Note
Go to the end to download the full example code
Examples for constraint aggregation¶
from __future__ import annotations
from copy import deepcopy
from gemseo import configure_logger
from gemseo import create_scenario
from gemseo.algos.design_space import DesignSpace
from gemseo.disciplines.analytic import AnalyticDiscipline
from gemseo.disciplines.concatenater import Concatenater
configure_logger()
<RootLogger root (INFO)>
Number of constraints
N = 100
Build the discipline
constraint_names = [f"g_{k + 1}" for k in range(N)]
function_names = ["o", *constraint_names]
function_expressions = ["y"] + [f"{k + 1}*x*exp(1-{k + 1}*x)-y" for k in range(N)]
disc = AnalyticDiscipline(
name="function",
expressions=dict(zip(function_names, function_expressions)),
)
# This step is required to put all constraints needed for aggregation in one variable.
concat = Concatenater(constraint_names, "g")
Build the design space
ds = DesignSpace()
ds.add_variable(
"x",
l_b=0.0,
u_b=1,
value=1.0 / N / 2.0,
var_type=DesignSpace.DesignVariableType.FLOAT,
)
ds.add_variable(
"y", l_b=0.0, u_b=1, value=1, var_type=DesignSpace.DesignVariableType.FLOAT
)
ds_new = deepcopy(ds)
Build the optimization solver options
max_iter = 1000
ineq_tol = 1e-5
convergence_tol = 1e-8
normalize = True
algo_options = {
"algo": "NLOPT_MMA",
"max_iter": max_iter,
"algo_options": {
"ineq_tolerance": ineq_tol,
"eq_tolerance": ineq_tol,
"xtol_rel": convergence_tol,
"xtol_abs": convergence_tol,
"ftol_rel": convergence_tol,
"ftol_abs": convergence_tol,
"ctol_abs": convergence_tol,
"normalize_design_space": normalize,
},
}
Build the optimization scenario
original_scenario = create_scenario(
[disc, concat],
"DisciplinaryOpt",
"o",
ds,
maximize_objective=False,
)
original_scenario.add_constraint("g", constraint_type="ineq")
original_scenario.execute(algo_options)
# Without constraint aggregation MMA iterations become more expensive, when a
# large number of constraints are activated.
INFO - 13:54:10:
INFO - 13:54:10: *** Start MDOScenario execution ***
INFO - 13:54:10: MDOScenario
INFO - 13:54:10: Disciplines: Concatenater function
INFO - 13:54:10: MDO formulation: DisciplinaryOpt
INFO - 13:54:10: Optimization problem:
INFO - 13:54:10: minimize o(x, y)
INFO - 13:54:10: with respect to x, y
INFO - 13:54:10: subject to constraints:
INFO - 13:54:10: g(x, y) <= 0.0
INFO - 13:54:10: over the design space:
INFO - 13:54:10: +------+-------------+-------+-------------+-------+
INFO - 13:54:10: | Name | Lower bound | Value | Upper bound | Type |
INFO - 13:54:10: +------+-------------+-------+-------------+-------+
INFO - 13:54:10: | x | 0 | 0.005 | 1 | float |
INFO - 13:54:10: | y | 0 | 1 | 1 | float |
INFO - 13:54:10: +------+-------------+-------+-------------+-------+
INFO - 13:54:10: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 13:54:10: 1%| | 6/1000 [00:00<01:11, 13.90 it/sec, obj=0.00931]
INFO - 13:54:10: 1%| | 7/1000 [00:00<01:08, 14.54 it/sec, obj=8.28e-5]
INFO - 13:54:10: 1%| | 8/1000 [00:00<01:05, 15.07 it/sec, obj=5.2e-9]
INFO - 13:54:25: 1%| | 9/1000 [00:14<26:51, 36.91 it/min, obj=0]
INFO - 13:54:25: Optimization result:
INFO - 13:54:25: Optimizer info:
INFO - 13:54:25: Status: 5
INFO - 13:54:25: Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
INFO - 13:54:25: Number of calls to the objective function by the optimizer: 1501
INFO - 13:54:25: Solution:
INFO - 13:54:25: The solution is feasible.
INFO - 13:54:25: Objective: 0.0
INFO - 13:54:25: Standardized constraints:
INFO - 13:54:25: g = [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
INFO - 13:54:25: 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
INFO - 13:54:25: 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
INFO - 13:54:25: 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
INFO - 13:54:25: 0. 0. 0. 0.]
INFO - 13:54:25: Design space:
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: | Name | Lower bound | Value | Upper bound | Type |
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: | x | 0 | 0 | 1 | float |
INFO - 13:54:25: | y | 0 | 0 | 1 | float |
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: *** End MDOScenario execution (time: 0:00:14.648397) ***
{'max_iter': 1000, 'algo_options': {'ineq_tolerance': 1e-05, 'eq_tolerance': 1e-05, 'xtol_rel': 1e-08, 'xtol_abs': 1e-08, 'ftol_rel': 1e-08, 'ftol_abs': 1e-08, 'ctol_abs': 1e-08, 'normalize_design_space': True}, 'algo': 'NLOPT_MMA'}
exploiting constraint aggregation on the same scenario:
new_scenario = create_scenario(
[disc, concat],
"DisciplinaryOpt",
"o",
ds_new,
maximize_objective=False,
)
new_scenario.add_constraint("g", constraint_type="ineq")
This method aggregates the constraints using the lower bound KS function
new_scenario.formulation.opt_problem.aggregate_constraint(
0, method="lower_bound_KS", rho=10.0
)
new_scenario.execute(algo_options)
INFO - 13:54:25:
INFO - 13:54:25: *** Start MDOScenario execution ***
INFO - 13:54:25: MDOScenario
INFO - 13:54:25: Disciplines: Concatenater function
INFO - 13:54:25: MDO formulation: DisciplinaryOpt
INFO - 13:54:25: Optimization problem:
INFO - 13:54:25: minimize o(x, y)
INFO - 13:54:25: with respect to x, y
INFO - 13:54:25: subject to constraints:
INFO - 13:54:25: lower_bound_KS() <= 0.0
INFO - 13:54:25: over the design space:
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: | Name | Lower bound | Value | Upper bound | Type |
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: | x | 0 | 0.005 | 1 | float |
INFO - 13:54:25: | y | 0 | 1 | 1 | float |
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 13:54:25: 1%| | 6/1000 [00:00<00:51, 19.44 it/sec, obj=0.00773]
INFO - 13:54:25: 1%| | 7/1000 [00:00<00:49, 20.10 it/sec, obj=5.72e-5]
INFO - 13:54:25: 1%| | 8/1000 [00:00<00:48, 20.57 it/sec, obj=2.63e-9]
INFO - 13:54:25: 1%| | 9/1000 [00:00<01:12, 13.60 it/sec, obj=0]
INFO - 13:54:25: Optimization result:
INFO - 13:54:25: Optimizer info:
INFO - 13:54:25: Status: 5
INFO - 13:54:25: Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
INFO - 13:54:25: Number of calls to the objective function by the optimizer: 1501
INFO - 13:54:25: Solution:
INFO - 13:54:25: The solution is feasible.
INFO - 13:54:25: Objective: 0.0
INFO - 13:54:25: Standardized constraints:
INFO - 13:54:25: lower_bound_KS(g) = 2.7755575615628914e-16
INFO - 13:54:25: Design space:
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: | Name | Lower bound | Value | Upper bound | Type |
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: | x | 0 | 0 | 1 | float |
INFO - 13:54:25: | y | 0 | 0 | 1 | float |
INFO - 13:54:25: +------+-------------+-------+-------------+-------+
INFO - 13:54:25: *** End MDOScenario execution (time: 0:00:00.675667) ***
{'max_iter': 1000, 'algo_options': {'ineq_tolerance': 1e-05, 'eq_tolerance': 1e-05, 'xtol_rel': 1e-08, 'xtol_abs': 1e-08, 'ftol_rel': 1e-08, 'ftol_abs': 1e-08, 'ctol_abs': 1e-08, 'normalize_design_space': True}, 'algo': 'NLOPT_MMA'}
with constraint aggregation the last iteration is faster.
Total running time of the script: (0 minutes 16.828 seconds)