Note
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IDF-based MDO on the Sobieski SSBJ test case¶
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
from matplotlib import pyplot as plt
configure_logger()
Out:
<RootLogger root (INFO)>
Instantiate the disciplines¶
First, we instantiate the four disciplines of the use case:
SobieskiPropulsion,
SobieskiAerodynamics,
SobieskiMission
and SobieskiStructure.
disciplines = create_discipline(
[
"SobieskiPropulsion",
"SobieskiAerodynamics",
"SobieskiMission",
"SobieskiStructure",
]
)
Build, execute and post-process the scenario¶
Then, we build the scenario which links the disciplines
with the formulation and the optimization algorithm. Here, we use the
IDF formulation. We tell the scenario to minimize -y_4 instead of
minimizing y_4 (range), which is the default option.
Instantiate the scenario¶
design_space = SobieskiProblem().design_space
scenario = create_scenario(
disciplines,
"IDF",
objective_name="y_4",
design_space=design_space,
maximize_objective=True,
)
Set the design constraints¶
for c_name in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(c_name, "ineq")
Define the algorithm inputs¶
We set the maximum number of iterations, the optimizer and the optimizer options
algo_options = {
"ftol_rel": 1e-10,
"ineq_tolerance": 1e-3,
"eq_tolerance": 1e-3,
"normalize_design_space": True,
}
scn_inputs = {"max_iter": 20, "algo": "SLSQP", "algo_options": algo_options}
Execute the scenario¶
scenario.execute(scn_inputs)
Out:
INFO - 10:05:40:
INFO - 10:05:40: *** Start MDOScenario execution ***
INFO - 10:05:40: MDOScenario
INFO - 10:05:40: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
INFO - 10:05:40: MDO formulation: IDF
INFO - 10:05:40: Optimization problem:
INFO - 10:05:40: minimize -y_4(x_shared, y_14, y_24, y_34)
INFO - 10:05:40: with respect to x_1, x_2, x_3, x_shared, y_12, y_14, y_21, y_23, y_24, y_31, y_32, y_34
INFO - 10:05:40: subject to constraints:
INFO - 10:05:40: g_1(x_shared, x_1, y_31, y_21) <= 0.0
INFO - 10:05:40: g_2(x_shared, x_2, y_32, y_12) <= 0.0
INFO - 10:05:40: g_3(x_shared, x_3, y_23) <= 0.0
INFO - 10:05:40: y_31_y_32_y_34: y_31#y_32#y_34(x_shared, x_3, y_23): y_31(x_shared, x_3, y_23) - y_31 == 0.0
INFO - 10:05:40: y_32(x_shared, x_3, y_23) - y_32 == 0.0
INFO - 10:05:40: y_34(x_shared, x_3, y_23) - y_34 == 0.0
INFO - 10:05:40: y_21_y_23_y_24: y_21#y_23#y_24(x_shared, x_2, y_32, y_12): y_21(x_shared, x_2, y_32, y_12) - y_21 == 0.0
INFO - 10:05:40: y_23(x_shared, x_2, y_32, y_12) - y_23 == 0.0
INFO - 10:05:40: y_24(x_shared, x_2, y_32, y_12) - y_24 == 0.0
INFO - 10:05:40: y_12_y_14: y_12#y_14(x_shared, x_1, y_31, y_21): y_12(x_shared, x_1, y_31, y_21) - y_12 == 0.0
INFO - 10:05:40: y_14(x_shared, x_1, y_31, y_21) - y_14 == 0.0
INFO - 10:05:40: over the design space:
INFO - 10:05:40: +----------+-------------+--------------------+-------------+-------+
INFO - 10:05:40: | name | lower_bound | value | upper_bound | type |
INFO - 10:05:40: +----------+-------------+--------------------+-------------+-------+
INFO - 10:05:40: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 10:05:40: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 10:05:40: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 10:05:40: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 10:05:40: | x_shared | 40 | 55 | 70 | float |
INFO - 10:05:40: | x_shared | 500 | 1000 | 1500 | float |
INFO - 10:05:40: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 10:05:40: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 10:05:40: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 10:05:40: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 10:05:40: | y_14 | 24850 | 50606.9741711 | 77100 | float |
INFO - 10:05:40: | y_14 | -7700 | 7306.20262124 | 45000 | float |
INFO - 10:05:40: | y_32 | 0.235 | 0.5027962499999999 | 0.795 | float |
INFO - 10:05:40: | y_31 | 2960 | 6354.32430691 | 10185 | float |
INFO - 10:05:40: | y_24 | 0.44 | 4.15006276 | 11.13 | float |
INFO - 10:05:40: | y_34 | 0.44 | 1.10754577 | 1.98 | float |
INFO - 10:05:40: | y_23 | 3365 | 12194.2671934 | 26400 | float |
INFO - 10:05:40: | y_21 | 24850 | 50606.9741711 | 77250 | float |
INFO - 10:05:40: | y_12 | 24850 | 50606.9742 | 77250 | float |
INFO - 10:05:40: | y_12 | 0.45 | 0.95 | 1.5 | float |
INFO - 10:05:40: +----------+-------------+--------------------+-------------+-------+
INFO - 10:05:40: Solving optimization problem with algorithm SLSQP:
INFO - 10:05:40: ... 0%| | 0/20 [00:00<?, ?it]
INFO - 10:05:40: ... 40%|████ | 8/20 [00:00<00:00, 191.28 it/sec, obj=-3.96e+3]
INFO - 10:05:40: ... 100%|██████████| 20/20 [00:00<00:00, 104.47 it/sec, obj=-3.96e+3]
INFO - 10:05:40: Optimization result:
INFO - 10:05:40: Optimizer info:
INFO - 10:05:40: Status: None
INFO - 10:05:40: Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 10:05:40: Number of calls to the objective function by the optimizer: 22
INFO - 10:05:40: Solution:
INFO - 10:05:40: The solution is feasible.
INFO - 10:05:40: Objective: -3966.790848506069
INFO - 10:05:40: Standardized constraints:
INFO - 10:05:40: g_1 = [-0.01812782 -0.03339445 -0.0442868 -0.0518651 -0.05735184 -0.13720865
INFO - 10:05:40: -0.10279135]
INFO - 10:05:40: g_2 = 2.535682693616259e-05
INFO - 10:05:40: g_3 = [-7.67489138e-01 -2.32510862e-01 9.20908972e-05 -1.83255000e-01]
INFO - 10:05:40: y_12_y_14 = [ 3.34629122e-05 -1.85828412e-05 3.35589780e-05 -5.48378413e-05]
INFO - 10:05:40: y_21_y_23_y_24 = [ 0.00000000e+00 9.05477756e-05 -2.83060860e-04]
INFO - 10:05:40: y_31_y_32_y_34 = [6.90641576e-08 6.03563891e-08 1.07078689e-04]
INFO - 10:05:40: Design space:
INFO - 10:05:40: +----------+-------------+---------------------+-------------+-------+
INFO - 10:05:40: | name | lower_bound | value | upper_bound | type |
INFO - 10:05:40: +----------+-------------+---------------------+-------------+-------+
INFO - 10:05:40: | x_shared | 0.01 | 0.06000633920673407 | 0.09 | float |
INFO - 10:05:40: | x_shared | 30000 | 60000 | 60000 | float |
INFO - 10:05:40: | x_shared | 1.4 | 1.4 | 1.8 | float |
INFO - 10:05:40: | x_shared | 2.5 | 2.5 | 8.5 | float |
INFO - 10:05:40: | x_shared | 40 | 70 | 70 | float |
INFO - 10:05:40: | x_shared | 500 | 1500 | 1500 | float |
INFO - 10:05:40: | x_1 | 0.1 | 0.4 | 0.4 | float |
INFO - 10:05:40: | x_1 | 0.75 | 0.75 | 1.25 | float |
INFO - 10:05:40: | x_2 | 0.75 | 0.75 | 1.25 | float |
INFO - 10:05:40: | x_3 | 0.1 | 0.156259134365097 | 1 | float |
INFO - 10:05:40: | y_14 | 24850 | 44746.56244377587 | 77100 | float |
INFO - 10:05:40: | y_14 | -7700 | 19355.27544458607 | 45000 | float |
INFO - 10:05:40: | y_32 | 0.235 | 0.7325108278699097 | 0.795 | float |
INFO - 10:05:40: | y_31 | 2960 | 9433.274956925387 | 10185 | float |
INFO - 10:05:40: | y_24 | 0.44 | 8.059470045805423 | 11.13 | float |
INFO - 10:05:40: | y_34 | 0.44 | 0.9237614560895575 | 1.98 | float |
INFO - 10:05:40: | y_23 | 3365 | 5552.047264915329 | 26400 | float |
INFO - 10:05:40: | y_21 | 24850 | 44746.56244377587 | 77250 | float |
INFO - 10:05:40: | y_12 | 24850 | 44746.56244377587 | 77250 | float |
INFO - 10:05:40: | y_12 | 0.45 | 0.9028108618065331 | 1.5 | float |
INFO - 10:05:40: +----------+-------------+---------------------+-------------+-------+
INFO - 10:05:40: *** End MDOScenario execution (time: 0:00:00.211049) ***
{'max_iter': 20, 'algo': 'SLSQP', 'algo_options': {'ftol_rel': 1e-10, 'ineq_tolerance': 0.001, 'eq_tolerance': 0.001, 'normalize_design_space': True}}
Save the optimization history¶
We can save the whole optimization problem and its history for further post processing:
scenario.save_optimization_history("idf_history.h5", file_format="hdf5")
Out:
INFO - 10:05:40: Export optimization problem to file: idf_history.h5
We can also save only calls to functions and design variables history:
scenario.save_optimization_history("idf_history.xml", file_format="ggobi")
Out:
INFO - 10:05:40: Export to ggobi for functions: ['-y_4', 'Iter', 'g_1', 'g_2', 'g_3', 'y_12_y_14', 'y_21_y_23_y_24', 'y_31_y_32_y_34']
INFO - 10:05:40: Export to ggobi file: idf_history.xml
Print optimization metrics¶
scenario.print_execution_metrics()
Out:
INFO - 10:05:40: Scenario Execution Statistics
INFO - 10:05:40: Discipline: SobieskiPropulsion
INFO - 10:05:40: Executions number: 20
INFO - 10:05:40: Execution time: 0.006103995990997646 s
INFO - 10:05:40: Linearizations number: 7
INFO - 10:05:40: Discipline: SobieskiAerodynamics
INFO - 10:05:40: Executions number: 20
INFO - 10:05:40: Execution time: 0.009110703998885583 s
INFO - 10:05:40: Linearizations number: 7
INFO - 10:05:40: Discipline: SobieskiMission
INFO - 10:05:40: Executions number: 20
INFO - 10:05:40: Execution time: 0.000919604986847844 s
INFO - 10:05:40: Linearizations number: 7
INFO - 10:05:40: Discipline: SobieskiStructure
INFO - 10:05:40: Executions number: 20
INFO - 10:05:40: Execution time: 0.03358767099416582 s
INFO - 10:05:40: Linearizations number: 7
INFO - 10:05:40: Total number of executions calls: 80
INFO - 10:05:40: Total number of linearizations: 28
Plot the optimization history view¶
scenario.post_process("OptHistoryView", save=False, show=False)
Out:
<gemseo.post.opt_history_view.OptHistoryView object at 0x7fdbe16cc760>
Plot the quadratic approximation of the objective¶
scenario.post_process("QuadApprox", function="-y_4", save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Total running time of the script: ( 0 minutes 3.112 seconds)