MDO formulations for a toy example in aerostructure

from __future__ import annotations

from copy import deepcopy

from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import generate_n2_plot
from gemseo.problems.aerostructure.aerostructure_design_space import (
    AerostructureDesignSpace,
)

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)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum
  • Hessian diagonal approximation
  • Evolution of the inequality constraints
  • Evolution of the equality constraints
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/gemseo/algos/design_space.py:426: ComplexWarning: Casting complex values to real discards the imaginary part
  self.__current_value[name] = array_value.astype(
    INFO - 08:37:25: Variable reserve_fact was removed from the Design Space, it is not an input of any discipline.
    INFO - 08:37:25:
    INFO - 08:37:25: *** Start MDOScenario execution ***
    INFO - 08:37:25: MDOScenario
    INFO - 08:37:25:    Disciplines: Aerodynamics Mission Structure
    INFO - 08:37:25:    MDO formulation: MDF
    INFO - 08:37:25: Optimization problem:
    INFO - 08:37:25:    minimize -range(thick_airfoils, thick_panels, sweep)
    INFO - 08:37:25:    with respect to sweep, thick_airfoils, thick_panels
    INFO - 08:37:25:    subject to constraints:
    INFO - 08:37:25:       reserve_fact(thick_airfoils, thick_panels, sweep) <= 0.5
    INFO - 08:37:25:       lift(thick_airfoils, thick_panels, sweep) == 0.5
    INFO - 08:37:25:    over the design space:
    INFO - 08:37:25:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:25:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:25:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:25:    | thick_airfoils |      5      |   15  |      25     | float |
    INFO - 08:37:25:    | thick_panels   |      1      |   3   |      20     | float |
    INFO - 08:37:25:    | sweep          |      10     |   25  |      35     | float |
    INFO - 08:37:25:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:25: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:25: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 08:37:25: ...  10%|█         | 1/10 [00:00<00:00, 30.25 it/sec, obj=-4.25e+3]
    INFO - 08:37:25: ...  20%|██        | 2/10 [00:00<00:00, 12.47 it/sec, obj=-4.51e+3]
    INFO - 08:37:25: ...  30%|███       | 3/10 [00:00<00:00, 14.59 it/sec, obj=-4.51e+3]
    INFO - 08:37:25: ...  40%|████      | 4/10 [00:00<00:00, 19.35 it/sec, obj=Not evaluated]
    INFO - 08:37:25: Optimization result:
    INFO - 08:37:25:    Optimizer info:
    INFO - 08:37:25:       Status: None
    INFO - 08:37:25:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
    INFO - 08:37:25:       Number of calls to the objective function by the optimizer: 4
    INFO - 08:37:25:    Solution:
    INFO - 08:37:25:       The solution is feasible.
    INFO - 08:37:25:       Objective: -4509.505446928907
    INFO - 08:37:25:       Standardized constraints:
    INFO - 08:37:25:          lift - 0.5 = 1.1963030566164434e-10
    INFO - 08:37:25:          reserve_fact - 0.5 = 2.204757620916098e-07
    INFO - 08:37:25:       Design space:
    INFO - 08:37:25:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:25:       | name           | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:25:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:25:       | thick_airfoils |      5      |         5         |      25     | float |
    INFO - 08:37:25:       | thick_panels   |      1      | 3.225589189454885 |      20     | float |
    INFO - 08:37:25:       | sweep          |      10     | 24.99326599322578 |      35     | float |
    INFO - 08:37:25:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:25: *** End MDOScenario execution (time: 0:00:00.220410) ***
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/genson/schema/strategies/base.py:42: UserWarning: Schema incompatible. Keyword 'description' has conflicting values ('The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.' vs. 'The width and height of the figure in inches, e.g. `(w, h)`.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'). Using 'The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'
  warn(('Schema incompatible. Keyword {0!r} has conflicting '
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/gemseo/post/opt_history_view.py:599: UserWarning: All values for SymLogScale are below linthresh, making it effectively linear. You likely should lower the value of linthresh.
  col_bar = fig.colorbar(

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f873bd0cdc0>

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()

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=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum
  • Evolution of the inequality constraints
  • Evolution of the equality constraints
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: MDOScenario MDOScenario Mission
    INFO - 08:37:26:    MDO formulation: BiLevel
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(sweep)
    INFO - 08:37:26:    with respect to sweep
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(sweep) <= 0.5
    INFO - 08:37:26:       lift(sweep) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +-------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name  | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +-------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | sweep |      10     |   25  |      35     | float |
    INFO - 08:37:26:    +-------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_COBYLA:
    INFO - 08:37:26: ...   0%|          | 0/7 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      |   15  |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 193.29 it/sec, obj=-4.27e+3]
    INFO - 08:37:26:
 WARNING - 08:37:26: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 166.93 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: 5
    INFO - 08:37:26:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:37:26:    Solution:
 WARNING - 08:37:26:       The solution is not feasible.
    INFO - 08:37:26:       Objective: -4513.429203824652
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = 0.008666666666666822
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.023816) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      |   3   |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 182.23 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
   ERROR - 08:37:26: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 173.99 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message:  GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 3
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4504.955637332531
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 1.062133492268913e-09
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 3.266666666489645 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.023019) ***
    INFO - 08:37:26: ...  14%|█▍        | 1/7 [00:00<00:00,  9.05 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 915.99 it/sec, obj=-4.27e+3]
    INFO - 08:37:26:
 WARNING - 08:37:26: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: 5
    INFO - 08:37:26:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:37:26:    Solution:
 WARNING - 08:37:26:       The solution is not feasible.
    INFO - 08:37:26:       Objective: -4267.910320106268
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = 0.12708333333392374
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.015504) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      | 3.266666666489645 |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 998.41 it/sec, obj=-4.27e+3]
    INFO - 08:37:26:
   ERROR - 08:37:26: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 309.99 it/sec, obj=-4.27e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message:  GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 3
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4270.047650043281
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 3.0379254667423083e-10
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |      value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 1.76499999995232 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.017453) ***
    INFO - 08:37:26: ...  29%|██▊       | 2/7 [00:00<00:00, 12.43 it/sec, obj=-4.27e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 796.64 it/sec, obj=-4.53e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 265.29 it/sec, obj=-3.83e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 381.03 it/sec, obj=-4.43e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 401.46 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ... 100%|██████████| 5/5 [00:00<00:00, 417.80 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
 WARNING - 08:37:26: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 7
    INFO - 08:37:26:    Solution:
 WARNING - 08:37:26:       The solution is not feasible.
    INFO - 08:37:26:       Objective: -3831.807218266315
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = -0.002337406467956049
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      |   25  |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.024183) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound |      value       | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      | 1.76499999995232 |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 755.32 it/sec, obj=-3.82e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 246.87 it/sec, obj=-3.82e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 269.16 it/sec, obj=-3.82e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 348.52 it/sec, obj=-3.82e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 5
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -3818.5902855979184
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 3.0950531026974204e-09
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 3.414591822343108 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.023024) ***
    INFO - 08:37:26: ...  43%|████▎     | 3/7 [00:00<00:00, 13.14 it/sec, obj=-3.82e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      |   25  |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 779.76 it/sec, obj=-3.82e+3]
    INFO - 08:37:26:
 WARNING - 08:37:26: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 267.31 it/sec, obj=-4.49e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: 5
    INFO - 08:37:26:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:37:26:    Solution:
 WARNING - 08:37:26:       The solution is not feasible.
    INFO - 08:37:26:       Objective: -4490.540174494245
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = 0.00918103190667352
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.018435) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      | 3.414591822343108 |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 758.74 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 244.30 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 268.94 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 348.21 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 5
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4503.594576639364
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 2.4330390147042635e-08
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 3.256301554313449 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.023404) ***
    INFO - 08:37:26: ...  57%|█████▋    | 4/7 [00:00<00:00, 13.84 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 917.19 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 271.05 it/sec, obj=-3.85e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 388.78 it/sec, obj=-4.48e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 395.91 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ... 100%|██████████| 5/5 [00:00<00:00, 400.04 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 7
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -3854.0820028049116
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = 0.0
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      | 24.35677013380376 |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.026010) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      | 3.256301554313449 |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 765.66 it/sec, obj=-3.84e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 244.07 it/sec, obj=-3.84e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 254.96 it/sec, obj=-3.84e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 317.29 it/sec, obj=Not evaluated]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 4
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -3843.382035512657
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 3.418136884647538e-10
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |      value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 3.30323358999496 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.023852) ***
    INFO - 08:37:26: ...  71%|███████▏  | 5/7 [00:00<00:00, 13.92 it/sec, obj=-3.85e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      | 24.35677013380376 |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 798.61 it/sec, obj=-3.85e+3]
    INFO - 08:37:26:
 WARNING - 08:37:26: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 268.53 it/sec, obj=-4.49e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: 5
    INFO - 08:37:26:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:37:26:    Solution:
 WARNING - 08:37:26:       The solution is not feasible.
    INFO - 08:37:26:       Objective: -4492.389207173915
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = 0.00858587312068304
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.019425) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound |      value       | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      | 3.30323358999496 |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 771.86 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
   ERROR - 08:37:26: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 284.54 it/sec, obj=-4.5e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message:  GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 3
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4504.850158522
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 3.3662672649370506e-10
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 3.264536835170201 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.017970) ***
    INFO - 08:37:26: ...  86%|████████▌ | 6/7 [00:00<00:00, 14.44 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Aerodynamics Mission
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_airfoils)
    INFO - 08:37:26:    with respect to thick_airfoils
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       lift(thick_airfoils) == 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:    | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:    +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 852.85 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 255.88 it/sec, obj=-4.48e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 367.98 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 380.31 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ... 100%|██████████| 5/5 [00:00<00:00, 379.53 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 7
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4509.519641910688
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = -0.0001369125221327705
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name           | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:37:26:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.027257) ***
    INFO - 08:37:26:
    INFO - 08:37:26: *** Start MDOScenario execution ***
    INFO - 08:37:26: MDOScenario
    INFO - 08:37:26:    Disciplines: Mission Structure
    INFO - 08:37:26:    MDO formulation: DisciplinaryOpt
    INFO - 08:37:26: Optimization problem:
    INFO - 08:37:26:    minimize -range(thick_panels)
    INFO - 08:37:26:    with respect to thick_panels
    INFO - 08:37:26:    subject to constraints:
    INFO - 08:37:26:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:37:26:    over the design space:
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:    | thick_panels |      1      | 3.264536835170201 |      20     | float |
    INFO - 08:37:26:    +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:37:26: ...   0%|          | 0/5 [00:00<?, ?it]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  20%|██        | 1/5 [00:00<00:00, 1018.78 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  40%|████      | 2/5 [00:00<00:00, 249.33 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  60%|██████    | 3/5 [00:00<00:00, 271.67 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26: ...  80%|████████  | 4/5 [00:00<00:00, 351.69 it/sec, obj=-4.51e+3]
    INFO - 08:37:26:
    INFO - 08:37:26:
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 5
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4509.583287354345
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          reserve_fact - 0.5 = 3.0278073381850845e-08
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | name         | lower_bound |       value       | upper_bound | type  |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26:       | thick_panels |      1      | 3.225021421746108 |      20     | float |
    INFO - 08:37:26:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.023639) ***
    INFO - 08:37:26: ... 100%|██████████| 7/7 [00:00<00:00, 14.36 it/sec, obj=-4.51e+3]
    INFO - 08:37:26: Optimization result:
    INFO - 08:37:26:    Optimizer info:
    INFO - 08:37:26:       Status: None
    INFO - 08:37:26:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 08:37:26:       Number of calls to the objective function by the optimizer: 9
    INFO - 08:37:26:    Solution:
    INFO - 08:37:26:       The solution is feasible.
    INFO - 08:37:26:       Objective: -4509.243708600623
    INFO - 08:37:26:       Standardized constraints:
    INFO - 08:37:26:          lift - 0.5 = 5.903055821931957e-13
    INFO - 08:37:26:          reserve_fact - 0.5 = -0.2599999989201578
    INFO - 08:37:26:       Design space:
    INFO - 08:37:26:       +-------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | name  | lower_bound | value | upper_bound | type  |
    INFO - 08:37:26:       +-------+-------------+-------+-------------+-------+
    INFO - 08:37:26:       | sweep |      10     |   25  |      35     | float |
    INFO - 08:37:26:       +-------+-------------+-------+-------------+-------+
    INFO - 08:37:26: *** End MDOScenario execution (time: 0:00:00.501726) ***
 WARNING - 08:37:27: Failed to create Hessian approximation.
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/gemseo/post/opt_history_view.py", line 621, in _create_hessian_approx_plot
    _, diag, _, _ = SR1Approx(history).build_approximation(
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/gemseo/post/core/hessians.py", line 379, in build_approximation
    x_hist, grad_hist, _, _ = self.get_x_grad_history(
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.1/lib/python3.9/site-packages/gemseo/post/core/hessians.py", line 170, in get_x_grad_history
    raise ValueError(
ValueError: Cannot build approximation for function: -range because its gradient history is too small: 0.

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f873b76c940>

Total running time of the script: ( 0 minutes 3.251 seconds)

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