Note
Click here to download the full example code
BiLevel-based MDO on the Sobieski SSBJ test case¶
from __future__ import division, unicode_literals
from copy import deepcopy
from future import standard_library
from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
standard_library.install_aliases()
configure_logger()
Out:
<RootLogger root (INFO)>
Instantiate the disciplines¶
First, we instantiate the four disciplines of the use case:
SobieskiPropulsion
,
SobieskiAerodynamics
,
SobieskiMission
and SobieskiStructure
.
propu, aero, mission, struct = 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
BiLevel
formulation. We tell the scenario to minimize -y_4
instead of minimizing y_4 (range), which is the default option.
We need to define the design space.
design_space = SobieskiProblem().read_design_space()
Then, we build a sub-scenario for each strongly coupled disciplines, using the following algorithm, maximum number of iterations and algorithm options:
algo_options = {
"xtol_rel": 1e-7,
"xtol_abs": 1e-7,
"ftol_rel": 1e-7,
"ftol_abs": 1e-7,
"ineq_tolerance": 1e-4,
}
sub_sc_opts = {"max_iter": 30, "algo": "SLSQP", "algo_options": algo_options}
Build a sub-scenario for Propulsion¶
This sub-scenario will minimize SFC.
sc_prop = create_scenario(
propu,
"DisciplinaryOpt",
"y_34",
design_space=deepcopy(design_space).filter("x_3"),
name="PropulsionScenario",
)
sc_prop.default_inputs = sub_sc_opts
sc_prop.add_constraint("g_3", constraint_type="ineq")
Build a sub-scenario for Aerodynamics¶
This sub-scenario will minimize L/D.
sc_aero = create_scenario(
aero,
"DisciplinaryOpt",
"y_24",
deepcopy(design_space).filter("x_2"),
name="AerodynamicsScenario",
maximize_objective=True,
)
sc_aero.default_inputs = sub_sc_opts
sc_aero.add_constraint("g_2", constraint_type="ineq")
Build a sub-scenario for Structure¶
This sub-scenario will maximize log(aircraft total weight / (aircraft total weight - fuel weight)).
sc_str = create_scenario(
struct,
"DisciplinaryOpt",
"y_11",
deepcopy(design_space).filter("x_1"),
name="StructureScenario",
maximize_objective=True,
)
sc_str.add_constraint("g_1", constraint_type="ineq")
sc_str.default_inputs = sub_sc_opts
Build a scenario for Mission¶
This scenario is based on the three previous sub-scenarios and on the Mission and aims to maximize the range (Breguet).
sub_disciplines = [sc_prop, sc_aero, sc_str] + [mission]
design_space = deepcopy(design_space).filter("x_shared")
system_scenario = create_scenario(
sub_disciplines,
"BiLevel",
"y_4",
design_space,
apply_cstr_tosub_scenarios=False,
parallel_scenarios=False,
multithread_scenarios=True,
tolerance=1e-14,
max_mda_iter=30,
maximize_objective=True,
)
system_scenario.add_constraint(["g_1", "g_2", "g_3"], "ineq")
# system_scenario.xdsmize(open_browser=True)
system_scenario.execute(
{"max_iter": 50, "algo": "NLOPT_COBYLA", "algo_options": algo_options}
)
Out:
{'max_iter': 50, 'algo': 'NLOPT_COBYLA', 'algo_options': {'xtol_rel': 1e-07, 'xtol_abs': 1e-07, 'ftol_rel': 1e-07, 'ftol_abs': 1e-07, 'ineq_tolerance': 0.0001}}
Plot the history of the MDA residuals¶
For the first MDA:
system_scenario.formulation.mda1.plot_residual_history(show=True, save=False)
# For the second MDA:
system_scenario.formulation.mda2.plot_residual_history(show=True, save=False)
Plot the optimization history view¶
system_scenario.post_process("OptHistoryView", show=True, save=False)
for disc in [propu, aero, mission, struct]:
print("{}: {} calls.".format(disc.name, disc.n_calls))
Out:
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.0.3/lib/python3.8/site-packages/gemseo/post/opt_history_view.py:312: UserWarning: FixedFormatter should only be used together with FixedLocator
ax1.set_yticklabels(y_labels)
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.0.3/lib/python3.8/site-packages/gemseo/post/opt_history_view.py:626: MatplotlibDeprecationWarning: default base will change from np.e to 10 in 3.4. To suppress this warning specify the base keyword argument.
norm=SymLogNorm(linthresh=1.0, vmin=-vmax, vmax=vmax),
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.0.3/lib/python3.8/site-packages/gemseo/post/opt_history_view.py:619: MatplotlibDeprecationWarning: Passing parameters norm and vmin/vmax simultaneously is deprecated since 3.3 and will become an error two minor releases later. Please pass vmin/vmax directly to the norm when creating it.
im1 = ax1.imshow(
SobieskiPropulsion: 1274 calls.
SobieskiAerodynamics: 1514 calls.
SobieskiMission: 50 calls.
SobieskiStructure: 1577 calls.
Total running time of the script: ( 0 minutes 12.313 seconds)