# Correlations¶

In this example, we illustrate the use of the Correlations 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)>


## 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 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 - 09:25:18:
INFO - 09:25:18: *** Start MDO Scenario execution ***
INFO - 09:25:18: MDOScenario
INFO - 09:25:18:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 09:25:18:    MDOFormulation: MDF
INFO - 09:25:18:    Algorithm: SLSQP
INFO - 09:25:18: Optimization problem:
INFO - 09:25:18:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
INFO - 09:25:18:    With respect to: x_shared, x_1, x_2, x_3
INFO - 09:25:18:    Subject to constraints:
INFO - 09:25:18:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 09:25:18:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 09:25:18:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 09:25:18: Design Space:
INFO - 09:25:18: +----------+-------------+-------+-------------+-------+
INFO - 09:25:18: | name     | lower_bound | value | upper_bound | type  |
INFO - 09:25:18: +----------+-------------+-------+-------------+-------+
INFO - 09:25:18: | x_shared |     0.01    |  0.05 |     0.09    | float |
INFO - 09:25:18: | x_shared |    30000    | 45000 |    60000    | float |
INFO - 09:25:18: | x_shared |     1.4     |  1.6  |     1.8     | float |
INFO - 09:25:18: | x_shared |     2.5     |  5.5  |     8.5     | float |
INFO - 09:25:18: | x_shared |      40     |   55  |      70     | float |
INFO - 09:25:18: | x_shared |     500     |  1000 |     1500    | float |
INFO - 09:25:18: | x_1      |     0.1     |  0.25 |     0.4     | float |
INFO - 09:25:18: | x_1      |     0.75    |   1   |     1.25    | float |
INFO - 09:25:18: | x_2      |     0.75    |   1   |     1.25    | float |
INFO - 09:25:18: | x_3      |     0.1     |  0.5  |      1      | float |
INFO - 09:25:18: +----------+-------------+-------+-------------+-------+
INFO - 09:25:18: Optimization:   0%|          | 0/10 [00:00<?, ?it]
INFO - 09:25:18: Optimization:  20%|██        | 2/10 [00:00<00:00, 67.05 it/sec, obj=536]
INFO - 09:25:19: Optimization:  40%|████      | 4/10 [00:00<00:00, 21.74 it/sec, obj=3.8e+3]
WARNING - 09:25:19: Optimization found no feasible point !  The least infeasible point is selected.
INFO - 09:25:19: Optimization:  40%|████      | 4/10 [00:00<00:00, 16.26 it/sec, obj=3.96e+3]
INFO - 09:25:19: Optimization result:
INFO - 09:25:19: Objective value = 3795.0851933441872
INFO - 09:25:19: The result is not feasible.
INFO - 09:25:19: Status: 8
INFO - 09:25:19: Optimizer message: Positive directional derivative for linesearch
INFO - 09:25:19: Number of calls to the objective function by the optimizer: 5
INFO - 09:25:19: Constraints values w.r.t. 0:
INFO - 09:25:19:    g_1 = [-0.01940553 -0.03430815 -0.04499528 -0.05244303 -0.05783964 -0.13706197
INFO - 09:25:19:  -0.10293803]
INFO - 09:25:19:    g_2 = 0.0003917260521535404
INFO - 09:25:19:    g_3 = [-0.6301543  -0.3698457  -0.14096439 -0.18315803]
INFO - 09:25:19: Design Space:
INFO - 09:25:19: +----------+-------------+---------------------+-------------+-------+
INFO - 09:25:19: | name     | lower_bound |        value        | upper_bound | type  |
INFO - 09:25:19: +----------+-------------+---------------------+-------------+-------+
INFO - 09:25:19: | x_shared |     0.01    | 0.06009793151303839 |     0.09    | float |
INFO - 09:25:19: | x_shared |    30000    |        60000        |    60000    | float |
INFO - 09:25:19: | x_shared |     1.4     |  1.400744940049757  |     1.8     | float |
INFO - 09:25:19: | x_shared |     2.5     |         2.5         |     8.5     | float |
INFO - 09:25:19: | x_shared |      40     |          70         |      70     | float |
INFO - 09:25:19: | x_shared |     500     |         1500        |     1500    | float |
INFO - 09:25:19: | x_1      |     0.1     |  0.3991428961174674 |     0.4     | float |
INFO - 09:25:19: | x_1      |     0.75    |         0.75        |     1.25    | float |
INFO - 09:25:19: | x_2      |     0.75    |         0.75        |     1.25    | float |
INFO - 09:25:19: | x_3      |     0.1     |  0.1343078243802689 |      1      | float |
INFO - 09:25:19: +----------+-------------+---------------------+-------------+-------+
INFO - 09:25:19: *** MDO Scenario run terminated in 0:00:00.631289 ***

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


## Post-process scenario¶

Lastly, we post-process the scenario by means of the Correlations plot which provides scatter plots of correlated variables among design variables, outputs functions and constraints any of the constraint or objective functions w.r.t. optimization iterations or sampling snapshots. This method requires the list of functions names to plot.

scenario.post_process("Correlations", save=False, show=False)
# Workaround for HTML rendering, instead of show=True
plt.show()


Out:

INFO - 09:25:19: Detected 59 correlations > 0.95


Total running time of the script: ( 0 minutes 5.683 seconds)

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