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.problems.aerostructure.aerostructure_design_space import (


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,
Traceback (most recent call last):
  File "/home/docs/checkouts/", line 31, in <module>
    from gemseo.problems.aerostructure.aerostructure_design_space import (
ModuleNotFoundError: No module named 'gemseo.problems.aerostructure'

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)

Create an MDO scenario with MDF formulation

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

design_space = AerostructureDesignSpace()
scenario = create_scenario(
scenario.add_constraint("reserve_fact", constraint_type="ineq", value=0.5)
scenario.add_constraint("lift", value=0.5)
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 10, "algo_options": algo_options})
scenario.post_process("OptHistoryView", save=False, show=True)

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.

aero_scenario = create_scenario(
    [aerodynamics, mission],
    design_space_ref.filter(["thick_airfoils"], copy=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.

struct_scenario = create_scenario(
    [structure, mission],
    design_space_ref.filter(["thick_panels"], copy=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 = design_space_ref.filter(["sweep"], copy=True)
system_scenario = create_scenario(
    [aero_scenario, struct_scenario, mission],
system_scenario.add_constraint("reserve_fact", constraint_type="ineq", value=0.5)
system_scenario.add_constraint("lift", value=0.5)
    "algo": "NLOPT_COBYLA",
    "max_iter": 7,
    "algo_options": algo_options,
system_scenario.post_process("OptHistoryView", save=False, show=True)

Total running time of the script: (0 minutes 0.001 seconds)

Gallery generated by Sphinx-Gallery