Note
Click here to download the full example code
Basic history¶
In this example, we illustrate the use of the BasicHistory
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)>
Description¶
The BasicHistory
post-processing
plots any of the constraint or objective functions
w.r.t. the optimization iterations or sampling snapshots.
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().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.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
Out:
INFO - 21:50:57:
INFO - 21:50:57: *** Start MDO Scenario execution ***
INFO - 21:50:57: MDOScenario
INFO - 21:50:57: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 21:50:57: MDOFormulation: MDF
INFO - 21:50:57: Algorithm: SLSQP
INFO - 21:50:57: Optimization problem:
INFO - 21:50:57: Minimize: -y_4(x_shared, x_1, x_2, x_3)
INFO - 21:50:57: With respect to: x_shared, x_1, x_2, x_3
INFO - 21:50:57: Subject to constraints:
INFO - 21:50:57: g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 21:50:57: g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 21:50:57: g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 21:50:57: Design space:
INFO - 21:50:57: +----------+-------------+-------+-------------+-------+
INFO - 21:50:57: | name | lower_bound | value | upper_bound | type |
INFO - 21:50:57: +----------+-------------+-------+-------------+-------+
INFO - 21:50:57: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 21:50:57: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 21:50:57: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 21:50:57: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 21:50:57: | x_shared | 40 | 55 | 70 | float |
INFO - 21:50:57: | x_shared | 500 | 1000 | 1500 | float |
INFO - 21:50:57: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 21:50:57: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 21:50:57: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 21:50:57: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 21:50:57: +----------+-------------+-------+-------------+-------+
INFO - 21:50:57: Optimization: 0%| | 0/10 [00:00<?, ?it]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.2.0/lib/python3.8/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:407: SparseEfficiencyWarning: splu requires CSC matrix format
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
INFO - 21:50:57: Optimization: 20%|██ | 2/10 [00:00<00:00, 53.47 it/sec, obj=2.12e+3]
INFO - 21:50:57: Optimization: 40%|████ | 4/10 [00:00<00:00, 21.47 it/sec, obj=3.97e+3]
INFO - 21:50:57: Optimization: 50%|█████ | 5/10 [00:00<00:00, 16.75 it/sec, obj=3.96e+3]
INFO - 21:50:58: Optimization: 60%|██████ | 6/10 [00:00<00:00, 13.71 it/sec, obj=3.96e+3]
INFO - 21:50:58: Optimization: 70%|███████ | 7/10 [00:00<00:00, 11.61 it/sec, obj=3.96e+3]
INFO - 21:50:58: Optimization: 90%|█████████ | 9/10 [00:01<00:00, 9.91 it/sec, obj=3.96e+3]
INFO - 21:50:58: Optimization: 100%|██████████| 10/10 [00:01<00:00, 9.23 it/sec, obj=3.96e+3]
INFO - 21:50:58: Optimization result:
INFO - 21:50:58: Objective value = 3963.595455433326
INFO - 21:50:58: The result is feasible.
INFO - 21:50:58: Status: None
INFO - 21:50:58: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 21:50:58: Number of calls to the objective function by the optimizer: 12
INFO - 21:50:58: Constraints values:
INFO - 21:50:58: g_1 = [-0.01814919 -0.03340982 -0.04429875 -0.05187486 -0.05736009 -0.13720854
INFO - 21:50:58: -0.10279146]
INFO - 21:50:58: g_2 = 3.236261671801799e-05
INFO - 21:50:58: g_3 = [-7.67067574e-01 -2.32932426e-01 -9.19662628e-05 -1.83255000e-01]
INFO - 21:50:58: Design space:
INFO - 21:50:58: +----------+-------------+--------------------+-------------+-------+
INFO - 21:50:58: | name | lower_bound | value | upper_bound | type |
INFO - 21:50:58: +----------+-------------+--------------------+-------------+-------+
INFO - 21:50:58: | x_shared | 0.01 | 0.0600080906541795 | 0.09 | float |
INFO - 21:50:58: | x_shared | 30000 | 60000 | 60000 | float |
INFO - 21:50:58: | x_shared | 1.4 | 1.4 | 1.8 | float |
INFO - 21:50:58: | x_shared | 2.5 | 2.5 | 8.5 | float |
INFO - 21:50:58: | x_shared | 40 | 70 | 70 | float |
INFO - 21:50:58: | x_shared | 500 | 1500 | 1500 | float |
INFO - 21:50:58: | x_1 | 0.1 | 0.3999993439500847 | 0.4 | float |
INFO - 21:50:58: | x_1 | 0.75 | 0.75 | 1.25 | float |
INFO - 21:50:58: | x_2 | 0.75 | 0.75 | 1.25 | float |
INFO - 21:50:58: | x_3 | 0.1 | 0.156230376400943 | 1 | float |
INFO - 21:50:58: +----------+-------------+--------------------+-------------+-------+
INFO - 21:50:58: *** MDO Scenario run terminated in 0:00:01.093580 ***
{'algo': 'SLSQP', 'max_iter': 10}
Post-process scenario¶
Lastly, we post-process the scenario by means of the BasicHistory
plot which plots any of the constraint or objective functions
w.r.t. optimization iterations or sampling snapshots.
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:
Options for Post-processing algorithms.
scenario.post_process(
"BasicHistory", data_list=["g_1", "g_2", "g_3"], save=False, show=False
)
Out:
<gemseo.post.basic_history.BasicHistory object at 0x7f618fe3f4c0>
Warning
In the Database
, when the aim of the
optimization problem is to maximize the objective function,
the objective function name is preceded by a “-” and the stored values are
the opposite of the objective function.
scenario.post_process("BasicHistory", data_list=["-y_4"], save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Total running time of the script: ( 0 minutes 1.601 seconds)