MDO formulations for a toy example in aerostructure#

from __future__ import annotations

from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import generate_n2_plot
from gemseo.algos.opt.nlopt.settings.nlopt_cobyla_settings import NLOPT_COBYLA_Settings
from gemseo.algos.opt.nlopt.settings.nlopt_slsqp_settings import NLOPT_SLSQP_Settings
from gemseo.problems.mdo.aerostructure.aerostructure_design_space import (
    AerostructureDesignSpace,
)

configure_logger()

# Passed to algo settings
cobyla_settings = NLOPT_COBYLA_Settings(
    max_iter=7,
    xtol_rel=1e-8,
    xtol_abs=1e-8,
    ftol_rel=1e-8,
    ftol_abs=1e-8,
    ineq_tolerance=1e-5,
    eq_tolerance=1e-3,
)

slsqp_settings = NLOPT_SLSQP_Settings(
    max_iter=10,
    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,
    "range",
    design_space,
    maximize_objective=True,
    formulation_name="MDF",
)
scenario.add_constraint("reserve_fact", constraint_type="ineq", value=0.5)
scenario.add_constraint("lift", value=0.5)
scenario.execute(slsqp_settings)
scenario.post_process(post_name="OptHistoryView", save=False, show=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Evolution of the distance to the optimum
  • Evolution of the inequality constraints
  • Evolution of the equality constraints
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/design_space.py:424: ComplexWarning: Casting complex values to real discards the imaginary part
  self.__current_value[name] = array_value.astype(
    INFO - 08:36:30: Variable reserve_fact was removed from the Design Space, it is not an input of any discipline.
    INFO - 08:36:30:
    INFO - 08:36:30: *** Start MDOScenario execution ***
    INFO - 08:36:30: MDOScenario
    INFO - 08:36:30:    Disciplines: Aerodynamics Mission Structure
    INFO - 08:36:30:    MDO formulation: MDF
    INFO - 08:36:30: Optimization problem:
    INFO - 08:36:30:    minimize -range(thick_airfoils, thick_panels, sweep)
    INFO - 08:36:30:    with respect to sweep, thick_airfoils, thick_panels
    INFO - 08:36:30:    subject to constraints:
    INFO - 08:36:30:       reserve_fact(thick_airfoils, thick_panels, sweep) <= 0.5
    INFO - 08:36:30:       lift(thick_airfoils, thick_panels, sweep) == 0.5
    INFO - 08:36:30:    over the design space:
    INFO - 08:36:30:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:30:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:30:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:30:       | thick_airfoils |      5      |   15  |      25     | float |
    INFO - 08:36:30:       | thick_panels   |      1      |   3   |      20     | float |
    INFO - 08:36:30:       | sweep          |      10     |   25  |      35     | float |
    INFO - 08:36:30:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:30: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:30:     10%|█         | 1/10 [00:00<00:00, 76.36 it/sec, obj=-4.25e+3]
    INFO - 08:36:30:     20%|██        | 2/10 [00:00<00:00, 26.79 it/sec, obj=-4.51e+3]
    INFO - 08:36:30:     30%|███       | 3/10 [00:00<00:00, 30.89 it/sec, obj=-4.51e+3]
    INFO - 08:36:30:     40%|████      | 4/10 [00:00<00:00, 40.80 it/sec, obj=Not evaluated]
    INFO - 08:36:30: Optimization result:
    INFO - 08:36:30:    Optimizer info:
    INFO - 08:36:30:       Status: None
    INFO - 08:36:30:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
    INFO - 08:36:30:       Number of calls to the objective function by the optimizer: 4
    INFO - 08:36:30:    Solution:
    INFO - 08:36:30:       The solution is feasible.
    INFO - 08:36:30:       Objective: -4509.505446934416
    INFO - 08:36:30:       Standardized constraints:
    INFO - 08:36:30:          [lift-0.5] = 8.881784197001252e-15
    INFO - 08:36:30:          [reserve_fact-0.5] = 6.464347279688809e-09
    INFO - 08:36:30:       Design space:
    INFO - 08:36:30:          +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:30:          | Name           | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:30:          +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:30:          | thick_airfoils |      5      |         5         |      25     | float |
    INFO - 08:36:30:          | thick_panels   |      1      | 3.225589224567829 |      20     | float |
    INFO - 08:36:30:          | sweep          |      10     | 24.99326599309897 |      35     | float |
    INFO - 08:36:30:          +----------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:30: *** End MDOScenario execution (time: 0:00:00.105435) ***

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f24f4372d90>

Create an MDO scenario with bilevel formulation#

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

design_space_ref = AerostructureDesignSpace()
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/design_space.py:424: 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.

aero_scenario = create_scenario(
    [aerodynamics, mission],
    "range",
    design_space_ref.filter(["thick_airfoils"], copy=True),
    maximize_objective=True,
    formulation_name="DisciplinaryOpt",
)
aero_scenario.set_algorithm(slsqp_settings)

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.

struct_scenario = create_scenario(
    [structure, mission],
    "range",
    design_space_ref.filter(["thick_panels"], copy=True),
    maximize_objective=True,
    formulation_name="DisciplinaryOpt",
)
struct_scenario.set_algorithm(slsqp_settings)

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 = design_space_ref.filter(["sweep"], copy=True)
system_scenario = create_scenario(
    [aero_scenario, struct_scenario, mission],
    "range",
    design_space_system,
    formulation_name="BiLevel",
    maximize_objective=True,
    main_mda_settings={"inner_mda_name": "MDAJacobi", "tolerance": 1e-8},
)
system_scenario.add_constraint("reserve_fact", constraint_type="ineq", value=0.5)
system_scenario.add_constraint("lift", value=0.5)
system_scenario.execute(cobyla_settings)

system_scenario.post_process(post_name="OptHistoryView", save=False, show=True)
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Evolution of the distance to the optimum
  • Evolution of the inequality constraints
  • Evolution of the equality constraints
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: MDOScenario MDOScenario Mission
    INFO - 08:36:31:    MDO formulation: BiLevel
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(sweep)
    INFO - 08:36:31:    with respect to sweep
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(sweep) <= 0.5
    INFO - 08:36:31:       lift(sweep) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +-------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name  | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +-------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | sweep |      10     |   25  |      35     | float |
    INFO - 08:36:31:       +-------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_COBYLA:
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      |   15  |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1032.32 it/sec, obj=-4.27e+3]
 WARNING - 08:36:31: Optimization found no feasible point; the least infeasible point is selected.
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 284.59 it/sec, obj=-4.51e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: 5
    INFO - 08:36:31:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 16
    INFO - 08:36:31:    Solution:
 WARNING - 08:36:31:       The solution is not feasible.
    INFO - 08:36:31:       Objective: -4513.429203824652
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = 0.008666666666666822
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.010399) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      |   3   |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 989.69 it/sec, obj=-4.51e+3]
   ERROR - 08:36:31: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 361.00 it/sec, obj=-4.5e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 3
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4504.955637332531
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = 1.062133492268913e-09
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 3.266666666489645 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.008853) ***
    INFO - 08:36:31:     14%|█▍        | 1/7 [00:00<00:00, 31.79 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1521.33 it/sec, obj=-4.27e+3]
 WARNING - 08:36:31: Optimization found no feasible point; the least infeasible point is selected.
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: 5
    INFO - 08:36:31:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 16
    INFO - 08:36:31:    Solution:
 WARNING - 08:36:31:       The solution is not feasible.
    INFO - 08:36:31:       Objective: -4267.910320106269
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = 0.12708333333392363
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.007220) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      | 3.266666666489645 |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1824.40 it/sec, obj=-4.27e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 381.32 it/sec, obj=-4.27e+3]
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 414.16 it/sec, obj=-4.27e+3]
    INFO - 08:36:31:     40%|████      | 4/10 [00:00<00:00, 533.73 it/sec, obj=-4.27e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 5
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4270.047650046897
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = 1.5540514652911952e-08
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 1.764999997412866 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.010854) ***
    INFO - 08:36:31:     29%|██▊       | 2/7 [00:00<00:00, 32.33 it/sec, obj=-4.27e+3]
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1512.01 it/sec, obj=-4.53e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 419.51 it/sec, obj=-3.83e+3]
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 597.88 it/sec, obj=-4.43e+3]
    INFO - 08:36:31:     40%|████      | 4/10 [00:00<00:00, 639.23 it/sec, obj=-4.5e+3]
    INFO - 08:36:31:     50%|█████     | 5/10 [00:00<00:00, 658.32 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     60%|██████    | 6/10 [00:00<00:00, 677.23 it/sec, obj=-4.52e+3]
    INFO - 08:36:31:     70%|███████   | 7/10 [00:00<00:00, 691.72 it/sec, obj=-4.52e+3]
    INFO - 08:36:31:     80%|████████  | 8/10 [00:00<00:00, 699.62 it/sec, obj=-4.52e+3]
    INFO - 08:36:31:     90%|█████████ | 9/10 [00:00<00:00, 709.03 it/sec, obj=-4.53e+3]
    INFO - 08:36:31:    100%|██████████| 10/10 [00:00<00:00, 716.55 it/sec, obj=-4.53e+3]
 WARNING - 08:36:31: Optimization found no feasible point; the least infeasible point is selected.
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 12
    INFO - 08:36:31:    Solution:
 WARNING - 08:36:31:       The solution is not feasible.
    INFO - 08:36:31:       Objective: -3831.807218275781
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = -0.0023374064594913757
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      |   25  |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.018177) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      | 1.764999997412866 |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1251.66 it/sec, obj=-3.82e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 372.73 it/sec, obj=-3.82e+3]
   ERROR - 08:36:31: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 414.01 it/sec, obj=-3.82e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 4
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -3818.5902856031416
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = 2.8144597763457568e-11
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 3.414591822896584 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.010139) ***
    INFO - 08:36:31:     43%|████▎     | 3/7 [00:00<00:00, 29.19 it/sec, obj=-3.82e+3]
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      |   25  |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1516.93 it/sec, obj=-3.82e+3]
 WARNING - 08:36:31: Optimization found no feasible point; the least infeasible point is selected.
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 322.50 it/sec, obj=-4.49e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: 5
    INFO - 08:36:31:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 16
    INFO - 08:36:31:    Solution:
 WARNING - 08:36:31:       The solution is not feasible.
    INFO - 08:36:31:       Objective: -4490.54017449428
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = 0.00918103190482844
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.009193) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      | 3.414591822896584 |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1223.90 it/sec, obj=-4.5e+3]
   ERROR - 08:36:31: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 403.09 it/sec, obj=-4.5e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 3
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4503.594576633829
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = 1.1323209037072957e-10
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 3.256301558340416 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.007852) ***
    INFO - 08:36:31:     57%|█████▋    | 4/7 [00:00<00:00, 30.45 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1278.36 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 391.66 it/sec, obj=-3.85e+3]
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 559.94 it/sec, obj=-4.48e+3]
    INFO - 08:36:31:     40%|████      | 4/10 [00:00<00:00, 564.57 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     50%|█████     | 5/10 [00:00<00:00, 573.18 it/sec, obj=-4.51e+3]
   ERROR - 08:36:31: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:31:     60%|██████    | 6/10 [00:00<00:00, 464.41 it/sec, obj=-3.85e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -3854.0819929120544
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = 0.0
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+------------------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound |      Value       | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+------------------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      | 24.3567703351527 |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.015879) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      | 3.256301558340416 |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1252.40 it/sec, obj=-3.84e+3]
   ERROR - 08:36:31: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 410.40 it/sec, obj=-3.84e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 3
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -3843.382025541499
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = -1.1290524071227992e-10
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 3.303233590674794 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.007817) ***
    INFO - 08:36:31:     71%|███████▏  | 5/7 [00:00<00:00, 30.00 it/sec, obj=-3.85e+3]
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+------------------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound |      Value       | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+------------------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      | 24.3567703351527 |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1513.10 it/sec, obj=-3.85e+3]
 WARNING - 08:36:31: Optimization found no feasible point; the least infeasible point is selected.
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 323.63 it/sec, obj=-4.49e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: 5
    INFO - 08:36:31:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 16
    INFO - 08:36:31:    Solution:
 WARNING - 08:36:31:       The solution is not feasible.
    INFO - 08:36:31:       Objective: -4492.38920700084
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = 0.00858587320790527
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.009178) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      | 3.303233590674794 |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1138.21 it/sec, obj=-4.5e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 367.21 it/sec, obj=-4.5e+3]
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 407.33 it/sec, obj=-4.5e+3]
    INFO - 08:36:31:     40%|████      | 4/10 [00:00<00:00, 525.17 it/sec, obj=-4.5e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 5
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4504.850158478924
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = 5.3804996014150674e-09
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 3.264536834765667 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.011248) ***
    INFO - 08:36:31:     86%|████████▌ | 6/7 [00:00<00:00, 30.06 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Aerodynamics Mission
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_airfoils)
    INFO - 08:36:31:    with respect to thick_airfoils
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       lift(thick_airfoils) == 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:       | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:       +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1512.01 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 415.42 it/sec, obj=-4.48e+3]
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 592.05 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     40%|████      | 4/10 [00:00<00:00, 592.63 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     50%|█████     | 5/10 [00:00<00:00, 595.39 it/sec, obj=-4.51e+3]
   ERROR - 08:36:31: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/nlopt/nlopt.py", line 384, in _run
    nlopt_problem.optimize(x_0.real)
  File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
    return _nlopt.opt_optimize(self, *args)
nlopt.RoundoffLimited: NLopt roundoff-limited
    INFO - 08:36:31:     60%|██████    | 6/10 [00:00<00:00, 456.78 it/sec, obj=-4.48e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 8
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4509.519641910682
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = -0.0001369125207841826
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name           | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | thick_airfoils |      5      |   5   |      25     | float |
    INFO - 08:36:31:          +----------------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.016110) ***
    INFO - 08:36:31:
    INFO - 08:36:31: *** Start MDOScenario execution ***
    INFO - 08:36:31: MDOScenario
    INFO - 08:36:31:    Disciplines: Mission Structure
    INFO - 08:36:31:    MDO formulation: DisciplinaryOpt
    INFO - 08:36:31: Optimization problem:
    INFO - 08:36:31:    minimize -range(thick_panels)
    INFO - 08:36:31:    with respect to thick_panels
    INFO - 08:36:31:    subject to constraints:
    INFO - 08:36:31:       reserve_fact(thick_panels) <= 0.5
    INFO - 08:36:31:    over the design space:
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:       | thick_panels |      1      | 3.264536834765667 |      20     | float |
    INFO - 08:36:31:       +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: Solving optimization problem with algorithm NLOPT_SLSQP:
    INFO - 08:36:31:     10%|█         | 1/10 [00:00<00:00, 1342.18 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     20%|██        | 2/10 [00:00<00:00, 376.75 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     30%|███       | 3/10 [00:00<00:00, 393.19 it/sec, obj=-4.51e+3]
    INFO - 08:36:31:     40%|████      | 4/10 [00:00<00:00, 474.11 it/sec, obj=Not evaluated]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: Successive iterates of the design variables are closer than xtol_rel or xtol_abs. GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 4
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4509.583287345491
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [reserve_fact-0.5] = -2.105693397425057e-10
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | Name         | Lower bound |       Value       | Upper bound | Type  |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31:          | thick_panels |      1      | 3.225021426834291 |      20     | float |
    INFO - 08:36:31:          +--------------+-------------+-------------------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.011317) ***
    INFO - 08:36:31:    100%|██████████| 7/7 [00:00<00:00, 29.13 it/sec, obj=-4.51e+3]
    INFO - 08:36:31: Optimization result:
    INFO - 08:36:31:    Optimizer info:
    INFO - 08:36:31:       Status: None
    INFO - 08:36:31:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
    INFO - 08:36:31:       Number of calls to the objective function by the optimizer: 9
    INFO - 08:36:31:    Solution:
    INFO - 08:36:31:       The solution is feasible.
    INFO - 08:36:31:       Objective: -4509.243708600623
    INFO - 08:36:31:       Standardized constraints:
    INFO - 08:36:31:          [lift-0.5] = 5.903055821931957e-13
    INFO - 08:36:31:          [reserve_fact-0.5] = -0.2599999989201578
    INFO - 08:36:31:       Design space:
    INFO - 08:36:31:          +-------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | Name  | Lower bound | Value | Upper bound | Type  |
    INFO - 08:36:31:          +-------+-------------+-------+-------------+-------+
    INFO - 08:36:31:          | sweep |      10     |   25  |      35     | float |
    INFO - 08:36:31:          +-------+-------------+-------+-------------+-------+
    INFO - 08:36:31: *** End MDOScenario execution (time: 0:00:00.245404) ***

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f24f4430670>

Total running time of the script: (0 minutes 3.154 seconds)

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