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

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 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()
for constraint in ["g_1", "g_2", "g_3"]:
    scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
    INFO - 20:57:37:
    INFO - 20:57:37: *** Start MDOScenario execution ***
    INFO - 20:57:37: MDOScenario
    INFO - 20:57:37:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
    INFO - 20:57:37:    MDO formulation: MDF
    INFO - 20:57:37: Optimization problem:
    INFO - 20:57:37:    minimize -y_4(x_shared, x_1, x_2, x_3)
    INFO - 20:57:37:    with respect to x_1, x_2, x_3, x_shared
    INFO - 20:57:37:    subject to constraints:
    INFO - 20:57:37:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 20:57:37:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 20:57:37:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 20:57:37:    over the design space:
    INFO - 20:57:37:    +-------------+-------------+-------+-------------+-------+
    INFO - 20:57:37:    | name        | lower_bound | value | upper_bound | type  |
    INFO - 20:57:37:    +-------------+-------------+-------+-------------+-------+
    INFO - 20:57:37:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
    INFO - 20:57:37:    | x_shared[1] |    30000    | 45000 |    60000    | float |
    INFO - 20:57:37:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
    INFO - 20:57:37:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
    INFO - 20:57:37:    | x_shared[4] |      40     |   55  |      70     | float |
    INFO - 20:57:37:    | x_shared[5] |     500     |  1000 |     1500    | float |
    INFO - 20:57:37:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
    INFO - 20:57:37:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
    INFO - 20:57:37:    | x_2         |     0.75    |   1   |     1.25    | float |
    INFO - 20:57:37:    | x_3         |     0.1     |  0.5  |      1      | float |
    INFO - 20:57:37:    +-------------+-------------+-------+-------------+-------+
    INFO - 20:57:37: Solving optimization problem with algorithm SLSQP:
    INFO - 20:57:37: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 20:57:37: ...  10%|█         | 1/10 [00:00<00:00, 99.45 it/sec, obj=-536]
    INFO - 20:57:37: ...  20%|██        | 2/10 [00:00<00:00, 39.33 it/sec, obj=-2.12e+3]
 WARNING - 20:57:37: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
    INFO - 20:57:37: ...  30%|███       | 3/10 [00:00<00:00, 22.68 it/sec, obj=-3.75e+3]
    INFO - 20:57:37: ...  40%|████      | 4/10 [00:00<00:00, 16.62 it/sec, obj=-4.01e+3]
 WARNING - 20:57:37: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
    INFO - 20:57:37: ...  50%|█████     | 5/10 [00:00<00:00, 12.64 it/sec, obj=-4.49e+3]
    INFO - 20:57:37: ...  60%|██████    | 6/10 [00:00<00:00, 10.72 it/sec, obj=-3.4e+3]
    INFO - 20:57:38: ...  80%|████████  | 8/10 [00:01<00:00,  9.16 it/sec, obj=-4.76e+3]
    INFO - 20:57:38: ... 100%|██████████| 10/10 [00:01<00:00,  8.00 it/sec, obj=-4.56e+3]
    INFO - 20:57:38: ... 100%|██████████| 10/10 [00:01<00:00,  7.97 it/sec, obj=-4.56e+3]
    INFO - 20:57:38: Optimization result:
    INFO - 20:57:38:    Optimizer info:
    INFO - 20:57:38:       Status: None
    INFO - 20:57:38:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 20:57:38:       Number of calls to the objective function by the optimizer: 12
    INFO - 20:57:38:    Solution:
    INFO - 20:57:38:       The solution is feasible.
    INFO - 20:57:38:       Objective: -3749.8868975554387
    INFO - 20:57:38:       Standardized constraints:
    INFO - 20:57:38:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
    INFO - 20:57:38:  -0.10219342]
    INFO - 20:57:38:          g_2 = -0.0004062839430756249
    INFO - 20:57:38:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
    INFO - 20:57:38:       Design space:
    INFO - 20:57:38:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 20:57:38:       | name        | lower_bound |        value        | upper_bound | type  |
    INFO - 20:57:38:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 20:57:38:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
    INFO - 20:57:38:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
    INFO - 20:57:38:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
    INFO - 20:57:38:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
    INFO - 20:57:38:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
    INFO - 20:57:38:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
    INFO - 20:57:38:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
    INFO - 20:57:38:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
    INFO - 20:57:38:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
    INFO - 20:57:38:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
    INFO - 20:57:38:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 20:57:38: *** End MDOScenario execution (time: 0:00:01.271071) ***

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

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(
    "RadarChart",
    constraint_names=["g_1", "g_2", "g_3"],
    save=False,
    show=True,
    fig_size=(5, 5),
)
Constraints at iteration 2 (optimum)
<gemseo.post.radar_chart.RadarChart object at 0x7f317bf01f70>

Total running time of the script: ( 0 minutes 1.538 seconds)

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