Note
Click here to download the full example code
Scalable problem¶
We want to solve the Aerostructure MDO problem
by means of the MDF
formulation
with a higher dimension for the sweep parameter.
For that, we use the ScalableProblem
class.
from gemseo.api import configure_logger
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.problems.aerostructure.aerostructure_design_space import (
AerostructureDesignSpace,
)
from gemseo.problems.scalable.data_driven.problem import ScalableProblem
from matplotlib import pyplot as plt
configure_logger()
Out:
<RootLogger root (INFO)>
Define the design problem¶
In a first step, we define the design problem in terms of objective function (to maximize or minimize), design variables (local and global) and constraints (equality and inequality).
design_variables = ["thick_airfoils", "thick_panels", "sweep"]
objective_function = "range"
eq_constraints = ["c_rf"]
ineq_constraints = ["c_lift"]
maximize_objective = True
Create the disciplinary datasets¶
Then, we create the disciplinary AbstractFullCache
datasets
based on a DiagonalDOE
.
disciplines = create_discipline(["Aerodynamics", "Structure", "Mission"])
datasets = []
for discipline in disciplines:
design_space = AerostructureDesignSpace()
design_space.filter(discipline.get_input_data_names())
output_names = iter(discipline.get_output_data_names())
scenario = create_scenario(
discipline,
"DisciplinaryOpt",
next(output_names),
design_space,
scenario_type="DOE",
)
for output_name in output_names:
scenario.add_observable(output_name)
scenario.execute({"algo": "DiagonalDOE", "n_samples": 10})
datasets.append(scenario.export_to_dataset(name=discipline.name, opt_naming=False))
Out:
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/lib/python3.9/site-packages/gemseo/algos/design_space.py:448: ComplexWarning: Casting complex values to real discards the imaginary part
self.__current_value[name] = array_value.astype(
INFO - 10:03:58:
INFO - 10:03:58: *** Start DOEScenario execution ***
INFO - 10:03:58: DOEScenario
INFO - 10:03:58: Disciplines: Aerodynamics
INFO - 10:03:58: MDO formulation: DisciplinaryOpt
INFO - 10:03:58: Optimization problem:
INFO - 10:03:58: minimize drag(thick_airfoils, sweep, displ)
INFO - 10:03:58: with respect to displ, sweep, thick_airfoils
INFO - 10:03:58: over the design space:
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | thick_airfoils | 5 | 15 | 25 | float |
INFO - 10:03:58: | sweep | 10 | 25 | 35 | float |
INFO - 10:03:58: | displ | -1000 | -700 | 1000 | float |
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: Solving optimization problem with algorithm DiagonalDOE:
INFO - 10:03:58: ... 0%| | 0/10 [00:00<?, ?it]
INFO - 10:03:58: ... 100%|██████████| 10/10 [00:00<00:00, 790.83 it/sec, obj=-320]
INFO - 10:03:58: Optimization result:
INFO - 10:03:58: Optimizer info:
INFO - 10:03:58: Status: None
INFO - 10:03:58: Message: None
INFO - 10:03:58: Number of calls to the objective function by the optimizer: 10
INFO - 10:03:58: Solution:
INFO - 10:03:58: Objective: -319.99905478395067
INFO - 10:03:58: Design space:
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | thick_airfoils | 5 | 25 | 25 | float |
INFO - 10:03:58: | sweep | 10 | 35 | 35 | float |
INFO - 10:03:58: | displ | -1000 | 1000 | 1000 | float |
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: *** End DOEScenario execution (time: 0:00:00.021544) ***
INFO - 10:03:58:
INFO - 10:03:58: *** Start DOEScenario execution ***
INFO - 10:03:58: DOEScenario
INFO - 10:03:58: Disciplines: Structure
INFO - 10:03:58: MDO formulation: DisciplinaryOpt
INFO - 10:03:58: Optimization problem:
INFO - 10:03:58: minimize mass(thick_panels, sweep, forces)
INFO - 10:03:58: with respect to forces, sweep, thick_panels
INFO - 10:03:58: over the design space:
INFO - 10:03:58: +--------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +--------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | thick_panels | 1 | 3 | 20 | float |
INFO - 10:03:58: | sweep | 10 | 25 | 35 | float |
INFO - 10:03:58: | forces | -1000 | 400 | 1000 | float |
INFO - 10:03:58: +--------------+-------------+-------+-------------+-------+
INFO - 10:03:58: Solving optimization problem with algorithm DiagonalDOE:
INFO - 10:03:58: ... 0%| | 0/10 [00:00<?, ?it]
INFO - 10:03:58: ... 100%|██████████| 10/10 [00:00<00:00, 797.00 it/sec, obj=4.02e+5]
INFO - 10:03:58: Optimization result:
INFO - 10:03:58: Optimizer info:
INFO - 10:03:58: Status: None
INFO - 10:03:58: Message: None
INFO - 10:03:58: Number of calls to the objective function by the optimizer: 10
INFO - 10:03:58: Solution:
INFO - 10:03:58: Objective: 100.08573388203513
INFO - 10:03:58: Design space:
INFO - 10:03:58: +--------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +--------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | thick_panels | 1 | 1 | 20 | float |
INFO - 10:03:58: | sweep | 10 | 10 | 35 | float |
INFO - 10:03:58: | forces | -1000 | -1000 | 1000 | float |
INFO - 10:03:58: +--------------+-------------+-------+-------------+-------+
INFO - 10:03:58: *** End DOEScenario execution (time: 0:00:00.021672) ***
INFO - 10:03:58:
INFO - 10:03:58: *** Start DOEScenario execution ***
INFO - 10:03:58: DOEScenario
INFO - 10:03:58: Disciplines: Mission
INFO - 10:03:58: MDO formulation: DisciplinaryOpt
INFO - 10:03:58: Optimization problem:
INFO - 10:03:58: minimize range(drag, lift, mass, reserve_fact)
INFO - 10:03:58: with respect to drag, lift, mass, reserve_fact
INFO - 10:03:58: over the design space:
INFO - 10:03:58: +--------------+-------------+--------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +--------------+-------------+--------+-------------+-------+
INFO - 10:03:58: | drag | 100 | 340 | 1000 | float |
INFO - 10:03:58: | lift | 0.1 | 0.5 | 1 | float |
INFO - 10:03:58: | mass | 100000 | 100000 | 500000 | float |
INFO - 10:03:58: | reserve_fact | -1000 | 0 | 1000 | float |
INFO - 10:03:58: +--------------+-------------+--------+-------------+-------+
INFO - 10:03:58: Solving optimization problem with algorithm DiagonalDOE:
INFO - 10:03:58: ... 0%| | 0/10 [00:00<?, ?it]
INFO - 10:03:58: ... 100%|██████████| 10/10 [00:00<00:00, 741.33 it/sec, obj=1.6e+3+j]
INFO - 10:03:58: Optimization result:
INFO - 10:03:58: Optimizer info:
INFO - 10:03:58: Status: None
INFO - 10:03:58: Message: None
INFO - 10:03:58: Number of calls to the objective function by the optimizer: 10
INFO - 10:03:58: Solution:
INFO - 10:03:58: Objective: (1600+0j)
INFO - 10:03:58: Design space:
INFO - 10:03:58: +--------------+-------------+--------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +--------------+-------------+--------+-------------+-------+
INFO - 10:03:58: | drag | 100 | 1000 | 1000 | float |
INFO - 10:03:58: | lift | 0.1 | 1 | 1 | float |
INFO - 10:03:58: | mass | 100000 | 500000 | 500000 | float |
INFO - 10:03:58: | reserve_fact | -1000 | 1000 | 1000 | float |
INFO - 10:03:58: +--------------+-------------+--------+-------------+-------+
INFO - 10:03:58: *** End DOEScenario execution (time: 0:00:00.023752) ***
Instantiate a scalable problem¶
In a third stage, we instantiate a ScalableProblem
from these disciplinary datasets and from the definition of the MDO problem.
We also increase the dimension of the sweep parameter.
problem = ScalableProblem(
datasets,
design_variables,
objective_function,
eq_constraints,
ineq_constraints,
maximize_objective,
sizes={"sweep": 2},
)
print(problem)
Out:
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/lib/python3.9/site-packages/gemseo/problems/scalable/data_driven/model.py:147: ComplexWarning: Casting complex values to real discards the imaginary part
data[:, indices] = (value - lower_bound) / (upper_bound - lower_bound)
MDO problem
Disciplines: Aerodynamics, Structure, Mission
Design variables: thick_airfoils, thick_panels, sweep
Objective function: range (to maximize)
Inequality constraints: c_lift
Equality constraints: c_rf
Sizes: displ (1), sweep (2), thick_airfoils (1), drag (1), forces (1), lift (1), thick_panels (1), mass (1), reserve_fact (1), c_lift (1), c_rf (1), range (1)
Note
We could also provide options to the ScalableModel
objects
by means of the constructor of ScalableProblem
,
e.g. fill_factor
in the frame of the ScalableDiagonalModel
.
In this example, we use the standard ones.
Visualize the N2 chart¶
We can see the coupling between disciplines through this N2 chart:
problem.plot_n2_chart(save=False, show=True)
Create an MDO scenario¶
Lastly, we create a MDOScenario
with the MDF
formulation
and start the optimization at equilibrium,
thus ensuring the feasibility of the first iterate.
scenario = problem.create_scenario("MDF", start_at_equilibrium=True)
Out:
INFO - 10:03:58: Build a preliminary MDA to start at equilibrium
Note
We could also provide options for the scalable models to the constructor
of ScalableProblem
, e.g. fill_factor
in the frame of
the ScalableDiagonalModel
.
In this example, we use the standard ones.
Once the scenario is created, we can execute it as any scenario.
Here, we use the NLOPT_SLSQP
optimization algorithm
with no more than 100 iterations.
scenario.execute({"algo": "NLOPT_SLSQP", "max_iter": 100})
Out:
INFO - 10:03:58:
INFO - 10:03:58: *** Start MDOScenario execution ***
INFO - 10:03:58: MDOScenario
INFO - 10:03:58: Disciplines: sdm_Aerodynamics sdm_Structure sdm_Mission
INFO - 10:03:58: MDO formulation: MDF
INFO - 10:03:58: Optimization problem:
INFO - 10:03:58: minimize -range(thick_airfoils, thick_panels, sweep)
INFO - 10:03:58: with respect to sweep, thick_airfoils, thick_panels
INFO - 10:03:58: subject to constraints:
INFO - 10:03:58: c_lift(thick_airfoils, thick_panels, sweep) <= [0.74804822]
INFO - 10:03:58: c_rf(thick_airfoils, thick_panels, sweep) == 0.4974338463722027
INFO - 10:03:58: over the design space:
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: | thick_airfoils | 0 | 0.5 | 1 | float |
INFO - 10:03:58: | thick_panels | 0 | 0.5 | 1 | float |
INFO - 10:03:58: | sweep | 0 | 0.5 | 1 | float |
INFO - 10:03:58: | sweep | 0 | 0.5 | 1 | float |
INFO - 10:03:58: +----------------+-------------+-------+-------------+-------+
INFO - 10:03:58: Solving optimization problem with algorithm NLOPT_SLSQP:
INFO - 10:03:58: ... 0%| | 0/100 [00:00<?, ?it]
INFO - 10:03:58: ... 3%|▎ | 3/100 [00:00<00:00, 762.69 it/sec]
INFO - 10:03:58: ... 6%|▌ | 6/100 [00:00<00:00, 399.09 it/sec]
WARNING - 10:03:58: MDAJacobi has reached its maximum number of iterations but the normed residual 0.25 is still above the tolerance 1e-06.
INFO - 10:03:58: ... 8%|▊ | 8/100 [00:00<00:00, 307.47 it/sec, obj=-.299]
INFO - 10:03:58: Optimization result:
INFO - 10:03:58: Optimizer info:
INFO - 10:03:58: Status: None
INFO - 10:03:58: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 10:03:58: Number of calls to the objective function by the optimizer: 9
INFO - 10:03:58: Solution:
INFO - 10:03:58: The solution is feasible.
INFO - 10:03:58: Objective: -0.29852766251563395
INFO - 10:03:58: Standardized constraints:
INFO - 10:03:58: c_lift + offset = [-0.49234168]
INFO - 10:03:58: c_rf - 0.4974338463722027 = -6.494804694057166e-15
INFO - 10:03:58: Design space:
INFO - 10:03:58: +----------------+-------------+--------------------+-------------+-------+
INFO - 10:03:58: | name | lower_bound | value | upper_bound | type |
INFO - 10:03:58: +----------------+-------------+--------------------+-------------+-------+
INFO - 10:03:58: | thick_airfoils | 0 | 1 | 1 | float |
INFO - 10:03:58: | thick_panels | 0 | 0.5155052311584897 | 1 | float |
INFO - 10:03:58: | sweep | 0 | 1 | 1 | float |
INFO - 10:03:58: | sweep | 0 | 1 | 1 | float |
INFO - 10:03:58: +----------------+-------------+--------------------+-------------+-------+
INFO - 10:03:58: *** End MDOScenario execution (time: 0:00:00.336370) ***
{'max_iter': 100, 'algo': 'NLOPT_SLSQP'}
We can post-process the results.
Here, we use the standard OptHistoryView
.
scenario.post_process("OptHistoryView", save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Total running time of the script: ( 0 minutes 1.906 seconds)