# Constraints history¶

In this example, we illustrate the use of the ConstraintsHistory 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")
all_constraints = ["g_1", "g_2", "g_3"]
for constraint in all_constraints:
scenario.execute({"algo": "SLSQP", "max_iter": 10})


Out:

    INFO - 09:25:16:
INFO - 09:25:16: *** Start MDO Scenario execution ***
INFO - 09:25:16: MDOScenario
INFO - 09:25:16:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 09:25:16:    MDOFormulation: MDF
INFO - 09:25:16:    Algorithm: SLSQP
INFO - 09:25:16: Optimization problem:
INFO - 09:25:16:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
INFO - 09:25:16:    With respect to: x_shared, x_1, x_2, x_3
INFO - 09:25:16:    Subject to constraints:
INFO - 09:25:16:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 09:25:16:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 09:25:16:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 09:25:16: Design Space:
INFO - 09:25:16: +----------+-------------+-------+-------------+-------+
INFO - 09:25:16: | name     | lower_bound | value | upper_bound | type  |
INFO - 09:25:16: +----------+-------------+-------+-------------+-------+
INFO - 09:25:16: | x_shared |     0.01    |  0.05 |     0.09    | float |
INFO - 09:25:16: | x_shared |    30000    | 45000 |    60000    | float |
INFO - 09:25:16: | x_shared |     1.4     |  1.6  |     1.8     | float |
INFO - 09:25:16: | x_shared |     2.5     |  5.5  |     8.5     | float |
INFO - 09:25:16: | x_shared |      40     |   55  |      70     | float |
INFO - 09:25:16: | x_shared |     500     |  1000 |     1500    | float |
INFO - 09:25:16: | x_1      |     0.1     |  0.25 |     0.4     | float |
INFO - 09:25:16: | x_1      |     0.75    |   1   |     1.25    | float |
INFO - 09:25:16: | x_2      |     0.75    |   1   |     1.25    | float |
INFO - 09:25:16: | x_3      |     0.1     |  0.5  |      1      | float |
INFO - 09:25:16: +----------+-------------+-------+-------------+-------+
INFO - 09:25:16: Optimization:   0%|          | 0/10 [00:00<?, ?it]
INFO - 09:25:16: Optimization:  20%|██        | 2/10 [00:00<00:00, 67.45 it/sec, obj=536]
INFO - 09:25:17: Optimization:  40%|████      | 4/10 [00:00<00:00, 21.03 it/sec, obj=3.8e+3]
WARNING - 09:25:17: Optimization found no feasible point !  The least infeasible point is selected.
INFO - 09:25:17: Optimization:  40%|████      | 4/10 [00:00<00:00, 15.87 it/sec, obj=3.96e+3]
INFO - 09:25:17: Optimization result:
INFO - 09:25:17: Objective value = 3795.0851933441872
INFO - 09:25:17: The result is not feasible.
INFO - 09:25:17: Status: 8
INFO - 09:25:17: Optimizer message: Positive directional derivative for linesearch
INFO - 09:25:17: Number of calls to the objective function by the optimizer: 5
INFO - 09:25:17: Constraints values w.r.t. 0:
INFO - 09:25:17:    g_1 = [-0.01940553 -0.03430815 -0.04499528 -0.05244303 -0.05783964 -0.13706197
INFO - 09:25:17:  -0.10293803]
INFO - 09:25:17:    g_2 = 0.0003917260521535404
INFO - 09:25:17:    g_3 = [-0.6301543  -0.3698457  -0.14096439 -0.18315803]
INFO - 09:25:17: Design Space:
INFO - 09:25:17: +----------+-------------+---------------------+-------------+-------+
INFO - 09:25:17: | name     | lower_bound |        value        | upper_bound | type  |
INFO - 09:25:17: +----------+-------------+---------------------+-------------+-------+
INFO - 09:25:17: | x_shared |     0.01    | 0.06009793151303839 |     0.09    | float |
INFO - 09:25:17: | x_shared |    30000    |        60000        |    60000    | float |
INFO - 09:25:17: | x_shared |     1.4     |  1.400744940049757  |     1.8     | float |
INFO - 09:25:17: | x_shared |     2.5     |         2.5         |     8.5     | float |
INFO - 09:25:17: | x_shared |      40     |          70         |      70     | float |
INFO - 09:25:17: | x_shared |     500     |         1500        |     1500    | float |
INFO - 09:25:17: | x_1      |     0.1     |  0.3991428961174674 |     0.4     | float |
INFO - 09:25:17: | x_1      |     0.75    |         0.75        |     1.25    | float |
INFO - 09:25:17: | x_2      |     0.75    |         0.75        |     1.25    | float |
INFO - 09:25:17: | x_3      |     0.1     |  0.1343078243802689 |      1      | float |
INFO - 09:25:17: +----------+-------------+---------------------+-------------+-------+
INFO - 09:25:17: *** MDO Scenario run terminated in 0:00:00.646541 ***

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


## 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.

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


Total running time of the script: ( 0 minutes 1.079 seconds)

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