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(
    disciplines=[disc, concat],
    formulation="DisciplinaryOpt",
    objective_name="o",
    design_space=ds,
    maximize_objective=False,
)
original_scenario.add_constraint("g", "ineq")

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

    INFO - 13:50:51:
    INFO - 13:50:51: *** Start MDOScenario execution ***
    INFO - 13:50:51: MDOScenario
    INFO - 13:50:51:    Disciplines: Concatenater function
    INFO - 13:50:51:    MDO formulation: DisciplinaryOpt
    INFO - 13:50:51: Optimization problem:
    INFO - 13:50:51:    minimize o(x, y)
    INFO - 13:50:51:    with respect to x, y
    INFO - 13:50:51:    subject to constraints:
    INFO - 13:50:51:       g(x, y) <= 0.0
    INFO - 13:50:51:    over the design space:
    INFO - 13:50:51:    +------+-------------+-------+-------------+-------+
    INFO - 13:50:51:    | name | lower_bound | value | upper_bound | type  |
    INFO - 13:50:51:    +------+-------------+-------+-------------+-------+
    INFO - 13:50:51:    | x    |      0      | 0.005 |      1      | float |
    INFO - 13:50:51:    | y    |      0      |   1   |      1      | float |
    INFO - 13:50:51:    +------+-------------+-------+-------------+-------+
    INFO - 13:50:51: Solving optimization problem with algorithm NLOPT_MMA:
    INFO - 13:50:51: ...   0%|          | 0/1000 [00:00<?, ?it]
    INFO - 13:50:51: ...   0%|          | 1/1000 [00:00<02:02,  8.15 it/sec, obj=1]
    INFO - 13:50:51: ...   0%|          | 2/1000 [00:00<02:21,  7.04 it/sec, obj=0.866]
    INFO - 13:50:51: ...   0%|          | 3/1000 [00:00<01:54,  8.72 it/sec, obj=0.616]
    INFO - 13:50:51: ...   0%|          | 4/1000 [00:00<01:40,  9.91 it/sec, obj=0.312]
    INFO - 13:50:51: ...   0%|          | 5/1000 [00:00<01:32, 10.76 it/sec, obj=0.0944]
    INFO - 13:50:51: ...   1%|          | 6/1000 [00:00<01:27, 11.42 it/sec, obj=0.00931]
    INFO - 13:50:51: ...   1%|          | 7/1000 [00:00<01:23, 11.96 it/sec, obj=8.28e-5]
    INFO - 13:50:51: ...   1%|          | 8/1000 [00:00<01:19, 12.41 it/sec, obj=5.2e-9]
    INFO - 13:51:08: ...   1%|          | 9/1000 [00:17<32:07, 30.85 it/min, obj=0]
    INFO - 13:51:08: Optimization result:
    INFO - 13:51:08:    Optimizer info:
    INFO - 13:51:08:       Status: 5
    INFO - 13:51:08:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 13:51:08:       Number of calls to the objective function by the optimizer: 1501
    INFO - 13:51:08:    Solution:
    INFO - 13:51:08:       The solution is feasible.
    INFO - 13:51:08:       Objective: 0.0
    INFO - 13:51:08:       Standardized constraints:
    INFO - 13:51:08:          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 - 13:51:08:  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 - 13:51:08:  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 - 13:51:08:  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 - 13:51:08:  0. 0. 0. 0.]
    INFO - 13:51:08:       Design space:
    INFO - 13:51:08:       +------+-------------+-------+-------------+-------+
    INFO - 13:51:08:       | name | lower_bound | value | upper_bound | type  |
    INFO - 13:51:08:       +------+-------------+-------+-------------+-------+
    INFO - 13:51:08:       | x    |      0      |   0   |      1      | float |
    INFO - 13:51:08:       | y    |      0      |   0   |      1      | float |
    INFO - 13:51:08:       +------+-------------+-------+-------------+-------+
    INFO - 13:51:08: *** End MDOScenario execution (time: 0:00:17.518967) ***

{'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(
    disciplines=[disc, concat],
    formulation="DisciplinaryOpt",
    objective_name="o",
    design_space=ds_new,
    maximize_objective=False,
)
new_scenario.add_constraint("g", "ineq")

This method aggregates the constraints using the KS function

new_scenario.formulation.opt_problem.aggregate_constraint(0, method="KS", rho=10.0)
new_scenario.execute(algo_options)

    INFO - 13:51:08:
    INFO - 13:51:08: *** Start MDOScenario execution ***
    INFO - 13:51:08: MDOScenario
    INFO - 13:51:08:    Disciplines: Concatenater function
    INFO - 13:51:08:    MDO formulation: DisciplinaryOpt
    INFO - 13:51:08: Optimization problem:
    INFO - 13:51:08:    minimize o(x, y)
    INFO - 13:51:08:    with respect to x, y
    INFO - 13:51:08:    subject to constraints:
    INFO - 13:51:08:       KS() <= 0.0
    INFO - 13:51:08:    over the design space:
    INFO - 13:51:08:    +------+-------------+-------+-------------+-------+
    INFO - 13:51:08:    | name | lower_bound | value | upper_bound | type  |
    INFO - 13:51:08:    +------+-------------+-------+-------------+-------+
    INFO - 13:51:08:    | x    |      0      | 0.005 |      1      | float |
    INFO - 13:51:08:    | y    |      0      |   1   |      1      | float |
    INFO - 13:51:08:    +------+-------------+-------+-------------+-------+
    INFO - 13:51:08: Solving optimization problem with algorithm NLOPT_MMA:
    INFO - 13:51:08: ...   0%|          | 0/1000 [00:00<?, ?it]
    INFO - 13:51:08: ...   0%|          | 1/1000 [00:00<00:44, 22.25 it/sec, obj=1]
    INFO - 13:51:08: ...   0%|          | 2/1000 [00:00<01:32, 10.80 it/sec, obj=0.866]
    INFO - 13:51:08: ...   0%|          | 3/1000 [00:00<01:17, 12.83 it/sec, obj=0.592]
    INFO - 13:51:08: ...   0%|          | 4/1000 [00:00<01:10, 14.15 it/sec, obj=0.295]
    INFO - 13:51:09: ...   0%|          | 5/1000 [00:00<01:06, 15.07 it/sec, obj=0.0857]
    INFO - 13:51:09: ...   1%|          | 6/1000 [00:00<01:03, 15.69 it/sec, obj=0.00773]
    INFO - 13:51:09: ...   1%|          | 7/1000 [00:00<01:01, 16.23 it/sec, obj=5.72e-5]
    INFO - 13:51:09: ...   1%|          | 8/1000 [00:00<00:59, 16.63 it/sec, obj=2.62e-9]
    INFO - 13:51:09: ...   1%|          | 9/1000 [00:00<01:28, 11.20 it/sec, obj=0]
    INFO - 13:51:09: Optimization result:
    INFO - 13:51:09:    Optimizer info:
    INFO - 13:51:09:       Status: 5
    INFO - 13:51:09:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 13:51:09:       Number of calls to the objective function by the optimizer: 1501
    INFO - 13:51:09:    Solution:
    INFO - 13:51:09:       The solution is feasible.
    INFO - 13:51:09:       Objective: 0.0
    INFO - 13:51:09:       Standardized constraints:
    INFO - 13:51:09:          KS(g) = 4.440892098500626e-16
    INFO - 13:51:09:       Design space:
    INFO - 13:51:09:       +------+-------------+-------+-------------+-------+
    INFO - 13:51:09:       | name | lower_bound | value | upper_bound | type  |
    INFO - 13:51:09:       +------+-------------+-------+-------------+-------+
    INFO - 13:51:09:       | x    |      0      |   0   |      1      | float |
    INFO - 13:51:09:       | y    |      0      |   0   |      1      | float |
    INFO - 13:51:09:       +------+-------------+-------+-------------+-------+
    INFO - 13:51:09: *** End MDOScenario execution (time: 0:00:00.817794) ***

{'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.