Note
Click here to download the full example code
MDF-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
MDF
formulation. We tell the scenario to minimize -y_4 instead of
minimizing y_4 (range), which is the default option.
Instantiate the scenario¶
During the instantiation of the scenario, we provide some options for the MDF formulations:
formulation_options = {
"tolerance": 1e-10,
"max_mda_iter": 50,
"warm_start": True,
"use_lu_fact": True,
"linear_solver_tolerance": 1e-15,
}
'warm_start
: warm starts MDA,'warm_start
: optimize the adjoints resolution by storing the Jacobian matrix LU factorization for the multiple RHS (objective + constraints). This saves CPU time if you can pay for the memory and have the full Jacobians available, not just matrix vector products.'linear_solver_tolerance'
: set the linear solver tolerance, idem we need full convergence
design_space = SobieskiProblem().design_space
scenario = create_scenario(
disciplines,
"MDF",
objective_name="y_4",
design_space=design_space,
maximize_objective=True,
**formulation_options,
)
Set the design constraints¶
for c_name in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(c_name, "ineq")
XDSMIZE the scenario¶
Generate the XDSM file on the fly, setting print_statuses=true will print the status in the console html_output (default True), will generate a self contained html file, that can be automatically open using open_browser=True
scenario.xdsmize(html_output=True, print_statuses=False, open_browser=False)
Out:
INFO - 10:05:51: Generating HTML XDSM file in : xdsm.html
Define the algorithm inputs¶
We set the maximum number of iterations, the optimizer
and the optimizer options. Algorithm specific options are passed there.
Use get_algorithm_options_schema()
API function for more
information or read the documentation.
Here ftol_rel option is a stop criteria based on the relative difference in the objective between two iterates ineq_tolerance the tolerance determination of the optimum; this is specific to the GEMSEO wrapping and not in the solver.
algo_options = {
"ftol_rel": 1e-10,
"ineq_tolerance": 2e-3,
"normalize_design_space": True,
}
scn_inputs = {"max_iter": 10, "algo": "SLSQP", "algo_options": algo_options}
See also
We can also generates a backup file for the optimization,
as well as plots on the fly of the optimization history if option
generate_opt_plot
is True
.
This slows down a lot the process, here since SSBJ is very light
scenario.set_optimization_history_backup(file_path="mdf_backup.h5",
each_new_iter=True,
each_store=False, erase=True,
pre_load=False,
generate_opt_plot=True)
Execute the scenario¶
scenario.execute(scn_inputs)
Out:
INFO - 10:05:51:
INFO - 10:05:51: *** Start MDOScenario execution ***
INFO - 10:05:51: MDOScenario
INFO - 10:05:51: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
INFO - 10:05:51: MDO formulation: MDF
INFO - 10:05:51: Optimization problem:
INFO - 10:05:51: minimize -y_4(x_shared, x_1, x_2, x_3)
INFO - 10:05:51: with respect to x_1, x_2, x_3, x_shared
INFO - 10:05:51: subject to constraints:
INFO - 10:05:51: g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 10:05:51: g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 10:05:51: g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 10:05:51: over the design space:
INFO - 10:05:51: +----------+-------------+-------+-------------+-------+
INFO - 10:05:51: | name | lower_bound | value | upper_bound | type |
INFO - 10:05:51: +----------+-------------+-------+-------------+-------+
INFO - 10:05:51: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 10:05:51: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 10:05:51: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 10:05:51: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 10:05:51: | x_shared | 40 | 55 | 70 | float |
INFO - 10:05:51: | x_shared | 500 | 1000 | 1500 | float |
INFO - 10:05:51: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 10:05:51: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 10:05:51: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 10:05:51: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 10:05:51: +----------+-------------+-------+-------------+-------+
INFO - 10:05:51: Solving optimization problem with algorithm SLSQP:
INFO - 10:05:51: ... 0%| | 0/10 [00:00<?, ?it]
INFO - 10:05:51: ... 10%|█ | 1/10 [00:00<00:00, 99.52 it/sec]
INFO - 10:05:51: ... 30%|███ | 3/10 [00:00<00:00, 29.47 it/sec, obj=-3.76e+3]
INFO - 10:05:51: ... 50%|█████ | 5/10 [00:00<00:00, 20.02 it/sec, obj=-3.96e+3]
INFO - 10:05:51: ... 70%|███████ | 7/10 [00:00<00:00, 12.20 it/sec, obj=-4.51e+3]
INFO - 10:05:51: ... 80%|████████ | 8/10 [00:00<00:00, 10.67 it/sec, obj=-4.52e+3]
INFO - 10:05:52: ... 90%|█████████ | 9/10 [00:01<00:00, 9.10 it/sec, obj=-4.53e+3]
INFO - 10:05:52: ... 100%|██████████| 10/10 [00:01<00:00, 8.01 it/sec, obj=-4.52e+3]
INFO - 10:05:52: ... 100%|██████████| 10/10 [00:01<00:00, 7.99 it/sec, obj=-4.52e+3]
INFO - 10:05:52: Optimization result:
INFO - 10:05:52: Optimizer info:
INFO - 10:05:52: Status: None
INFO - 10:05:52: Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 10:05:52: Number of calls to the objective function by the optimizer: 12
INFO - 10:05:52: Solution:
INFO - 10:05:52: The solution is feasible.
INFO - 10:05:52: Objective: -3963.5131848833107
INFO - 10:05:52: Standardized constraints:
INFO - 10:05:52: g_1 = [-0.01809992 -0.03337438 -0.0442712 -0.05185236 -0.05734108 -0.13720865
INFO - 10:05:52: -0.10279135]
INFO - 10:05:52: g_2 = 1.6156768581687686e-05
INFO - 10:05:52: g_3 = [-7.67159033e-01 -2.32840967e-01 -2.38127604e-06 -1.83255000e-01]
INFO - 10:05:52: Design space:
INFO - 10:05:52: +----------+-------------+--------------------+-------------+-------+
INFO - 10:05:52: | name | lower_bound | value | upper_bound | type |
INFO - 10:05:52: +----------+-------------+--------------------+-------------+-------+
INFO - 10:05:52: | x_shared | 0.01 | 0.0600040391921454 | 0.09 | float |
INFO - 10:05:52: | x_shared | 30000 | 60000 | 60000 | float |
INFO - 10:05:52: | x_shared | 1.4 | 1.4 | 1.8 | float |
INFO - 10:05:52: | x_shared | 2.5 | 2.5 | 8.5 | float |
INFO - 10:05:52: | x_shared | 40 | 70 | 70 | float |
INFO - 10:05:52: | x_shared | 500 | 1500 | 1500 | float |
INFO - 10:05:52: | x_1 | 0.1 | 0.4 | 0.4 | float |
INFO - 10:05:52: | x_1 | 0.75 | 0.75 | 1.25 | float |
INFO - 10:05:52: | x_2 | 0.75 | 0.75 | 1.25 | float |
INFO - 10:05:52: | x_3 | 0.1 | 0.1562443735844188 | 1 | float |
INFO - 10:05:52: +----------+-------------+--------------------+-------------+-------+
INFO - 10:05:52: *** End MDOScenario execution (time: 0:00:01.264564) ***
{'max_iter': 10, 'algo': 'SLSQP', 'algo_options': {'ftol_rel': 1e-10, 'ineq_tolerance': 0.002, '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("mdf_history.h5", file_format="hdf5")
Out:
INFO - 10:05:52: Export optimization problem to file: mdf_history.h5
We can also save only calls to functions and design variables history:
scenario.save_optimization_history("mdf_history.xml", file_format="ggobi")
Out:
INFO - 10:05:52: Export to ggobi for functions: ['-y_4', 'Iter', 'g_1', 'g_2', 'g_3']
INFO - 10:05:52: Export to ggobi file: mdf_history.xml
Print optimization metrics¶
scenario.print_execution_metrics()
Out:
INFO - 10:05:52: Scenario Execution Statistics
INFO - 10:05:52: Discipline: SobieskiPropulsion
INFO - 10:05:52: Executions number: 204
INFO - 10:05:52: Execution time: 0.06386255096731475 s
INFO - 10:05:52: Linearizations number: 8
INFO - 10:05:52: Discipline: SobieskiAerodynamics
INFO - 10:05:52: Executions number: 211
INFO - 10:05:52: Execution time: 0.2723141269743792 s
INFO - 10:05:52: Linearizations number: 8
INFO - 10:05:52: Discipline: SobieskiMission
INFO - 10:05:52: Executions number: 10
INFO - 10:05:52: Execution time: 0.0007255200034705922 s
INFO - 10:05:52: Linearizations number: 8
INFO - 10:05:52: Discipline: SobieskiStructure
INFO - 10:05:52: Executions number: 208
INFO - 10:05:52: Execution time: 0.37073408701689914 s
INFO - 10:05:52: Linearizations number: 8
INFO - 10:05:52: Total number of executions calls: 633
INFO - 10:05:52: Total number of linearizations: 32
Post-process the results¶
Plot the optimization history view¶
scenario.post_process("OptHistoryView", save=False, show=False)
Out:
<gemseo.post.opt_history_view.OptHistoryView object at 0x7fdbe1775ca0>
Plot the basic history view¶
scenario.post_process(
"BasicHistory", variable_names=["x_shared"], save=False, show=False
)
Out:
<gemseo.post.basic_history.BasicHistory object at 0x7fdbe1d67d00>
Plot the constraints and objective history¶
scenario.post_process("ObjConstrHist", save=False, show=False)
Out:
<gemseo.post.obj_constr_hist.ObjConstrHist object at 0x7fdbe0f0fe50>
Plot the constraints history¶
scenario.post_process(
"ConstraintsHistory", save=False, show=False, constraint_names=["g_1", "g_2", "g_3"]
)
Out:
<gemseo.post.constraints_history.ConstraintsHistory object at 0x7fdbf81328e0>
Plot the constraints history using a radar chart¶
scenario.post_process(
"RadarChart", save=False, show=False, constraint_names=["g_1", "g_2", "g_3"]
)
Out:
<gemseo.post.radar_chart.RadarChart object at 0x7fdbfa5ae670>
Plot the quadratic approximation of the objective¶
scenario.post_process("QuadApprox", function="-y_4", save=False, show=False)
Out:
<gemseo.post.quad_approx.QuadApprox object at 0x7fdbf8064250>
Plot the functions using a SOM¶
scenario.post_process("SOM", save=False, show=False)
Out:
INFO - 10:05:55: Building Self Organizing Map from optimization history:
INFO - 10:05:55: Number of neurons in x direction = 4
INFO - 10:05:55: Number of neurons in y direction = 4
<gemseo.post.som.SOM object at 0x7fdbf84a9910>
Plot the scatter matrix of variables of interest¶
scenario.post_process(
"ScatterPlotMatrix",
save=False,
show=False,
variable_names=["-y_4", "g_1"],
fig_size=(14, 14),
)
Out:
<gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7fdbfa3bdfd0>
Plot the variables using the parallel coordinates¶
scenario.post_process("ParallelCoordinates", save=False, show=False)
Out:
<gemseo.post.para_coord.ParallelCoordinates object at 0x7fdbe05ce460>
Plot the robustness of the solution¶
scenario.post_process("Robustness", save=False, show=False)
Out:
<gemseo.post.robustness.Robustness object at 0x7fdbe037fbe0>
Plot the influence of the design variables¶
scenario.post_process("VariableInfluence", save=False, show=False, fig_size=(14, 14))
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Out:
INFO - 10:06:00: VariableInfluence for function -y_4
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [1 4 3 2 5 9 7 8 0]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/lib/python3.9/site-packages/gemseo/post/variable_influence.py:234: UserWarning: FixedFormatter should only be used together with FixedLocator
axe.set_xticklabels(x_labels, fontsize=font_size, rotation=rotation)
INFO - 10:06:00: VariableInfluence for function g_1_0
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [0 7 3 5 6]
INFO - 10:06:00: VariableInfluence for function g_1_1
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [7 0 3 5 6]
INFO - 10:06:00: VariableInfluence for function g_1_2
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [7 0 3 5 6]
INFO - 10:06:00: VariableInfluence for function g_1_3
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [7 0 3 5 6]
INFO - 10:06:00: VariableInfluence for function g_1_4
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [7 0 3 5 6]
INFO - 10:06:00: VariableInfluence for function g_1_5
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [3 7 5 6]
INFO - 10:06:00: VariableInfluence for function g_1_6
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [3 7 5 6]
INFO - 10:06:00: VariableInfluence for function g_2
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [0]
INFO - 10:06:00: VariableInfluence for function g_3_0
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [1 9 5 2 4 0 8]
INFO - 10:06:00: VariableInfluence for function g_3_1
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [1 9 5 2 4 0 8]
INFO - 10:06:00: VariableInfluence for function g_3_2
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [1 9 2]
INFO - 10:06:00: VariableInfluence for function g_3_3
INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99
INFO - 10:06:00: [9 1 2]
Total running time of the script: ( 0 minutes 10.142 seconds)