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 - 16:21:47: *** Start MDOScenario execution ***
INFO - 16:21:47: MDOScenario
INFO - 16:21:47:    Disciplines: Concatenater function
INFO - 16:21:47:    MDO formulation: DisciplinaryOpt
INFO - 16:21:47: Optimization problem:
INFO - 16:21:47:    minimize o(x, y)
INFO - 16:21:47:    with respect to x, y
INFO - 16:21:47:    under the inequality constraints
INFO - 16:21:47:       g(x, y) <= 0
INFO - 16:21:47:    over the design space:
INFO - 16:21:47:       +------+-------------+-------+-------------+-------+
INFO - 16:21:47:       | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:21:47:       +------+-------------+-------+-------------+-------+
INFO - 16:21:47:       | x    |      0      | 0.005 |      1      | float |
INFO - 16:21:47:       | y    |      0      |   1   |      1      | float |
INFO - 16:21:47:       +------+-------------+-------+-------------+-------+
INFO - 16:21:47: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 16:21:47:      1%|          | 6/1000 [00:00<00:29, 33.56 it/sec, feas=True, obj=0.00931]
INFO - 16:21:47:      1%|          | 7/1000 [00:00<00:28, 35.18 it/sec, feas=True, obj=8.28e-5]
INFO - 16:21:47:      1%|          | 8/1000 [00:00<00:27, 36.67 it/sec, feas=True, obj=5.51e-9]
INFO - 16:21:54:      1%|          | 9/1000 [00:06<12:10,  1.36 it/sec, feas=True, obj=0]
INFO - 16:21:54: Optimization result:
INFO - 16:21:54:    Optimizer info:
INFO - 16:21:54:       Status: 5
INFO - 16:21:54:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
INFO - 16:21:54:    Solution:
INFO - 16:21:54:       The solution is feasible.
INFO - 16:21:54:       Objective: 0.0
INFO - 16:21:54:       Standardized constraints:
INFO - 16:21:54:          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 - 16:21:54:  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 - 16:21:54:  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 - 16:21:54:  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 - 16:21:54:  0. 0. 0. 0.]
INFO - 16:21:54:       Design space:
INFO - 16:21:54:          +------+-------------+-------+-------------+-------+
INFO - 16:21:54:          | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:21:54:          +------+-------------+-------+-------------+-------+
INFO - 16:21:54:          | x    |      0      |   0   |      1      | float |
INFO - 16:21:54:          | y    |      0      |   0   |      1      | float |
INFO - 16:21:54:          +------+-------------+-------+-------------+-------+
INFO - 16:21:54: *** 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 - 16:21:54: *** Start MDOScenario execution ***
INFO - 16:21:54: MDOScenario
INFO - 16:21:54:    Disciplines: Concatenater function
INFO - 16:21:54:    MDO formulation: DisciplinaryOpt
INFO - 16:21:54: Optimization problem:
INFO - 16:21:54:    minimize o(x, y)
INFO - 16:21:54:    with respect to x, y
INFO - 16:21:54:    under the inequality constraints
INFO - 16:21:54:       lower_bound_KS() <= 0.0
INFO - 16:21:54:    over the design space:
INFO - 16:21:54:       +------+-------------+-------+-------------+-------+
INFO - 16:21:54:       | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:21:54:       +------+-------------+-------+-------------+-------+
INFO - 16:21:54:       | x    |      0      | 0.005 |      1      | float |
INFO - 16:21:54:       | y    |      0      |   1   |      1      | float |
INFO - 16:21:54:       +------+-------------+-------+-------------+-------+
INFO - 16:21:54: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 16:21:54:      1%|          | 6/1000 [00:00<00:14, 68.39 it/sec, feas=True, obj=0.00773]
INFO - 16:21:54:      1%|          | 7/1000 [00:00<00:14, 68.32 it/sec, feas=True, obj=5.72e-5]
INFO - 16:21:54:      1%|          | 8/1000 [00:00<00:14, 68.17 it/sec, feas=True, obj=2.6e-9]
INFO - 16:21:54:      1%|          | 9/1000 [00:00<00:27, 35.74 it/sec, feas=True, obj=0]
INFO - 16:21:54: Optimization result:
INFO - 16:21:54:    Optimizer info:
INFO - 16:21:54:       Status: 5
INFO - 16:21:54:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
INFO - 16:21:54:    Solution:
INFO - 16:21:54:       The solution is feasible.
INFO - 16:21:54:       Objective: 0.0
INFO - 16:21:54:       Standardized constraints:
INFO - 16:21:54:          lower_bound_KS(g) = 2.7755575615628914e-16
INFO - 16:21:54:       Design space:
INFO - 16:21:54:          +------+-------------+-------+-------------+-------+
INFO - 16:21:54:          | Name | Lower bound | Value | Upper bound | Type  |
INFO - 16:21:54:          +------+-------------+-------+-------------+-------+
INFO - 16:21:54:          | x    |      0      |   0   |      1      | float |
INFO - 16:21:54:          | y    |      0      |   0   |      1      | float |
INFO - 16:21:54:          +------+-------------+-------+-------------+-------+
INFO - 16:21:54: *** End MDOScenario execution ***

with constraint aggregation the last iteration is faster.