.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/constraint_aggregation/plot_constraint_aggregation_example.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_constraint_aggregation_plot_constraint_aggregation_example.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_constraint_aggregation_plot_constraint_aggregation_example.py:


Examples for constraint aggregation
===================================

.. GENERATED FROM PYTHON SOURCE LINES 20-32

.. code-block:: Python


    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()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 33-34

Number of constraints

.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: Python

    N = 100








.. GENERATED FROM PYTHON SOURCE LINES 37-38

Build the discipline

.. GENERATED FROM PYTHON SOURCE LINES 38-48

.. code-block:: Python

    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")








.. GENERATED FROM PYTHON SOURCE LINES 49-50

Build the design space

.. GENERATED FROM PYTHON SOURCE LINES 50-63

.. code-block:: Python

    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)







.. GENERATED FROM PYTHON SOURCE LINES 64-65

Build the optimization solver options

.. GENERATED FROM PYTHON SOURCE LINES 65-84

.. code-block:: Python

    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,
        },
    }








.. GENERATED FROM PYTHON SOURCE LINES 85-86

Build the optimization scenario

.. GENERATED FROM PYTHON SOURCE LINES 86-99

.. code-block:: Python

    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.





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 08:55:46:  
        INFO - 08:55:46: *** Start MDOScenario execution ***
        INFO - 08:55:46: MDOScenario
        INFO - 08:55:46:    Disciplines: Concatenater function
        INFO - 08:55:46:    MDO formulation: DisciplinaryOpt
        INFO - 08:55:46: Optimization problem:
        INFO - 08:55:46:    minimize o(x, y)
        INFO - 08:55:46:    with respect to x, y
        INFO - 08:55:46:    subject to constraints:
        INFO - 08:55:46:       g(x, y) <= 0.0
        INFO - 08:55:46:    over the design space:
        INFO - 08:55:46:       +------+-------------+-------+-------------+-------+
        INFO - 08:55:46:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:55:46:       +------+-------------+-------+-------------+-------+
        INFO - 08:55:46:       | x    |      0      | 0.005 |      1      | float |
        INFO - 08:55:46:       | y    |      0      |   1   |      1      | float |
        INFO - 08:55:46:       +------+-------------+-------+-------------+-------+
        INFO - 08:55:46: Solving optimization problem with algorithm NLOPT_MMA:
        INFO - 08:55:46:      1%|          | 6/1000 [00:00<01:04, 15.36 it/sec, obj=0.00931]
        INFO - 08:55:47:      1%|          | 7/1000 [00:00<01:01, 16.10 it/sec, obj=8.28e-5]
        INFO - 08:55:47:      1%|          | 8/1000 [00:00<00:59, 16.74 it/sec, obj=5.2e-9]
        INFO - 08:55:59:      1%|          | 9/1000 [00:13<24:16, 40.83 it/min, obj=0]
        INFO - 08:55:59: Optimization result:
        INFO - 08:55:59:    Optimizer info:
        INFO - 08:55:59:       Status: 5
        INFO - 08:55:59:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
        INFO - 08:55:59:       Number of calls to the objective function by the optimizer: 1501
        INFO - 08:55:59:    Solution:
        INFO - 08:55:59:       The solution is feasible.
        INFO - 08:55:59:       Objective: 0.0
        INFO - 08:55:59:       Standardized constraints:
        INFO - 08:55:59:          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 - 08:55:59:  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 - 08:55:59:  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 - 08:55:59:  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 - 08:55:59:  0. 0. 0. 0.]
        INFO - 08:55:59:       Design space:
        INFO - 08:55:59:          +------+-------------+-------+-------------+-------+
        INFO - 08:55:59:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:55:59:          +------+-------------+-------+-------------+-------+
        INFO - 08:55:59:          | x    |      0      |   0   |      1      | float |
        INFO - 08:55:59:          | y    |      0      |   0   |      1      | float |
        INFO - 08:55:59:          +------+-------------+-------+-------------+-------+
        INFO - 08:55:59: *** End MDOScenario execution (time: 0:00:13.240145) ***

    {'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'}



.. GENERATED FROM PYTHON SOURCE LINES 100-101

exploiting constraint aggregation on the same scenario:

.. GENERATED FROM PYTHON SOURCE LINES 101-110

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 111-112

This method aggregates the constraints using the lower bound KS function

.. GENERATED FROM PYTHON SOURCE LINES 112-117

.. code-block:: Python

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





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        INFO - 08:55:59:  
        INFO - 08:55:59: *** Start MDOScenario execution ***
        INFO - 08:55:59: MDOScenario
        INFO - 08:55:59:    Disciplines: Concatenater function
        INFO - 08:55:59:    MDO formulation: DisciplinaryOpt
        INFO - 08:55:59: Optimization problem:
        INFO - 08:55:59:    minimize o(x, y)
        INFO - 08:55:59:    with respect to x, y
        INFO - 08:55:59:    subject to constraints:
        INFO - 08:55:59:       lower_bound_KS() <= 0.0
        INFO - 08:55:59:    over the design space:
        INFO - 08:55:59:       +------+-------------+-------+-------------+-------+
        INFO - 08:55:59:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:55:59:       +------+-------------+-------+-------------+-------+
        INFO - 08:55:59:       | x    |      0      | 0.005 |      1      | float |
        INFO - 08:55:59:       | y    |      0      |   1   |      1      | float |
        INFO - 08:55:59:       +------+-------------+-------+-------------+-------+
        INFO - 08:55:59: Solving optimization problem with algorithm NLOPT_MMA:
        INFO - 08:56:00:      1%|          | 6/1000 [00:00<00:46, 21.53 it/sec, obj=0.00773]
        INFO - 08:56:00:      1%|          | 7/1000 [00:00<00:44, 22.28 it/sec, obj=5.72e-5]
        INFO - 08:56:00:      1%|          | 8/1000 [00:00<00:43, 22.89 it/sec, obj=2.63e-9]
        INFO - 08:56:00:      1%|          | 9/1000 [00:00<01:05, 15.05 it/sec, obj=0]
        INFO - 08:56:00: Optimization result:
        INFO - 08:56:00:    Optimizer info:
        INFO - 08:56:00:       Status: 5
        INFO - 08:56:00:       Message: NLOPT_MAXEVAL_REACHED: Optimization stopped because maxeval (above) was reached
        INFO - 08:56:00:       Number of calls to the objective function by the optimizer: 1501
        INFO - 08:56:00:    Solution:
        INFO - 08:56:00:       The solution is feasible.
        INFO - 08:56:00:       Objective: 0.0
        INFO - 08:56:00:       Standardized constraints:
        INFO - 08:56:00:          lower_bound_KS(g) = 2.7755575615628914e-16
        INFO - 08:56:00:       Design space:
        INFO - 08:56:00:          +------+-------------+-------+-------------+-------+
        INFO - 08:56:00:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:56:00:          +------+-------------+-------+-------------+-------+
        INFO - 08:56:00:          | x    |      0      |   0   |      1      | float |
        INFO - 08:56:00:          | y    |      0      |   0   |      1      | float |
        INFO - 08:56:00:          +------+-------------+-------+-------------+-------+
        INFO - 08:56:00: *** End MDOScenario execution (time: 0:00:00.611147) ***

    {'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'}



.. GENERATED FROM PYTHON SOURCE LINES 118-119

with constraint aggregation the last iteration is faster.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 15.373 seconds)


.. _sphx_glr_download_examples_constraint_aggregation_plot_constraint_aggregation_example.py:

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