MDO formulations for a toy example in aerostructure

from __future__ import division, unicode_literals

from copy import deepcopy

from matplotlib import pyplot as plt

from gemseo.api import (
    configure_logger,
    create_discipline,
    create_scenario,
    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_dict=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_dict=struc_formulas
)
mission_formulas = {"range": "8e11*lift/(mass*drag)"}
mission = create_discipline(
    "AnalyticDiscipline", name="Mission", expressions_dict=mission_formulas
)

disciplines = [aerodynamics, structure, mission]

We can see that structure and aerodynamics are strongly coupled:

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

Create an MDO scenario with MDF formulation

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

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

Out:

    INFO - 14:43:18:
    INFO - 14:43:18: *** Start MDO Scenario execution ***
    INFO - 14:43:18: MDOScenario
    INFO - 14:43:18:    Disciplines: Aerodynamics Structure Mission
    INFO - 14:43:18:    MDOFormulation: MDF
    INFO - 14:43:18:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils, thick_panels, sweep)
    INFO - 14:43:19:    With respect to: thick_airfoils, thick_panels, sweep
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_airfoils, thick_panels, sweep) <= 0.5
    INFO - 14:43:19:       lift(thick_airfoils, thick_panels, sweep) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |  value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (15+0j) |      25     | float |
    INFO - 14:43:19: | thick_panels   |      1      |  (3+0j) |      20     | float |
    INFO - 14:43:19: | sweep          |      10     | (25+0j) |      35     | float |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/10 [00:00<?, ?it]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:407: SparseEfficiencyWarning: splu requires CSC matrix format
  warn('splu requires CSC matrix format', SparseEfficiencyWarning)
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt/lib_nlopt.py:278: ComplexWarning: Casting complex values to real discards the imaginary part
  grad[:] = obj_func.jac(xn_vect)
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt/lib_nlopt.py:319: ComplexWarning: Casting complex values to real discards the imaginary part
  grad[:] = atleast_2d(cstr_jac)[
    INFO - 14:43:19: Optimization:  40%|████      | 4/10 [00:00<00:00, 92.38 it/sec]
    INFO - 14:43:19: Optimization:  40%|████      | 4/10 [00:00<00:00, 91.74 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4509.5054469281
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 4
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 1.196277521486877e-10
    INFO - 14:43:19:    reserve_fact - 0.5 = 2.1966985030985597e-07
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      |          (5+0j)         |      25     | float |
    INFO - 14:43:19: | thick_panels   |      1      | (3.2255891895822506+0j) |      20     | float |
    INFO - 14:43:19: | sweep          |      10     | (24.993265993246517+0j) |      35     | float |
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.116870 ***

<gemseo.post.opt_history_view.OptHistoryView object at 0x7f3b512db4f0>

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,
    mda_name="MDAJacobi",
    tolerance=1e-8,
)
system_scenario.add_constraint("reserve_fact", "ineq", value=0.5)
system_scenario.add_constraint("lift", "eq", value=0.5)
system_scenario.execute(
    {"algo": "NLOPT_COBYLA", "max_iter": 7, "algo_options": algo_options}
)
system_scenario.post_process("OptHistoryView", save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
  • Evolution of the optimization variables
  • Evolution of the objective value
  • Distance to the optimum
  • Evolution of the inequality constraints
  • Evolution of the equality constraints

Out:

    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: MDOScenario MDOScenario Mission
    INFO - 14:43:19:    MDOFormulation: BiLevel
    INFO - 14:43:19:    Algorithm: NLOPT_COBYLA
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(sweep)
    INFO - 14:43:19:    With respect to: sweep
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(sweep) <= 0.5
    INFO - 14:43:19:       lift(sweep) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +-------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | name  | lower_bound |  value  | upper_bound | type  |
    INFO - 14:43:19: +-------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | sweep |      10     | (25+0j) |      35     | float |
    INFO - 14:43:19: +-------+-------------+---------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/7 [00:00<?, ?it]
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |  value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (15+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt/lib_nlopt.py:278: ComplexWarning: Casting complex values to real discards the imaginary part
  grad[:] = obj_func.jac(xn_vect)
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/stable/lib/python3.8/site-packages/gemseo/algos/opt/lib_nlopt.py:319: ComplexWarning: Casting complex values to real discards the imaginary part
  grad[:] = atleast_2d(cstr_jac)[
 WARNING - 14:43:19: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 14:43:19: Optimization:  40%|████      | 2/5 [00:00<00:00, 588.18 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4500.62486797491
    INFO - 14:43:19: The result is not feasible.
    INFO - 14:43:19: Status: 5
    INFO - 14:43:19: Optimizer message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 8
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 0.005333333333333634
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.014307 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization:  80%|████████  | 4/5 [00:00<00:00, 473.43 it/sec, obj=4.51e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4506.645473559042
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 5
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = 4.75033345992415e-10
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.2499999999208278+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.016429 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
 WARNING - 14:43:19: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 14:43:19: Optimization:  20%|██        | 1/5 [00:00<00:00, 1250.84 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4267.901616337772
    INFO - 14:43:19: The result is not feasible.
    INFO - 14:43:19: Status: 5
    INFO - 14:43:19: Optimizer message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 8
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 0.12713888888915292
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.009383 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.2499999999208278+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
   ERROR - 14:43:19: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    INFO - 14:43:19: Optimization:  40%|████      | 2/5 [00:00<00:00, 1088.30 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4270.014801163224
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message:  GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 3
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = 1.3178436120142578e-10
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (1.7652777777571345+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.009844 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
 WARNING - 14:43:19: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 14:43:19: Optimization: 100%|██████████| 5/5 [00:00<00:00, 607.68 it/sec, obj=4.51e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 3831.8061828212526
    INFO - 14:43:19: The result is not feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 7
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = -0.0023383323939722422
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |  value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (25+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.013713 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (1.7652777777571345+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization:  80%|████████  | 4/5 [00:00<00:00, 623.13 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 3818.589637887225
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 4
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = -1.0631850955178379e-10
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.4145871932465894+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.013569 ***
    INFO - 14:43:19: Optimization:  43%|████▎     | 3/7 [00:00<00:00, 52.38 it/sec, obj=3.82e+3]
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |  value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (25+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+---------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
 WARNING - 14:43:19: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 14:43:19: Optimization:  40%|████      | 2/5 [00:00<00:00, 838.93 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4490.540174198762
    INFO - 14:43:19: The result is not feasible.
    INFO - 14:43:19: Status: 5
    INFO - 14:43:19: Optimizer message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 8
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 0.009181047336995207
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.011578 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.4145871932465894+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization:  80%|████████  | 4/5 [00:00<00:00, 637.99 it/sec, obj=4.5e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4503.594568762557
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 5
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = 4.5724135588898207e-10
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |         value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.256301635443915+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.013177 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization: 100%|██████████| 5/5 [00:00<00:00, 519.61 it/sec, obj=4.51e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 3854.0818034962194
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 7
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 0.0
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (24.356774190325545+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.015208 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |         value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.256301635443915+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization:  80%|████████  | 4/5 [00:00<00:00, 607.61 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 3843.3818346286994
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 4
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = -1.0020073659688933e-10
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |         value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.303233602238194+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.013536 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (24.356774190325545+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
 WARNING - 14:43:19: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 14:43:19: Optimization:  40%|████      | 2/5 [00:00<00:00, 889.49 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4492.389203686935
    INFO - 14:43:19: The result is not feasible.
    INFO - 14:43:19: Status: 5
    INFO - 14:43:19: Optimizer message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 8
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 0.008585874882770628
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.011078 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |         value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.303233602238194+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
   ERROR - 14:43:19: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    INFO - 14:43:19: Optimization:  40%|████      | 2/5 [00:00<00:00, 1087.00 it/sec]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4504.850157624369
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message:  GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 3
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = -2.198845550083206e-10
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.2645368440733904+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.009841 ***
    INFO - 14:43:19: Optimization:  86%|████████▌ | 6/7 [00:00<00:00, 28.23 it/sec, obj=4.51e+3]
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Aerodynamics Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_airfoils)
    INFO - 14:43:19:    With respect to: thick_airfoils
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       lift(thick_airfoils) == 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization: 100%|██████████| 5/5 [00:00<00:00, 507.74 it/sec, obj=4.51e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4509.519641910823
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 7
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = -0.00013691255181019768
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | name           | lower_bound | value  | upper_bound | type  |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: | thick_airfoils |      5      | (5+0j) |      25     | float |
    INFO - 14:43:19: +----------------+-------------+--------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.015392 ***
    INFO - 14:43:19:
    INFO - 14:43:19: *** Start MDO Scenario execution ***
    INFO - 14:43:19: MDOScenario
    INFO - 14:43:19:    Disciplines: Structure Mission
    INFO - 14:43:19:    MDOFormulation: DisciplinaryOpt
    INFO - 14:43:19:    Algorithm: NLOPT_SLSQP
    INFO - 14:43:19: Optimization problem:
    INFO - 14:43:19:    Minimize: -range(thick_panels)
    INFO - 14:43:19:    With respect to: thick_panels
    INFO - 14:43:19:    Subject to constraints:
    INFO - 14:43:19:       reserve_fact(thick_panels) <= 0.5
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |          value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.2645368440733904+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+-------------------------+-------------+-------+
    INFO - 14:43:19: Optimization:   0%|          | 0/5 [00:00<?, ?it]
    INFO - 14:43:19: 
    INFO - 14:43:19: Optimization:  80%|████████  | 4/5 [00:00<00:00, 642.65 it/sec, obj=4.51e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4509.583287367007
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 5
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    reserve_fact - 0.5 = 2.2632107743447705e-08
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | name         | lower_bound |         value          | upper_bound | type  |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: | thick_panels |      1      | (3.225021422872048+0j) |      20     | float |
    INFO - 14:43:19: +--------------+-------------+------------------------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.013078 ***
    INFO - 14:43:19: Optimization: 100%|██████████| 7/7 [00:00<00:00, 24.13 it/sec, obj=4.51e+3]
    INFO - 14:43:19: Optimization result:
    INFO - 14:43:19: Objective value = 4509.243436177998
    INFO - 14:43:19: The result is feasible.
    INFO - 14:43:19: Status: None
    INFO - 14:43:19: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 14:43:19: Number of calls to the objective function by the optimizer: 9
    INFO - 14:43:19: Constraints values:
    INFO - 14:43:19:    lift - 0.5 = 5.555555582015259e-05
    INFO - 14:43:19:    reserve_fact - 0.5 = -0.15833333285035422
    INFO - 14:43:19: Design space:
    INFO - 14:43:19: +-------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | name  | lower_bound |  value  | upper_bound | type  |
    INFO - 14:43:19: +-------+-------------+---------+-------------+-------+
    INFO - 14:43:19: | sweep |      10     | (25+0j) |      35     | float |
    INFO - 14:43:19: +-------+-------------+---------+-------------+-------+
    INFO - 14:43:19: *** MDO Scenario run terminated in 0:00:00.296629 ***

Total running time of the script: ( 0 minutes 1.871 seconds)

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