Constraints history

In this example, we illustrate the use of the ConstraintsHistory 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.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 ConstraintsHistory post-processing plots the constraints functions history in line charts with violation indication by color on the background.

This plot is more precise than the constraint plot provided by the opt_history_view but scales less with the number of constraints.

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()
all_constraints = ["g_1", "g_2", "g_3"]
for constraint in all_constraints:
    scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
    INFO - 13:55:50:
    INFO - 13:55:50: *** Start MDOScenario execution ***
    INFO - 13:55:50: MDOScenario
    INFO - 13:55:50:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
    INFO - 13:55:50:    MDO formulation: MDF
    INFO - 13:55:50: Optimization problem:
    INFO - 13:55:50:    minimize -y_4(x_shared, x_1, x_2, x_3)
    INFO - 13:55:50:    with respect to x_1, x_2, x_3, x_shared
    INFO - 13:55:50:    subject to constraints:
    INFO - 13:55:50:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 13:55:50:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 13:55:50:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 13:55:50:    over the design space:
    INFO - 13:55:50:    +-------------+-------------+-------+-------------+-------+
    INFO - 13:55:50:    | name        | lower_bound | value | upper_bound | type  |
    INFO - 13:55:50:    +-------------+-------------+-------+-------------+-------+
    INFO - 13:55:50:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
    INFO - 13:55:50:    | x_shared[1] |    30000    | 45000 |    60000    | float |
    INFO - 13:55:50:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
    INFO - 13:55:50:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
    INFO - 13:55:50:    | x_shared[4] |      40     |   55  |      70     | float |
    INFO - 13:55:50:    | x_shared[5] |     500     |  1000 |     1500    | float |
    INFO - 13:55:50:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
    INFO - 13:55:50:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
    INFO - 13:55:50:    | x_2         |     0.75    |   1   |     1.25    | float |
    INFO - 13:55:50:    | x_3         |     0.1     |  0.5  |      1      | float |
    INFO - 13:55:50:    +-------------+-------------+-------+-------------+-------+
    INFO - 13:55:50: Solving optimization problem with algorithm SLSQP:
    INFO - 13:55:50: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 13:55:50: ...  10%|█         | 1/10 [00:00<00:01,  8.84 it/sec, obj=-536]
    INFO - 13:55:50: ...  20%|██        | 2/10 [00:00<00:01,  6.50 it/sec, obj=-2.12e+3]
 WARNING - 13:55:50: MDAJacobi has reached its maximum number of iterations but the normed residual 1.7130677857005655e-05 is still above the tolerance 1e-06.
    INFO - 13:55:50: ...  30%|███       | 3/10 [00:00<00:01,  5.50 it/sec, obj=-3.75e+3]
    INFO - 13:55:51: ...  40%|████      | 4/10 [00:00<00:01,  5.28 it/sec, obj=-3.96e+3]
    INFO - 13:55:51: ...  50%|█████     | 5/10 [00:01<00:01,  4.95 it/sec, obj=-3.96e+3]
    INFO - 13:55:51: Optimization result:
    INFO - 13:55:51:    Optimizer info:
    INFO - 13:55:51:       Status: 8
    INFO - 13:55:51:       Message: Positive directional derivative for linesearch
    INFO - 13:55:51:       Number of calls to the objective function by the optimizer: 6
    INFO - 13:55:51:    Solution:
    INFO - 13:55:51:       The solution is feasible.
    INFO - 13:55:51:       Objective: -3963.408265187933
    INFO - 13:55:51:       Standardized constraints:
    INFO - 13:55:51:          g_1 = [-0.01806104 -0.03334642 -0.04424946 -0.0518346  -0.05732607 -0.13720865
    INFO - 13:55:51:  -0.10279135]
    INFO - 13:55:51:          g_2 = 3.333278582928756e-06
    INFO - 13:55:51:          g_3 = [-7.67181773e-01 -2.32818227e-01  8.30379541e-07 -1.83255000e-01]
    INFO - 13:55:51:       Design space:
    INFO - 13:55:51:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 13:55:51:       | name        | lower_bound |        value        | upper_bound | type  |
    INFO - 13:55:51:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 13:55:51:       | x_shared[0] |     0.01    | 0.06000083331964572 |     0.09    | float |
    INFO - 13:55:51:       | x_shared[1] |    30000    |        60000        |    60000    | float |
    INFO - 13:55:51:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
    INFO - 13:55:51:       | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
    INFO - 13:55:51:       | x_shared[4] |      40     |          70         |      70     | float |
    INFO - 13:55:51:       | x_shared[5] |     500     |         1500        |     1500    | float |
    INFO - 13:55:51:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
    INFO - 13:55:51:       | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
    INFO - 13:55:51:       | x_2         |     0.75    |         0.75        |     1.25    | float |
    INFO - 13:55:51:       | x_3         |     0.1     |  0.1562448753887276 |      1      | float |
    INFO - 13:55:51:       +-------------+-------------+---------------------+-------------+-------+
    INFO - 13:55:51: *** End MDOScenario execution (time: 0:00:01.163994) ***

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

Post-process scenario

Lastly, we post-process the scenario by means of the ConstraintsHistory plot which plots the history of constraints passed as argument by the user. Each constraint history is represented by a subplot where the value of the constraints is drawn by a line. Moreover, the background color represents a qualitative view of these values: active areas are white, violated ones are red and satisfied ones are green.

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(
    "ConstraintsHistory",
    constraint_names=all_constraints,
    save=False,
    show=True,
)
Evolution of the constraints w.r.t. iterations, g_1[0] (inequality), g_1[1] (inequality), g_1[2] (inequality), g_1[3] (inequality), g_1[4] (inequality), g_1[5] (inequality), g_1[6] (inequality), g_2 (inequality), g_3[0] (inequality), g_3[1] (inequality), g_3[2] (inequality), g_3[3] (inequality)
<gemseo.post.constraints_history.ConstraintsHistory object at 0x7f006e38f0a0>

Total running time of the script: (0 minutes 2.457 seconds)

Gallery generated by Sphinx-Gallery