Radar chart

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

from __future__ import annotations

from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace

Import

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

configure_logger()

<RootLogger root (INFO)>

Description

The RadarChart post-processing plots on a radar style chart a list of constraint functions at a given iteration.

By default, the last iteration is used. This plot scales better with the number of constraints than the constraint plot provided by the opt_history_view.

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 create the SobieskiDesignSpace.

design_space = SobieskiDesignSpace()

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,
    "y_4",
    design_space,
    formulation_name="MDF",
    maximize_objective=True,
)
scenario.set_differentiation_method()
for constraint in ["g_1", "g_2", "g_3"]:
    scenario.add_constraint(constraint, constraint_type="ineq")
scenario.execute(algo_name="SLSQP", max_iter=10)

WARNING - 08:38:50: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
WARNING - 08:38:50: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
   INFO - 08:38:50:
   INFO - 08:38:50: *** Start MDOScenario execution ***
   INFO - 08:38:50: MDOScenario
   INFO - 08:38:50:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
   INFO - 08:38:50:    MDO formulation: MDF
   INFO - 08:38:50: Optimization problem:
   INFO - 08:38:50:    minimize -y_4(x_shared, x_1, x_2, x_3)
   INFO - 08:38:50:    with respect to x_1, x_2, x_3, x_shared
   INFO - 08:38:50:    subject to constraints:
   INFO - 08:38:50:       g_1(x_shared, x_1, x_2, x_3) <= 0
   INFO - 08:38:50:       g_2(x_shared, x_1, x_2, x_3) <= 0
   INFO - 08:38:50:       g_3(x_shared, x_1, x_2, x_3) <= 0
   INFO - 08:38:50:    over the design space:
   INFO - 08:38:50:       +-------------+-------------+-------+-------------+-------+
   INFO - 08:38:50:       | Name        | Lower bound | Value | Upper bound | Type  |
   INFO - 08:38:50:       +-------------+-------------+-------+-------------+-------+
   INFO - 08:38:50:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
   INFO - 08:38:50:       | x_shared[1] |    30000    | 45000 |    60000    | float |
   INFO - 08:38:50:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
   INFO - 08:38:50:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
   INFO - 08:38:50:       | x_shared[4] |      40     |   55  |      70     | float |
   INFO - 08:38:50:       | x_shared[5] |     500     |  1000 |     1500    | float |
   INFO - 08:38:50:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
   INFO - 08:38:50:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
   INFO - 08:38:50:       | x_2         |     0.75    |   1   |     1.25    | float |
   INFO - 08:38:50:       | x_3         |     0.1     |  0.5  |      1      | float |
   INFO - 08:38:50:       +-------------+-------------+-------+-------------+-------+
   INFO - 08:38:50: Solving optimization problem with algorithm SLSQP:
   INFO - 08:38:50:     10%|█         | 1/10 [00:00<00:00, 18.98 it/sec, obj=-536]
   INFO - 08:38:51:     20%|██        | 2/10 [00:00<00:00, 14.07 it/sec, obj=-2.12e+3]
WARNING - 08:38:51: MDAJacobi has reached its maximum number of iterations but the normed residual 5.741449586530469e-06 is still above the tolerance 1e-06.
   INFO - 08:38:51:     30%|███       | 3/10 [00:00<00:00, 11.41 it/sec, obj=-3.46e+3]
   INFO - 08:38:51:     40%|████      | 4/10 [00:00<00:00, 10.91 it/sec, obj=-3.96e+3]
   INFO - 08:38:51:     50%|█████     | 5/10 [00:00<00:00, 11.14 it/sec, obj=-4.61e+3]
   INFO - 08:38:51:     60%|██████    | 6/10 [00:00<00:00, 11.88 it/sec, obj=-4.5e+3]
   INFO - 08:38:51:     70%|███████   | 7/10 [00:00<00:00, 12.29 it/sec, obj=-4.26e+3]
   INFO - 08:38:51:     80%|████████  | 8/10 [00:00<00:00, 12.62 it/sec, obj=-4.11e+3]
   INFO - 08:38:51:     90%|█████████ | 9/10 [00:00<00:00, 12.89 it/sec, obj=-4.02e+3]
   INFO - 08:38:51:    100%|██████████| 10/10 [00:00<00:00, 13.12 it/sec, obj=-3.99e+3]
   INFO - 08:38:51: Optimization result:
   INFO - 08:38:51:    Optimizer info:
   INFO - 08:38:51:       Status: None
   INFO - 08:38:51:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
   INFO - 08:38:51:       Number of calls to the objective function by the optimizer: 12
   INFO - 08:38:51:    Solution:
   INFO - 08:38:51:       The solution is feasible.
   INFO - 08:38:51:       Objective: -3463.120411437138
   INFO - 08:38:51:       Standardized constraints:
   INFO - 08:38:51:          g_1 = [-0.01112145 -0.02847064 -0.04049911 -0.04878943 -0.05476349 -0.14014207
   INFO - 08:38:51:  -0.09985793]
   INFO - 08:38:51:          g_2 = -0.0020925663903177405
   INFO - 08:38:51:          g_3 = [-0.71359843 -0.28640157 -0.05926796 -0.183255  ]
   INFO - 08:38:51:       Design space:
   INFO - 08:38:51:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 08:38:51:          | Name        | Lower bound |        Value        | Upper bound | Type  |
   INFO - 08:38:51:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 08:38:51:          | x_shared[0] |     0.01    | 0.05947685840242058 |     0.09    | float |
   INFO - 08:38:51:          | x_shared[1] |    30000    |   59246.692998739   |    60000    | float |
   INFO - 08:38:51:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
   INFO - 08:38:51:          | x_shared[3] |     2.5     |   2.64097355362077  |     8.5     | float |
   INFO - 08:38:51:          | x_shared[4] |      40     |  69.32144380869019  |      70     | float |
   INFO - 08:38:51:          | x_shared[5] |     500     |  1478.031626737187  |     1500    | float |
   INFO - 08:38:51:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
   INFO - 08:38:51:          | x_1[1]      |     0.75    |  0.7608797907508461 |     1.25    | float |
   INFO - 08:38:51:          | x_2         |     0.75    |  0.7607584987262048 |     1.25    | float |
   INFO - 08:38:51:          | x_3         |     0.1     |  0.1514057659459843 |      1      | float |
   INFO - 08:38:51:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 08:38:51: *** End MDOScenario execution (time: 0:00:00.771547) ***

Post-process scenario

Lastly, we post-process the scenario by means of the RadarChart.

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(
    post_name="RadarChart",
    constraint_names=["g_1", "g_2", "g_3"],
    save=False,
    show=True,
    fig_size=(5, 5),
)

/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.0.0/lib/python3.9/site-packages/gemseo/post/dataset/plots/_matplotlib/plot.py:87: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  figure.tight_layout()

<gemseo.post.radar_chart.RadarChart object at 0x7f6dc104b6a0>