Variables influence

In this example, we illustrate the use of the VariableInfluence plot on the Sobieski’s SSBJ problem.

from __future__ import absolute_import, division, print_function, unicode_literals

from future import standard_library

Import

The first step is to import some functions from the API and a method to get the design space.

from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem

configure_logger()

standard_library.install_aliases()

Create disciplines

Then, we instantiate the disciplines of the 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().read_design_space()

Create and execute scenario

The next step is to build a 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:

{'algo': 'SLSQP', 'max_iter': 10}

Post-process scenario

Lastly, we post-process the scenario by means of the BasicHistory plot which performs first order variable influence analysis by computing df/dxi * (xi* - xi0) where xi0 is the initial value of the variable and xi* is the optimal value of the variable plots any of the constraint or objective functions w.r.t. optimization iterations or sampling snapshots.

scenario.post_process(
    "VariableInfluence", save=False, show=True, figsize_x=15, figsize_y=12
)

Out:

/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.0.3/lib/python3.8/site-packages/gemseo/post/variable_influence.py:242: UserWarning: FixedFormatter should only be used together with FixedLocator
  axe.set_xticklabels(x_labels, fontsize=14)

<gemseo.post.variable_influence.VariableInfluence object at 0x7fc299c77b80>