135]
INFO - 10:03:15:          g_2 = 2.9360600315442298e-06
INFO - 10:03:15:          g_3 = [-0.76310174 -0.23689826 -0.00553375 -0.183255  ]
INFO - 10:03:15:       Design space:
INFO - 10:03:15:       +----------+-------------+---------------------+-------------+-------+
INFO - 10:03:15:       | name     | lower_bound |        value        | upper_bound | type  |
INFO - 10:03:15:       +----------+-------------+---------------------+-------------+-------+
INFO - 10:03:15:       | x_shared |     0.01    | 0.06000073401500788 |     0.09    | float |
INFO - 10:03:15:       | x_shared |    30000    |        60000        |    60000    | float |
INFO - 10:03:15:       | x_shared |     1.4     |         1.4         |     1.8     | float |
INFO - 10:03:15:       | x_shared |     2.5     |         2.5         |     8.5     | float |
INFO - 10:03:15:       | x_shared |      40     |          70         |      70     | float |
INFO - 10:03:15:       | x_shared |     500     |         1500        |     1500    | float |
INFO - 10:03:15:       | x_1      |     0.1     |         0.4         |     0.4     | float |
INFO - 10:03:15:       | x_1      |     0.75    |         0.75        |     1.25    | float |
INFO - 10:03:15:       | x_2      |     0.75    |         0.75        |     1.25    | float |
INFO - 10:03:15:       | x_3      |     0.1     |  0.1553801266337427 |      1      | float |
INFO - 10:03:15:       +----------+-------------+---------------------+-------------+-------+
INFO - 10:03:15: *** End MDOScenario execution (time: 0:00:00.829450) ***

{'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 - 10:03:15: VariableInfluence for function -y_4
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [1 4 3 2 5 9 7 8 0]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/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 - 10:03:15: VariableInfluence for function g_1_0
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [0 7 3 5 6]
INFO - 10:03:15: VariableInfluence for function g_1_1
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [7 0 3 5 6]
INFO - 10:03:15: VariableInfluence for function g_1_2
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [7 0 3 5 6]
INFO - 10:03:15: VariableInfluence for function g_1_3
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [7 0 3 5 6]
INFO - 10:03:15: VariableInfluence for function g_1_4
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [7 0 3 5 6]
INFO - 10:03:15: VariableInfluence for function g_1_5
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [3 7 5 6]
INFO - 10:03:15: VariableInfluence for function g_1_6
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [3 7 5 6]
INFO - 10:03:15: VariableInfluence for function g_2
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [0]
INFO - 10:03:15: VariableInfluence for function g_3_0
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [1 9 5 2 4 0 8]
INFO - 10:03:15: VariableInfluence for function g_3_1
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [1 9 5 2 4 0 8]
INFO - 10:03:15: VariableInfluence for function g_3_2
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [1 9 2]
INFO - 10:03:15: VariableInfluence for function g_3_3
INFO - 10:03:15: Most influential variables indices to explain % of the function variation: 99
INFO - 10:03:15: [9 1 2]


Total running time of the script: ( 0 minutes 1.937 seconds)

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