MDO formulations for a toy example in aerostructure

from copy import deepcopy

from gemseo.api import configure_logger
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.api import generate_n2_plot
from gemseo.problems.aerostructure.aerostructure_design_space import (
    AerostructureDesignSpace,
)
from matplotlib import pyplot as plt

configure_logger()


algo_options = {
    "xtol_rel": 1e-8,
    "xtol_abs": 1e-8,
    "ftol_rel": 1e-8,
    "ftol_abs": 1e-8,
    "ineq_tolerance": 1e-5,
    "eq_tolerance": 1e-3,
}

Create discipline

First, we create disciplines (aero, structure, mission) with dummy formulas using the AnalyticDiscipline class.

aero_formulas = {
    "drag": "0.1*((sweep/360)**2 + 200 + "
    + "thick_airfoils**2-thick_airfoils -4*displ)",
    "forces": "10*sweep + 0.2*thick_airfoils-0.2*displ",
    "lift": "(sweep + 0.2*thick_airfoils-2.*displ)/3000.",
}
aerodynamics = create_discipline(
    "AnalyticDiscipline", name="Aerodynamics", expressions=aero_formulas
)
struc_formulas = {
    "mass": "4000*(sweep/360)**3 + 200000 + " + "100*thick_panels +200.0*forces",
    "reserve_fact": "-3*sweep " + "-6*thick_panels+0.1*forces+55",
    "displ": "2*sweep + 3*thick_panels-2.*forces",
}
structure = create_discipline(
    "AnalyticDiscipline", name="Structure", expressions=struc_formulas
)
mission_formulas = {"range": "8e11*lift/(mass*drag)"}
mission = create_discipline(
    "AnalyticDiscipline", name="Mission", expressions=mission_formulas
)

disciplines = [aerodynamics, structure, mission]

We can see that structure and aerodynamics are strongly coupled:

generate_n2_plot(disciplines, save=False, show=True)
plot aerostructure

Create an MDO scenario with MDF formulation

Then, we create an MDO scenario based on the MDF formulation

design_space = AerostructureDesignSpace()
scenario = create_scenario(
    disciplines=disciplines,
    formulation="MDF",
    objective_name="range",
    design_space=design_space,
    maximize_objective=True,
)
scenario.add_constraint("reserve_fact", "ineq", value=0.5)
scenario.add_constraint("lift", "eq", value=0.5)
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 10, "algo_options": algo_options})
scenario.post_process("OptHistoryView", save=False, show=True)

Out:

/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/develop/lib/python3.9/site-packages/gemseo/algos/design_space.py:450: ComplexWarning: Casting complex values to real discards the imaginary part
  self.__current_value[name] = array_value.astype(
    INFO - 15:04:32: Variable reserve_fact was removed from the Design Space, it is not an input of any discipline.
    INFO - 15:04:32:
    INFO - 15:04:32: *** Start MDOScenario execution ***
    INFO - 15:04:32: MDOScenario
    INFO - 15:04:32:    Disciplines: Aerodynamics Structure Mission
    INFO - 15:04:32:    MDO formulation: MDF
    INFO - 15:04:32: Optimization problem:
    INFO - 15:04:32:    minimize -range(thick_airfoils, thick_panels, sweep)
    INFO - 15:04:32:    with respect to sweep, thick_airfoils, thick_panels
    INFO - 15:04:32:    subject to constraints:
    INFO - 15:04:32:       reserve_fact(thick_airfoils, thick_panels, sweep) <= 0.5
    INFO - 15:04:32:       lift(thick_airfoils, thick_panels, sweep) == 0.5
    INFO - 15:04:32:    over the design space:
    INFO - 15:04:32:    +----------------+-------------+-------+-------------+-------+
    INFO - 15:04:32:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 15:04:32:    +----------------+-------------+-------+-------------+-------+
    INFO - 15:04:32:    | thick_airfoils |      5      |   15  |      25     | float |
    INFO - 15:04:32:    | thick_panels   |      1      |   3   |      20     | float |
    INFO - 15:04:32:    | sweep          |      10     |   25  |      35     | float |
    INFO - 15:04:32:    +----------------+-------------+-------+-------------+-------+
    INFO - 15:04:32: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 15:04:32: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:04:33: ...  30%|███       | 3/10 [00:00<00:00, 82.63 it/sec]
    INFO - 15:04:33: ...  40%|████      | 4/10 [00:00<00:00, 64.30 it/sec]
    INFO - 15:04:33: Optimization result:
    INFO - 15:04:33:    Optimizer info:
    INFO - 15:04:33:       Status: None
    INFO - 15:04:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 4
    INFO - 15:04:33:    Solution:
    INFO - 15:04:33:       The solution is feasible.
    INFO - 15:04:33:       Objective: -4509.505446939552
    INFO - 15:04:33:       Standardized constraints:
    INFO - 15:04:33:          lift - 0.5 = 1.5432100042289676e-14
    INFO - 15:04:33:          reserve_fact - 0.5 = 1.1578073610962747e-08
    INFO - 15:04:33:       Design space:
    INFO - 15:04:33:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 15:04:33:       | name           | lower_bound |       value       | upper_bound | type  |
    INFO - 15:04:33:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 15:04:33:       | thick_airfoils |      5      |         5         |      25     | float |
    INFO - 15:04:33:       | thick_panels   |      1      |  3.22558922375984 |      20     | float |
    INFO - 15:04:33:       | sweep          |      10     | 24.99326599296684 |      35     | float |
    INFO - 15:04:33:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.165933) ***

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f7f92183a30>

Create an MDO scenario with bilevel formulation

Then, we create an MDO scenario based on the bilevel formulation

sub_scenario_options = {
    "max_iter": 5,
    "algo": "NLOPT_SLSQP",
    "algo_options": algo_options,
}
design_space_ref = AerostructureDesignSpace()

Out:

/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/develop/lib/python3.9/site-packages/gemseo/algos/design_space.py:450: ComplexWarning: Casting complex values to real discards the imaginary part
  self.__current_value[name] = array_value.astype(

Create the aeronautics sub-scenario

For this purpose, we create a first sub-scenario to maximize the range with respect to the thick airfoils, based on the aerodynamics discipline.

design_space_aero = deepcopy(design_space_ref).filter(["thick_airfoils"])
aero_scenario = create_scenario(
    disciplines=[aerodynamics, mission],
    formulation="DisciplinaryOpt",
    objective_name="range",
    design_space=design_space_aero,
    maximize_objective=True,
)
aero_scenario.default_inputs = sub_scenario_options

Create the structure sub-scenario

We create a second sub-scenario to maximize the range with respect to the thick panels, based on the structure discipline.

design_space_struct = deepcopy(design_space_ref).filter(["thick_panels"])
struct_scenario = create_scenario(
    disciplines=[structure, mission],
    formulation="DisciplinaryOpt",
    objective_name="range",
    design_space=design_space_struct,
    maximize_objective=True,
)
struct_scenario.default_inputs = sub_scenario_options

Create the system scenario

Lastly, we build a system scenario to maximize the range with respect to the sweep, which is a shared variable, based on the previous sub-scenarios.

design_space_system = deepcopy(design_space_ref).filter(["sweep"])
system_scenario = create_scenario(
    disciplines=[aero_scenario, struct_scenario, mission],
    formulation="BiLevel",
    objective_name="range",
    design_space=design_space_system,
    maximize_objective=True,
    inner_mda_name="MDAJacobi",
    tolerance=1e-8,
)
system_scenario.add_constraint("reserve_fact", "ineq", value=0.5)
system_scenario.add_constraint("lift", "eq", value=0.5)
system_scenario.execute(
    {"algo": "NLOPT_COBYLA", "max_iter": 7, "algo_options": algo_options}
)
system_scenario.post_process("OptHistoryView", save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum
  • Evolution of the inequality constraints
  • Evolution of the equality constraints

Out:

   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: MDOScenario MDOScenario Mission
   INFO - 15:04:33:    MDO formulation: BiLevel
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(sweep)
   INFO - 15:04:33:    with respect to sweep
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(sweep) <= 0.5
   INFO - 15:04:33:       lift(sweep) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +-------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name  | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +-------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | sweep |      10     |   25  |      35     | float |
   INFO - 15:04:33:    +-------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_COBYLA:
   INFO - 15:04:33: ...   0%|          | 0/7 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      |   15  |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
WARNING - 15:04:33: Optimization found no feasible point !  The least infeasible point is selected.
   INFO - 15:04:33: ...  40%|████      | 2/5 [00:00<00:00, 450.46 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: 5
   INFO - 15:04:33:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 8
   INFO - 15:04:33:    Solution:
WARNING - 15:04:33:       The solution is not feasible.
   INFO - 15:04:33:       Objective: -4500.62486797491
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = 0.005333333333333634
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.020029) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      |   3   |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ...  80%|████████  | 4/5 [00:00<00:00, 320.09 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 5
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4506.645473559042
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = 4.75033345992415e-10
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 3.249999999920828 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.024335) ***
   INFO - 15:04:33: ...  14%|█▍        | 1/7 [00:00<00:00, 66.16 it/sec]
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
WARNING - 15:04:33: Optimization found no feasible point !  The least infeasible point is selected.
   INFO - 15:04:33: ...  20%|██        | 1/5 [00:00<00:00, 1127.93 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: 5
   INFO - 15:04:33:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 8
   INFO - 15:04:33:    Solution:
WARNING - 15:04:33:       The solution is not feasible.
   INFO - 15:04:33:       Objective: -4267.901616337772
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = 0.12713888888915292
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.007530) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      | 3.249999999920828 |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
  ERROR - 15:04:33: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
   INFO - 15:04:33: ...  40%|████      | 2/5 [00:00<00:00, 780.02 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message:  GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 3
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4270.014801163224
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = 1.3178436120142578e-10
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 1.765277777757134 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.009558) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
WARNING - 15:04:33: Optimization found no feasible point !  The least infeasible point is selected.
   INFO - 15:04:33: ... 100%|██████████| 5/5 [00:00<00:00, 424.11 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 7
   INFO - 15:04:33:    Solution:
WARNING - 15:04:33:       The solution is not feasible.
   INFO - 15:04:33:       Objective: -3831.8061828212526
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = -0.0023383323939722422
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      |   25  |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.014863) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      | 1.765277777757134 |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ...  80%|████████  | 4/5 [00:00<00:00, 414.47 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 4
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -3818.589637887225
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = -1.0631850955178379e-10
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 3.414587193246589 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.015116) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      |   25  |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
WARNING - 15:04:33: Optimization found no feasible point !  The least infeasible point is selected.
   INFO - 15:04:33: ...  40%|████      | 2/5 [00:00<00:00, 680.12 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: 5
   INFO - 15:04:33:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 8
   INFO - 15:04:33:    Solution:
WARNING - 15:04:33:       The solution is not feasible.
   INFO - 15:04:33:       Objective: -4490.540174198762
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = 0.009181047336995207
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.010492) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      | 3.414587193246589 |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ...  80%|████████  | 4/5 [00:00<00:00, 418.90 it/sec, obj=-4.5e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 5
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4503.594568762557
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = 4.5724135588898207e-10
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 3.256301635443915 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.015109) ***
   INFO - 15:04:33: ...  57%|█████▋    | 4/7 [00:00<00:00, 29.98 it/sec, obj=-4.51e+3]
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ... 100%|██████████| 5/5 [00:00<00:00, 343.25 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 7
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -3854.0818034962194
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = 0.0
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      | 24.35677419032555 |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.017672) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      | 3.256301635443915 |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ...  80%|████████  | 4/5 [00:00<00:00, 419.89 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 4
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -3843.3818346286994
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = -1.0020073659688933e-10
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 3.303233602238194 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.015043) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      | 24.35677419032555 |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
WARNING - 15:04:33: Optimization found no feasible point !  The least infeasible point is selected.
   INFO - 15:04:33: ...  40%|████      | 2/5 [00:00<00:00, 688.36 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: 5
   INFO - 15:04:33:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 8
   INFO - 15:04:33:    Solution:
WARNING - 15:04:33:       The solution is not feasible.
   INFO - 15:04:33:       Objective: -4492.389203686935
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = 0.008585874882770628
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.010417) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      | 3.303233602238194 |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
  ERROR - 15:04:33: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
   INFO - 15:04:33: ...  40%|████      | 2/5 [00:00<00:00, 741.33 it/sec]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message:  GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 3
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4504.850157624369
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = -2.198845550083206e-10
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |      value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 3.26453684407339 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.009799) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Aerodynamics Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_airfoils)
   INFO - 15:04:33:    with respect to thick_airfoils
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       lift(thick_airfoils) == 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:    | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:    +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ... 100%|██████████| 5/5 [00:00<00:00, 359.13 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 7
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4509.519641910823
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = -0.00013691255181019768
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name           | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | thick_airfoils |      5      |   5   |      25     | float |
   INFO - 15:04:33:       +----------------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.017187) ***
   INFO - 15:04:33:
   INFO - 15:04:33: *** Start MDOScenario execution ***
   INFO - 15:04:33: MDOScenario
   INFO - 15:04:33:    Disciplines: Structure Mission
   INFO - 15:04:33:    MDO formulation: DisciplinaryOpt
   INFO - 15:04:33: Optimization problem:
   INFO - 15:04:33:    minimize -range(thick_panels)
   INFO - 15:04:33:    with respect to thick_panels
   INFO - 15:04:33:    subject to constraints:
   INFO - 15:04:33:       reserve_fact(thick_panels) <= 0.5
   INFO - 15:04:33:    over the design space:
   INFO - 15:04:33:    +--------------+-------------+------------------+-------------+-------+
   INFO - 15:04:33:    | name         | lower_bound |      value       | upper_bound | type  |
   INFO - 15:04:33:    +--------------+-------------+------------------+-------------+-------+
   INFO - 15:04:33:    | thick_panels |      1      | 3.26453684407339 |      20     | float |
   INFO - 15:04:33:    +--------------+-------------+------------------+-------------+-------+
   INFO - 15:04:33: Solving optimization problem with algorithm NLOPT_SLSQP:
   INFO - 15:04:33: ...   0%|          | 0/5 [00:00<?, ?it]
   INFO - 15:04:33:
   INFO - 15:04:33: ...  80%|████████  | 4/5 [00:00<00:00, 440.13 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 5
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4509.583287367007
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          reserve_fact - 0.5 = 2.2632107743447705e-08
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | name         | lower_bound |       value       | upper_bound | type  |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33:       | thick_panels |      1      | 3.225021422872048 |      20     | float |
   INFO - 15:04:33:       +--------------+-------------+-------------------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.014484) ***
   INFO - 15:04:33: ... 100%|██████████| 7/7 [00:00<00:00, 18.69 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: ... 100%|██████████| 7/7 [00:00<00:00, 18.59 it/sec, obj=-4.51e+3]
   INFO - 15:04:33: Optimization result:
   INFO - 15:04:33:    Optimizer info:
   INFO - 15:04:33:       Status: None
   INFO - 15:04:33:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
   INFO - 15:04:33:       Number of calls to the objective function by the optimizer: 9
   INFO - 15:04:33:    Solution:
   INFO - 15:04:33:       The solution is feasible.
   INFO - 15:04:33:       Objective: -4509.243436177998
   INFO - 15:04:33:       Standardized constraints:
   INFO - 15:04:33:          lift - 0.5 = 5.5555555820374636e-05
   INFO - 15:04:33:          reserve_fact - 0.5 = -0.1583333328503187
   INFO - 15:04:33:       Design space:
   INFO - 15:04:33:       +-------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | name  | lower_bound | value | upper_bound | type  |
   INFO - 15:04:33:       +-------+-------------+-------+-------------+-------+
   INFO - 15:04:33:       | sweep |      10     |   25  |      35     | float |
   INFO - 15:04:33:       +-------+-------------+-------+-------------+-------+
   INFO - 15:04:33: *** End MDOScenario execution (time: 0:00:00.385870) ***

Total running time of the script: ( 0 minutes 2.118 seconds)

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