Examples for constraint aggregation

from __future__ import annotations

from copy import deepcopy

from gemseo.algos.design_space import DesignSpace
from gemseo.algos.design_space import DesignVariableType
from gemseo.api import configure_logger
from gemseo.api import create_scenario
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=DesignVariableType.FLOAT
)
ds.add_variable("y", l_b=0.0, u_b=1, value=1, var_type=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 - 16:38:37:
    INFO - 16:38:37: *** Start MDOScenario execution ***
    INFO - 16:38:37: MDOScenario
    INFO - 16:38:37:    Disciplines: Concatenater function
    INFO - 16:38:37:    MDO formulation: DisciplinaryOpt
    INFO - 16:38:37: Optimization problem:
    INFO - 16:38:37:    minimize o(x, y)
    INFO - 16:38:37:    with respect to x, y
    INFO - 16:38:37:    subject to constraints:
    INFO - 16:38:37:       g(x, y) <= 0.0
    INFO - 16:38:37:    over the design space:
    INFO - 16:38:37:    +------+-------------+-------+-------------+-------+
    INFO - 16:38:37:    | name | lower_bound | value | upper_bound | type  |
    INFO - 16:38:37:    +------+-------------+-------+-------------+-------+
    INFO - 16:38:37:    | x    |      0      | 0.005 |      1      | float |
    INFO - 16:38:37:    | y    |      0      |   1   |      1      | float |
    INFO - 16:38:37:    +------+-------------+-------+-------------+-------+
    INFO - 16:38:37: Solving optimization problem with algorithm NLOPT_MMA:
    INFO - 16:38:37: ...   0%|          | 0/1000 [00:00<?, ?it]
    INFO - 16:38:37: ...   0%|          | 1/1000 [00:00<01:48,  9.21 it/sec, obj=1]
    INFO - 16:38:38: ...   0%|          | 2/1000 [00:00<01:27, 11.38 it/sec, obj=0.866]
    INFO - 16:38:38: ...   0%|          | 3/1000 [00:00<01:08, 14.60 it/sec, obj=0.616]
    INFO - 16:38:38: ...   0%|          | 4/1000 [00:00<00:58, 17.03 it/sec, obj=0.312]
    INFO - 16:38:38: ...   0%|          | 5/1000 [00:00<00:52, 18.87 it/sec, obj=0.0944]
    INFO - 16:38:38: ...   1%|          | 6/1000 [00:00<00:48, 20.36 it/sec, obj=0.00931]
    INFO - 16:38:38: ...   1%|          | 7/1000 [00:00<00:46, 21.47 it/sec, obj=8.28e-5]
    INFO - 16:38:38: ...   1%|          | 8/1000 [00:00<00:44, 22.48 it/sec, obj=5.2e-9]
    INFO - 16:38:56: ...   1%|          | 9/1000 [00:18<33:53, 29.24 it/min, obj=0]
    INFO - 16:38:56: Optimization result:
    INFO - 16:38:56:    Optimizer info:
    INFO - 16:38:56:       Status: 5
    INFO - 16:38:56:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 16:38:56:       Number of calls to the objective function by the optimizer: 1501
    INFO - 16:38:56:    Solution:
    INFO - 16:38:56:       The solution is feasible.
    INFO - 16:38:56:       Objective: 0.0
    INFO - 16:38:56:       Standardized constraints:
    INFO - 16:38:56:          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 - 16:38:56:  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 - 16:38:56:  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 - 16:38:56:  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 - 16:38:56:  0. 0. 0. 0.]
    INFO - 16:38:56:       Design space:
    INFO - 16:38:56:       +------+-------------+-------+-------------+-------+
    INFO - 16:38:56:       | name | lower_bound | value | upper_bound | type  |
    INFO - 16:38:56:       +------+-------------+-------+-------------+-------+
    INFO - 16:38:56:       | x    |      0      |   0   |      1      | float |
    INFO - 16:38:56:       | y    |      0      |   0   |      1      | float |
    INFO - 16:38:56:       +------+-------------+-------+-------------+-------+
    INFO - 16:38:56: *** End MDOScenario execution (time: 0:00:18.483471) ***

{'max_iter': 1000, 'algo': 'NLOPT_MMA', '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}}

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(
    method="KS", rho=10.0, constr_id=0
)
new_scenario.execute(algo_options)

    INFO - 16:38:56:
    INFO - 16:38:56: *** Start MDOScenario execution ***
    INFO - 16:38:56: MDOScenario
    INFO - 16:38:56:    Disciplines: Concatenater function
    INFO - 16:38:56:    MDO formulation: DisciplinaryOpt
    INFO - 16:38:56: Optimization problem:
    INFO - 16:38:56:    minimize o(x, y)
    INFO - 16:38:56:    with respect to x, y
    INFO - 16:38:56:    subject to constraints:
    INFO - 16:38:56:       KS() <= 0.0
    INFO - 16:38:56:    over the design space:
    INFO - 16:38:56:    +------+-------------+-------+-------------+-------+
    INFO - 16:38:56:    | name | lower_bound | value | upper_bound | type  |
    INFO - 16:38:56:    +------+-------------+-------+-------------+-------+
    INFO - 16:38:56:    | x    |      0      | 0.005 |      1      | float |
    INFO - 16:38:56:    | y    |      0      |   1   |      1      | float |
    INFO - 16:38:56:    +------+-------------+-------+-------------+-------+
    INFO - 16:38:56: Solving optimization problem with algorithm NLOPT_MMA:
    INFO - 16:38:56: ...   0%|          | 0/1000 [00:00<?, ?it]
    INFO - 16:38:56: ...   0%|          | 1/1000 [00:00<00:43, 23.04 it/sec, obj=1]
    INFO - 16:38:56: ...   0%|          | 2/1000 [00:00<00:44, 22.49 it/sec, obj=0.866]
    INFO - 16:38:56: ...   0%|          | 3/1000 [00:00<00:35, 27.86 it/sec, obj=0.592]
    INFO - 16:38:56: ...   0%|          | 4/1000 [00:00<00:31, 31.67 it/sec, obj=0.295]
    INFO - 16:38:56: ...   0%|          | 5/1000 [00:00<00:28, 34.33 it/sec, obj=0.0857]
    INFO - 16:38:56: ...   1%|          | 6/1000 [00:00<00:27, 36.33 it/sec, obj=0.00773]
    INFO - 16:38:56: ...   1%|          | 7/1000 [00:00<00:26, 38.15 it/sec, obj=5.72e-5]
    INFO - 16:38:56: ...   1%|          | 8/1000 [00:00<00:25, 39.62 it/sec, obj=2.62e-9]
    INFO - 16:38:56: ...   1%|          | 9/1000 [00:00<00:58, 17.06 it/sec, obj=0]
    INFO - 16:38:56: Optimization result:
    INFO - 16:38:56:    Optimizer info:
    INFO - 16:38:56:       Status: 5
    INFO - 16:38:56:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
    INFO - 16:38:56:       Number of calls to the objective function by the optimizer: 1501
    INFO - 16:38:56:    Solution:
    INFO - 16:38:56:       The solution is feasible.
    INFO - 16:38:56:       Objective: 0.0
    INFO - 16:38:56:       Standardized constraints:
    INFO - 16:38:56:          KS(g) = 4.440892098500626e-16
    INFO - 16:38:56:       Design space:
    INFO - 16:38:56:       +------+-------------+-------+-------------+-------+
    INFO - 16:38:56:       | name | lower_bound | value | upper_bound | type  |
    INFO - 16:38:56:       +------+-------------+-------+-------------+-------+
    INFO - 16:38:56:       | x    |      0      |   0   |      1      | float |
    INFO - 16:38:56:       | y    |      0      |   0   |      1      | float |
    INFO - 16:38:56:       +------+-------------+-------+-------------+-------+
    INFO - 16:38:56: *** End MDOScenario execution (time: 0:00:00.540389) ***

{'max_iter': 1000, 'algo': 'NLOPT_MMA', '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}}

with constraint aggregation the last iteration is faster.