Note
Click here to download the full example code
Robustness¶
In this example, we illustrate the use of the Robustness
plot
on the Sobieski’s SSBJ problem.
from __future__ import division, unicode_literals
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.
from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
configure_logger()
Out:
<RootLogger root (INFO)>
Description¶
In the Robustness
post-processing,
the robustness of the optimum is represented by a box plot. Using the
quadratic approximations of all the output functions, we
propagate analytically a normal distribution with 1% standard deviation
on all the design variables, assuming no cross-correlations of inputs,
to obtain the mean and standard deviation of the resulting normal
distribution. A series of samples are randomly generated from the resulting
distribution, whose quartiles are plotted, relatively to the values of
the function at the optimum. For each function (in abscissa), the plot
shows the extreme values encountered in the samples (top and bottom
bars). Then, 95% of the values are within the blue boxes. The average is
given by the red bar.
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().read_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 - 12:58:05:
INFO - 12:58:05: *** Start MDO Scenario execution ***
INFO - 12:58:05: MDOScenario
INFO - 12:58:05: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 12:58:05: MDOFormulation: MDF
INFO - 12:58:05: Algorithm: SLSQP
INFO - 12:58:05: Optimization problem:
INFO - 12:58:05: Minimize: -y_4(x_shared, x_1, x_2, x_3)
INFO - 12:58:05: With respect to: x_shared, x_1, x_2, x_3
INFO - 12:58:05: Subject to constraints:
INFO - 12:58:05: g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 12:58:05: g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 12:58:05: g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 12:58:05: Design space:
INFO - 12:58:05: +----------+-------------+-------+-------------+-------+
INFO - 12:58:05: | name | lower_bound | value | upper_bound | type |
INFO - 12:58:05: +----------+-------------+-------+-------------+-------+
INFO - 12:58:05: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 12:58:05: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 12:58:05: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 12:58:05: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 12:58:05: | x_shared | 40 | 55 | 70 | float |
INFO - 12:58:05: | x_shared | 500 | 1000 | 1500 | float |
INFO - 12:58:05: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 12:58:05: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 12:58:05: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 12:58:05: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 12:58:05: +----------+-------------+-------+-------------+-------+
INFO - 12:58:05: Optimization: 0%| | 0/10 [00:00<?, ?it]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.2.1/lib/python3.8/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:407: SparseEfficiencyWarning: splu requires CSC matrix format
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
INFO - 12:58:05: Optimization: 20%|██ | 2/10 [00:00<00:00, 53.74 it/sec, obj=2.12e+3]
INFO - 12:58:05: Optimization: 40%|████ | 4/10 [00:00<00:00, 21.52 it/sec, obj=3.97e+3]
INFO - 12:58:05: Optimization: 50%|█████ | 5/10 [00:00<00:00, 16.76 it/sec, obj=3.96e+3]
INFO - 12:58:05: Optimization: 60%|██████ | 6/10 [00:00<00:00, 13.75 it/sec, obj=3.96e+3]
INFO - 12:58:05: Optimization: 70%|███████ | 7/10 [00:00<00:00, 11.65 it/sec, obj=3.96e+3]
INFO - 12:58:06: Optimization: 90%|█████████ | 9/10 [00:01<00:00, 9.93 it/sec, obj=3.96e+3]
INFO - 12:58:06: Optimization: 100%|██████████| 10/10 [00:01<00:00, 9.24 it/sec, obj=3.96e+3]
INFO - 12:58:06: Optimization result:
INFO - 12:58:06: Objective value = 3963.595455433326
INFO - 12:58:06: The result is feasible.
INFO - 12:58:06: Status: None
INFO - 12:58:06: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 12:58:06: Number of calls to the objective function by the optimizer: 12
INFO - 12:58:06: Constraints values:
INFO - 12:58:06: g_1 = [-0.01814919 -0.03340982 -0.04429875 -0.05187486 -0.05736009 -0.13720854
INFO - 12:58:06: -0.10279146]
INFO - 12:58:06: g_2 = 3.236261671801799e-05
INFO - 12:58:06: g_3 = [-7.67067574e-01 -2.32932426e-01 -9.19662628e-05 -1.83255000e-01]
INFO - 12:58:06: Design space:
INFO - 12:58:06: +----------+-------------+--------------------+-------------+-------+
INFO - 12:58:06: | name | lower_bound | value | upper_bound | type |
INFO - 12:58:06: +----------+-------------+--------------------+-------------+-------+
INFO - 12:58:06: | x_shared | 0.01 | 0.0600080906541795 | 0.09 | float |
INFO - 12:58:06: | x_shared | 30000 | 60000 | 60000 | float |
INFO - 12:58:06: | x_shared | 1.4 | 1.4 | 1.8 | float |
INFO - 12:58:06: | x_shared | 2.5 | 2.5 | 8.5 | float |
INFO - 12:58:06: | x_shared | 40 | 70 | 70 | float |
INFO - 12:58:06: | x_shared | 500 | 1500 | 1500 | float |
INFO - 12:58:06: | x_1 | 0.1 | 0.3999993439500847 | 0.4 | float |
INFO - 12:58:06: | x_1 | 0.75 | 0.75 | 1.25 | float |
INFO - 12:58:06: | x_2 | 0.75 | 0.75 | 1.25 | float |
INFO - 12:58:06: | x_3 | 0.1 | 0.156230376400943 | 1 | float |
INFO - 12:58:06: +----------+-------------+--------------------+-------------+-------+
INFO - 12:58:06: *** MDO Scenario run terminated in 0:00:01.091406 ***
{'algo': 'SLSQP', 'max_iter': 10}
Post-process scenario¶
Lastly, we post-process the scenario by means of the Robustness
which plots any of the constraint or
objective functions w.r.t. the optimization iterations or sampling snapshots.
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:
Options for Post-processing algorithms.
scenario.post_process("Robustness", save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Total running time of the script: ( 0 minutes 1.325 seconds)