Examples for constraint aggregation

from __future__ import annotations

from copy import deepcopy

from gemseo import create_scenario
from gemseo.algos.design_space import DesignSpace
from gemseo.disciplines.analytic import AnalyticDiscipline
from gemseo.disciplines.concatenater import Concatenater
from gemseo.settings.opt import NLOPT_MMA_Settings

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, strict=False)),
)
# 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",
    lower_bound=0.0,
    upper_bound=1,
    value=1.0 / N / 2.0,
    type_=DesignSpace.DesignVariableType.FLOAT,
)
ds.add_variable(
    "y",
    lower_bound=0.0,
    upper_bound=1,
    value=1,
    type_=DesignSpace.DesignVariableType.FLOAT,
)

ds_new = deepcopy(ds)

Build the optimization solver settings

mma_settings = NLOPT_MMA_Settings(
    ineq_tolerance=1e-5,
    eq_tolerance=1e-5,
    xtol_rel=1e-8,
    xtol_abs=1e-8,
    ftol_rel=1e-8,
    ftol_abs=1e-8,
    normalize_design_space=True,
    max_iter=1000,
)

Build the optimization scenario

original_scenario = create_scenario(
    [disc, concat],
    "o",
    ds,
    maximize_objective=False,
    formulation_name="DisciplinaryOpt",
)
original_scenario.add_constraint("g", constraint_type="ineq")

original_scenario.execute(mma_settings)
# Without constraint aggregation MMA iterations become more expensive, when a
# large number of constraints are activated.

INFO - 16:18:03: *** Start MDOScenario execution ***
INFO - 16:18:03: MDOScenario
INFO - 16:18:03:    Disciplines: Concatenater function
INFO - 16:18:03:    MDO formulation: DisciplinaryOpt
INFO - 16:18:03: Optimization problem:
INFO - 16:18:03:    minimize o(x, y)
INFO - 16:18:03:    with respect to x, y
INFO - 16:18:03:    under the inequality constraints
INFO - 16:18:03:       g(x, y) <= 0
INFO - 16:18:03:    over the design space:
INFO - 16:18:03:       +------+-------------+-------+-------------+-------+
INFO - 16:18:03:       | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:18:03:       +------+-------------+-------+-------------+-------+
INFO - 16:18:03:       | x    |      0      | 0.005 |      1      | float |
INFO - 16:18:03:       | y    |      0      |   1   |      1      | float |
INFO - 16:18:03:       +------+-------------+-------+-------------+-------+
INFO - 16:18:03: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 16:18:04:      1%|          | 6/1000 [00:00<00:39, 24.91 it/sec, feas=True, obj=0.00931]
INFO - 16:18:04:      1%|          | 7/1000 [00:00<00:38, 25.83 it/sec, feas=True, obj=8.28e-5]
INFO - 16:18:04:      1%|          | 8/1000 [00:00<00:37, 26.66 it/sec, feas=True, obj=5.51e-9]
INFO - 16:18:14:      1%|          | 9/1000 [00:10<19:46, 50.11 it/min, feas=True, obj=0]
INFO - 16:18:14: Optimization result:
INFO - 16:18:14:    Optimizer info:
INFO - 16:18:14:       Status: 5
INFO - 16:18:14:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
INFO - 16:18:14:    Solution:
INFO - 16:18:14:       The solution is feasible.
INFO - 16:18:14:       Objective: 0.0
INFO - 16:18:14:       Standardized constraints:
INFO - 16:18:14:          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 - 16:18:14:  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 - 16:18:14:  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 - 16:18:14:  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 - 16:18:14:  0. 0. 0. 0.]
INFO - 16:18:14:       Design space:
INFO - 16:18:14:          +------+-------------+-------+-------------+-------+
INFO - 16:18:14:          | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:18:14:          +------+-------------+-------+-------------+-------+
INFO - 16:18:14:          | x    |      0      |   0   |      1      | float |
INFO - 16:18:14:          | y    |      0      |   0   |      1      | float |
INFO - 16:18:14:          +------+-------------+-------+-------------+-------+
INFO - 16:18:14: *** End MDOScenario execution ***

exploiting constraint aggregation on the same scenario:

new_scenario = create_scenario(
    [disc, concat],
    "o",
    ds_new,
    maximize_objective=False,
    formulation_name="DisciplinaryOpt",
)
new_scenario.add_constraint("g", constraint_type="ineq")

This method aggregates the constraints using the lower bound KS function

new_scenario.formulation.optimization_problem.constraints.aggregate(
    0, method="lower_bound_KS", rho=10.0
)
new_scenario.execute(mma_settings)

INFO - 16:18:14: *** Start MDOScenario execution ***
INFO - 16:18:14: MDOScenario
INFO - 16:18:14:    Disciplines: Concatenater function
INFO - 16:18:14:    MDO formulation: DisciplinaryOpt
INFO - 16:18:14: Optimization problem:
INFO - 16:18:14:    minimize o(x, y)
INFO - 16:18:14:    with respect to x, y
INFO - 16:18:14:    under the inequality constraints
INFO - 16:18:14:       lower_bound_KS() <= 0.0
INFO - 16:18:14:    over the design space:
INFO - 16:18:14:       +------+-------------+-------+-------------+-------+
INFO - 16:18:14:       | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:18:14:       +------+-------------+-------+-------------+-------+
INFO - 16:18:14:       | x    |      0      | 0.005 |      1      | float |
INFO - 16:18:14:       | y    |      0      |   1   |      1      | float |
INFO - 16:18:14:       +------+-------------+-------+-------------+-------+
INFO - 16:18:14: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 16:18:14:      1%|          | 6/1000 [00:00<00:21, 47.07 it/sec, feas=True, obj=0.00773]
INFO - 16:18:14:      1%|          | 7/1000 [00:00<00:21, 47.09 it/sec, feas=True, obj=5.72e-5]
INFO - 16:18:14:      1%|          | 8/1000 [00:00<00:21, 47.08 it/sec, feas=True, obj=2.63e-9]
INFO - 16:18:14:      1%|          | 9/1000 [00:00<00:42, 23.30 it/sec, feas=True, obj=0]
INFO - 16:18:14: Optimization result:
INFO - 16:18:14:    Optimizer info:
INFO - 16:18:14:       Status: 5
INFO - 16:18:14:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
INFO - 16:18:14:    Solution:
INFO - 16:18:14:       The solution is feasible.
INFO - 16:18:14:       Objective: 0.0
INFO - 16:18:14:       Standardized constraints:
INFO - 16:18:14:          lower_bound_KS(g) = 2.7755575615628914e-16
INFO - 16:18:14:       Design space:
INFO - 16:18:14:          +------+-------------+-------+-------------+-------+
INFO - 16:18:14:          | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:18:14:          +------+-------------+-------+-------------+-------+
INFO - 16:18:14:          | x    |      0      |   0   |      1      | float |
INFO - 16:18:14:          | y    |      0      |   0   |      1      | float |
INFO - 16:18:14:          +------+-------------+-------+-------------+-------+
INFO - 16:18:14: *** End MDOScenario execution ***

with constraint aggregation the last iteration is faster.