BiLevel-based DOE on the Sobieski SSBJ test case

from __future__ import division, unicode_literals

from copy import deepcopy

from matplotlib import pyplot as plt

from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem

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",
)

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,
)

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,
)

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,
    parallel_scenarios=False,
    reset_x0_before_opt=True,
    scenario_type="DOE",
)

Note

Setting reset_x0_before_opt=True is mandatory when doing a DOE in parallel. If we want reproducible results, don’t reuse previous xopt.

system_scenario.formulation.mda1.warm_start = False
system_scenario.formulation.mda2.warm_start = False

Note

This is mandatory when doing a DOE in parallel if we want always exactly the same results, don’t warm start mda1 to have exactly the same process whatever the execution order and process dispatch.

for sub_sc in sub_disciplines[0:3]:
    sub_sc.default_inputs = {"max_iter": 20, "algo": "L-BFGS-B"}

Multiprocessing

It is possible to run a DOE in parallel using multiprocessing, in order to do this, we specify the number of processes to be used for the computation of the samples.

Warning

The multiprocessing option has some limitations on Windows. For Python versions < 3.7 and Numpy < 1.20.0, subprocesses may get hung randomly during execution. It is strongly recommended to update your environment to avoid this problem. The features MemoryFullCache and HDF5Cache are not available for multiprocessing on Windows. As an alternative, we recommend the method DOEScenario.set_optimization_history_backup().

n_processes = 4

run_inputs = {
    "n_samples": 30,
    "algo": "lhs",
    "algo_options": {"n_processes": n_processes},
}

Warning

When running a parallel DOE on Windows, the execution must be protected to avoid recursive calls:

if __name__ == "__main__":
    system_scenario.execute(run_inputs)

system_scenario.print_execution_metrics()

Out:

 INFO - 14:42:38:
 INFO - 14:42:38: *** Start DOE Scenario execution ***
 INFO - 14:42:38: DOEScenario
 INFO - 14:42:38:    Disciplines: PropulsionScenario AerodynamicsScenario StructureScenario SobieskiMission
 INFO - 14:42:38:    MDOFormulation: BiLevel
 INFO - 14:42:38:    Algorithm: lhs
 INFO - 14:42:38: Optimization problem:
 INFO - 14:42:38:    Minimize: y_4(x_shared)
 INFO - 14:42:38:    With respect to: x_shared
 INFO - 14:42:38: DOE sampling:   0%|          | 0/30 [00:00<?, ?it]
 INFO - 14:42:38: Running DOE in parallel on n_processes = 4
ERROR - 14:42:39: Failed to execute task indexed 0
ERROR - 14:42:39: math domain error
 INFO - 14:42:39: DOE sampling:   3%|▎         | 1/30 [00:00<00:00, 41.09 it/sec, obj=485]
 INFO - 14:42:40: DOE sampling:  10%|█         | 3/30 [00:01<00:00, 28.56 it/sec, obj=350]
 INFO - 14:42:40: DOE sampling:  17%|█▋        | 5/30 [00:01<00:01, 23.58 it/sec, obj=495]
 INFO - 14:42:40: DOE sampling:  23%|██▎       | 7/30 [00:01<00:01, 19.11 it/sec, obj=367]
 INFO - 14:42:41: DOE sampling:  33%|███▎      | 10/30 [00:02<00:01, 14.67 it/sec, obj=918]
 INFO - 14:42:41: DOE sampling:  40%|████      | 12/30 [00:02<00:01, 13.87 it/sec, obj=415]
 INFO - 14:42:41: DOE sampling:  47%|████▋     | 14/30 [00:02<00:01, 12.21 it/sec, obj=1.2e+3]
 INFO - 14:42:41: DOE sampling:  53%|█████▎    | 16/30 [00:02<00:01, 11.38 it/sec, obj=2.27e+3]
 INFO - 14:42:41: DOE sampling:  57%|█████▋    | 17/30 [00:02<00:01, 10.67 it/sec, obj=394]
 INFO - 14:42:42: DOE sampling:  63%|██████▎   | 19/30 [00:03<00:01,  9.38 it/sec, obj=829]
 INFO - 14:42:42: DOE sampling:  77%|███████▋  | 23/30 [00:03<00:00,  8.03 it/sec, obj=640]
 INFO - 14:42:43: DOE sampling:  90%|█████████ | 27/30 [00:04<00:00,  7.39 it/sec, obj=647]
 INFO - 14:42:43: DOE sampling:  97%|█████████▋| 29/30 [00:04<00:00,  7.23 it/sec, obj=293]
 INFO - 14:42:43: Optimization result:
 INFO - 14:42:43: Objective value = 292.91178826079175
 INFO - 14:42:43: The result is feasible.
 INFO - 14:42:43: Status: None
 INFO - 14:42:43: Optimizer message: None
 INFO - 14:42:43: Number of calls to the objective function by the optimizer: 30
 INFO - 14:42:43: Design space:
 INFO - 14:42:43: +----------+-------------+---------------------+-------------+-------+
 INFO - 14:42:43: | name     | lower_bound |        value        | upper_bound | type  |
 INFO - 14:42:43: +----------+-------------+---------------------+-------------+-------+
 INFO - 14:42:43: | x_shared |     0.01    | 0.04666883227502976 |     0.09    | float |
 INFO - 14:42:43: | x_shared |    30000    |  37789.27932845149  |    60000    | float |
 INFO - 14:42:43: | x_shared |     1.4     |  1.667044086506944  |     1.8     | float |
 INFO - 14:42:43: | x_shared |     2.5     |   8.29772323088249  |     8.5     | float |
 INFO - 14:42:43: | x_shared |      40     |  42.41730480236713  |      70     | float |
 INFO - 14:42:43: | x_shared |     500     |  724.9388551459947  |     1500    | float |
 INFO - 14:42:43: +----------+-------------+---------------------+-------------+-------+
 INFO - 14:42:43: *** DOE Scenario run terminated ***
 INFO - 14:42:43: * Scenario Executions statistics *
 INFO - 14:42:43: * Discipline: PropulsionScenario
 INFO - 14:42:43: Executions number: 30
 INFO - 14:42:43: Execution time:  0.9930245859995921 s
 INFO - 14:42:43: Linearizations number: 0
 INFO - 14:42:43: * Discipline: AerodynamicsScenario
 INFO - 14:42:43: Executions number: 30
 INFO - 14:42:43: Execution time:  1.1471837950011832 s
 INFO - 14:42:43: Linearizations number: 0
 INFO - 14:42:43: * Discipline: StructureScenario
 INFO - 14:42:43: Executions number: 30
 INFO - 14:42:43: Execution time:  5.416471589000139 s
 INFO - 14:42:43: Linearizations number: 0
 INFO - 14:42:43: * Discipline: SobieskiMission
 INFO - 14:42:43: Executions number: 29
 INFO - 14:42:43: Execution time:  0.0009374399942316813 s
 INFO - 14:42:43: Linearizations number: 0
 INFO - 14:42:43: Total number of executions calls 119
 INFO - 14:42:43: Total number of linearizations 0

Warning

On Windows, the progress bar may show duplicated instances during the initialization of each subprocess. In some cases it may also print the conclusion of an iteration ahead of another one that was concluded first. This is a consequence of the pickling process and does not affect the computations of the scenario.

Plot the optimization history view

system_scenario.post_process("OptHistoryView", show=False, save=False)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum

Out:

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f3b51726850>

Plot the scatter matrix

system_scenario.post_process(
    "ScatterPlotMatrix", show=False, save=False, variables_list=["y_4", "x_shared"]
)
plot doe sobieski bilevel example

Out:

<gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7f3b511c41c0>

Plot parallel coordinates

system_scenario.post_process("ParallelCoordinates", show=False, save=False)
  • Design variables history colored by 'y_4'  value
  • Objective function and constraints history colored by 'y_4' value

Out:

<gemseo.post.para_coord.ParallelCoordinates object at 0x7f3b51f97160>

Plot correlations

system_scenario.post_process("Correlations", show=False, save=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()

Out:

INFO - 14:42:45: Detected 0 correlations > 0.95

Total running time of the script: ( 0 minutes 7.014 seconds)

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