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

.. only:: html

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

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

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

.. _sphx_glr_examples_multi_objective_plot_pareto_front_binhkorn_bilevel.py:


Pareto front on the Binh and Korn problem using a BiLevel formulation
=====================================================================

In this example,
we illustrate the computation of a Pareto front plot for the Binh and Korn problem.
We use a BiLevel formulation in order to only compute the Pareto-optimal points.

.. GENERATED FROM PYTHON SOURCE LINES 31-35

Import
------
The first step is to import some high-level functions
and to configure the logger.

.. GENERATED FROM PYTHON SOURCE LINES 35-51

.. code-block:: Python

    from __future__ import annotations

    from copy import deepcopy
    from logging import WARNING

    from numpy import array

    from gemseo import configure_logger
    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import execute_post

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 52-58

Definition of the disciplines
-----------------------------

In this example,
we create the Binh and Korn disciplines from scratch by declaring
their expressions and using the :class:`.AnalyticDiscipline`.

.. GENERATED FROM PYTHON SOURCE LINES 58-66

.. code-block:: Python


    expr_binh_korn = {
        "obj1": "4*x1**2 + 4*x2**2",
        "obj2": "(x1-5.)**2 + (x2-5.)**2",
        "cstr1": "(x1-5.)**2 + x2**2 - 25.",
        "cstr2": "-(x1-8.)**2 - (x2+3)**2 + 7.7",
    }








.. GENERATED FROM PYTHON SOURCE LINES 67-69

This constraint will be used to set `obj1` to a target value for
the lower-level scenario.

.. GENERATED FROM PYTHON SOURCE LINES 69-72

.. code-block:: Python


    expr_cstr_obj1_target = {"cstr3": "obj1 - obj1_target"}








.. GENERATED FROM PYTHON SOURCE LINES 73-77

Instantiation of the disciplines
--------------------------------

Here, we create the disciplines from their expressions.

.. GENERATED FROM PYTHON SOURCE LINES 77-85

.. code-block:: Python


    discipline_binh_korn = create_discipline(
        "AnalyticDiscipline", expressions=expr_binh_korn
    )
    discipline_cstr_obj1 = create_discipline(
        "AnalyticDiscipline", expressions=expr_cstr_obj1_target
    )








.. GENERATED FROM PYTHON SOURCE LINES 86-88

Definition of the lower-level design space
------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 88-102

.. code-block:: Python


    design_space = create_design_space()
    design_space.add_variable(
        "x1", lower_bound=array([0.0]), upper_bound=array([5.0]), value=array([2.0])
    )
    design_space.add_variable(
        "x2", lower_bound=array([-5.0]), upper_bound=array([3.0]), value=array([2.0])
    )

    disciplines = [
        discipline_binh_korn,
        discipline_cstr_obj1,
    ]








.. GENERATED FROM PYTHON SOURCE LINES 103-106

Creation of the lower-level scenario
------------------------------------
This scenario aims at finding the `obj2` optimal value for a specific value of `obj1`.

.. GENERATED FROM PYTHON SOURCE LINES 106-116

.. code-block:: Python


    sub_scenario = create_scenario(
        disciplines,
        "obj2",
        design_space,
        formulation_name="DisciplinaryOpt",
    )

    sub_scenario.set_algorithm(algo_name="NLOPT_SLSQP", max_iter=100)








.. GENERATED FROM PYTHON SOURCE LINES 117-118

We add the Binh and Korn problem constraints.

.. GENERATED FROM PYTHON SOURCE LINES 118-121

.. code-block:: Python

    sub_scenario.add_constraint("cstr1", constraint_type="ineq")
    sub_scenario.add_constraint("cstr2", constraint_type="ineq")








.. GENERATED FROM PYTHON SOURCE LINES 122-126

Creation of the design space for the system-level scenario
----------------------------------------------------------
At the system level, we will fix a target for the `obj1` value of
the lower-level scenario.

.. GENERATED FROM PYTHON SOURCE LINES 126-134

.. code-block:: Python

    system_design_space = create_design_space()
    system_design_space.add_variable(
        "obj1_target",
        lower_bound=array([0.1]),
        upper_bound=array([100.0]),
        value=array([1.0]),
    )








.. GENERATED FROM PYTHON SOURCE LINES 135-142

Creation of the system-level DOE Scenario
-----------------------------------------
The system-level scenario will perform a DOE over the `obj1_target` variable.
We will use the `BiLevel` formulation to nest the lower-level scenario into the DOE.
The log level for the sub scenarios is set to `WARNING` to avoid getting the complete
log of each sub scenario, which would be too verbose. Set it to `INFO` if you wish to
keep the logs of each sub scenario as well.

.. GENERATED FROM PYTHON SOURCE LINES 142-152

.. code-block:: Python


    system_scenario = create_scenario(
        sub_scenario,
        "obj1",
        system_design_space,
        scenario_type="DOE",
        formulation_name="BiLevel",
        sub_scenarios_log_level=WARNING,
    )





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

 .. code-block:: none

     WARNING - 11:43:00: No strongly coupled disciplines detected, MDA1 is disabled in the BiLevel formulation




.. GENERATED FROM PYTHON SOURCE LINES 153-168

.. tip::

   When running BiLevel scenarios, it is interesting to access the optimization
   history of the sub-scenarios for each system iteration. By default, the setting
   ``keep_opt_history`` is set to ``True``. This allows you to store in memory the
   databases of the sub-scenarios (see the last section of this example for more
   details).
   In some cases, storing the databases in memory can take up too much space and cause
   performance issues. In these cases, set ``keep_opt_history=False`` and save the
   databases to the disk using ``save_opt_history=True``. If your sub-scenarios are
   running in parallel, and you are saving the optimization histories to the disk, set
   the ``naming`` setting to ``"UUID"``, which is multiprocessing-safe.
   The setting ``keep_opt_history`` will not work if the sub-scenarios are running in
   parallel because the databases are not copied from the sub-processes to the main
   process. In this case you shall always save the optimization history to the disk.

.. GENERATED FROM PYTHON SOURCE LINES 170-179

Add the system-level constraint and observables
-----------------------------------------------
Here, we add the constraint on the `obj1_target`, this way we make sure that the
lower-level scenario will respect the target imposed by the system.
The BiLevel formulation will automatically add the constraints from the system-level
to the lower-level, if you wish to handle the constraints manually, pass
`apply_cstr_tosub_scenarios=False` as an argument to `create_scenario`.
Note that `obj2` shall be added as an observable of `scenario_doe`,
otherwise it cannot be used by the ParetoFront post-processing.

.. GENERATED FROM PYTHON SOURCE LINES 179-182

.. code-block:: Python

    system_scenario.add_constraint("cstr3")
    system_scenario.add_observable("obj2")
    system_scenario.xdsmize(save_html=False, pdf_build=False)





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

        <script type="text/javascript">
            document.addEventListener('DOMContentLoaded', () => {
              const mdo = {
      "root": {
        "nodes": [
          {
            "id": "Opt",
            "name": "DOE",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "MDOScenario_scn-1-1",
            "type": "mdo",
            "subxdsm": "MDOScenario_scn-1-1",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "AnalyticDiscipline",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis3",
            "name": "AnalyticDiscipline",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "obj1_target^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "obj1^*, cstr3^*, obj2^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "obj1, obj2"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "obj1_target"
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          {
            "from": "Dis3",
            "to": "Opt",
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          {
            "from": "Dis2",
            "to": "_U_",
            "name": "cstr1^*, cstr2^*"
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          {
            "from": "Dis2",
            "to": "Opt",
            "name": "obj1, obj2"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "cstr3"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "x1, x2"
          },
          {
            "from": "Dis1",
            "to": "Dis3",
            "name": "obj1"
          },
          {
            "from": "Dis2",
            "to": "Dis3",
            "name": "obj1"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2",
              "Dis3"
            ]
          ]
        ],
        "optpb": ""
      },
      "MDOScenario_scn-1-1": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "AnalyticDiscipline",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "AnalyticDiscipline",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x1^(0), x2^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "obj2^*, cstr1^*, cstr2^*, cstr3^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x1, x2"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "cstr1, cstr2, obj2"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "cstr3"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "obj1^*"
          },
          {
            "from": "Dis1",
            "to": "Opt",
            "name": "obj2, cstr1, cstr2"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "cstr3"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "obj1"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2"
            ]
          ]
        ],
        "optpb": ""
      }
    };
              const config = {
                labelizer: {
                    ellipsis: 5,
                    subSupScript: false,
                    showLinkNbOnly: false,
                },
                layout: {
                    origin: { x: 50, y: 20 },
                    cellsize: { w: 150, h: 50 },
                    padding: 10,
                },
                withDefaultDriver: true,
                withTitleTooltip: true,
              };
              xdsmjs.XDSMjs(config).createXdsm(mdo);
            });
        </script>
        <div class='xdsm-toolbar'></div><div class='xdsm2'></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 183-186

Run the scenario
----------------
Finally, we run a full-factorial DOE using 100 samples and run the post-processing.

.. GENERATED FROM PYTHON SOURCE LINES 186-191

.. code-block:: Python

    system_scenario.execute(algo_name="PYDOE_FULLFACT", n_samples=50)
    system_scenario.post_process(
        post_name="ParetoFront", objectives=["obj1", "obj2"], save=False, show=True
    )




.. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_001.png
   :alt: Pareto front
   :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 11:43:00: *** Start DOEScenario execution ***
        INFO - 11:43:00: DOEScenario
        INFO - 11:43:00:    Disciplines: MDOScenario
        INFO - 11:43:00:    MDO formulation: BiLevel
        INFO - 11:43:00: Optimization problem:
        INFO - 11:43:00:    minimize obj1(obj1_target)
        INFO - 11:43:00:    with respect to obj1_target
        INFO - 11:43:00:    subject to constraints:
        INFO - 11:43:00:       cstr3(obj1_target) == 0
        INFO - 11:43:00:    over the design space:
        INFO - 11:43:00:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:43:00:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 11:43:00:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:43:00:       | obj1_target |     0.1     |   1   |     100     | float |
        INFO - 11:43:00:       +-------------+-------------+-------+-------------+-------+
        INFO - 11:43:00: Solving optimization problem with algorithm PYDOE_FULLFACT:
        INFO - 11:43:00:      2%|▏         | 1/50 [00:00<00:02, 17.83 it/sec, obj=0.108]
        INFO - 11:43:01:      4%|▍         | 2/50 [00:00<00:02, 23.11 it/sec, obj=2.14]
        INFO - 11:43:01:      6%|▌         | 3/50 [00:00<00:01, 27.49 it/sec, obj=4.18]
        INFO - 11:43:01:      8%|▊         | 4/50 [00:00<00:01, 30.49 it/sec, obj=6.22]
        INFO - 11:43:01:     10%|█         | 5/50 [00:00<00:01, 32.78 it/sec, obj=8.26]
        INFO - 11:43:01:     12%|█▏        | 6/50 [00:00<00:01, 33.85 it/sec, obj=10.3]
        INFO - 11:43:01:     14%|█▍        | 7/50 [00:00<00:01, 34.21 it/sec, obj=12.3]
        INFO - 11:43:01:     16%|█▌        | 8/50 [00:00<00:01, 34.67 it/sec, obj=14.4]
        INFO - 11:43:01:     18%|█▊        | 9/50 [00:00<00:01, 35.20 it/sec, obj=16.4]
        INFO - 11:43:01:     20%|██        | 10/50 [00:00<00:01, 35.61 it/sec, obj=18.5]
        INFO - 11:43:01:     22%|██▏       | 11/50 [00:00<00:01, 36.62 it/sec, obj=20.5]
        INFO - 11:43:01:     24%|██▍       | 12/50 [00:00<00:01, 37.43 it/sec, obj=22.5]
        INFO - 11:43:01:     26%|██▌       | 13/50 [00:00<00:00, 38.16 it/sec, obj=24.6]
        INFO - 11:43:01:     28%|██▊       | 14/50 [00:00<00:00, 38.81 it/sec, obj=26.6]
        INFO - 11:43:01:     30%|███       | 15/50 [00:00<00:00, 39.39 it/sec, obj=28.6]
        INFO - 11:43:01:     32%|███▏      | 16/50 [00:00<00:00, 39.92 it/sec, obj=30.7]
        INFO - 11:43:01:     34%|███▍      | 17/50 [00:00<00:00, 40.38 it/sec, obj=32.7]
        INFO - 11:43:01:     36%|███▌      | 18/50 [00:00<00:00, 40.67 it/sec, obj=34.8]
        INFO - 11:43:01:     38%|███▊      | 19/50 [00:00<00:00, 41.04 it/sec, obj=36.8]
        INFO - 11:43:01:     40%|████      | 20/50 [00:00<00:00, 39.70 it/sec, obj=38.8]
        INFO - 11:43:01:     42%|████▏     | 21/50 [00:00<00:00, 40.06 it/sec, obj=40.9]
        INFO - 11:43:01:     44%|████▍     | 22/50 [00:00<00:00, 40.36 it/sec, obj=42.9]
        INFO - 11:43:01:     46%|████▌     | 23/50 [00:00<00:00, 40.13 it/sec, obj=45]
        INFO - 11:43:01:     48%|████▊     | 24/50 [00:00<00:00, 40.35 it/sec, obj=47]
        INFO - 11:43:01:     50%|█████     | 25/50 [00:00<00:00, 40.58 it/sec, obj=49]
        INFO - 11:43:01:     52%|█████▏    | 26/50 [00:00<00:00, 40.40 it/sec, obj=51.1]
        INFO - 11:43:01:     54%|█████▍    | 27/50 [00:00<00:00, 40.63 it/sec, obj=53.1]
        INFO - 11:43:01:     56%|█████▌    | 28/50 [00:00<00:00, 40.85 it/sec, obj=55.1]
        INFO - 11:43:01:     58%|█████▊    | 29/50 [00:00<00:00, 41.06 it/sec, obj=57.2]
        INFO - 11:43:01:     60%|██████    | 30/50 [00:00<00:00, 41.24 it/sec, obj=59.2]
        INFO - 11:43:01:     62%|██████▏   | 31/50 [00:00<00:00, 41.35 it/sec, obj=61.3]
        INFO - 11:43:01:     64%|██████▍   | 32/50 [00:00<00:00, 41.37 it/sec, obj=63.3]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     66%|██████▌   | 33/50 [00:00<00:00, 41.54 it/sec, obj=65.3]
        INFO - 11:43:01:     68%|██████▊   | 34/50 [00:00<00:00, 41.67 it/sec, obj=67.4]
        INFO - 11:43:01:     70%|███████   | 35/50 [00:00<00:00, 41.82 it/sec, obj=69.4]
        INFO - 11:43:01:     72%|███████▏  | 36/50 [00:00<00:00, 42.04 it/sec, obj=71.5]
        INFO - 11:43:01:     74%|███████▍  | 37/50 [00:00<00:00, 42.44 it/sec, obj=73.5]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     76%|███████▌  | 38/50 [00:00<00:00, 42.80 it/sec, obj=75.5]
        INFO - 11:43:01:     78%|███████▊  | 39/50 [00:00<00:00, 43.14 it/sec, obj=77.6]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     80%|████████  | 40/50 [00:00<00:00, 43.60 it/sec, obj=79.6]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     82%|████████▏ | 41/50 [00:00<00:00, 44.05 it/sec, obj=81.7]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     84%|████████▍ | 42/50 [00:00<00:00, 44.49 it/sec, obj=83.7]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     86%|████████▌ | 43/50 [00:00<00:00, 44.83 it/sec, obj=85.7]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     88%|████████▊ | 44/50 [00:00<00:00, 45.23 it/sec, obj=87.8]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     90%|█████████ | 45/50 [00:00<00:00, 45.64 it/sec, obj=89.8]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     92%|█████████▏| 46/50 [00:00<00:00, 46.04 it/sec, obj=91.8]
        INFO - 11:43:01:     94%|█████████▍| 47/50 [00:01<00:00, 46.40 it/sec, obj=93.9]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     96%|█████████▌| 48/50 [00:01<00:00, 46.78 it/sec, obj=95.9]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:     98%|█████████▊| 49/50 [00:01<00:00, 47.14 it/sec, obj=98]
       ERROR - 11:43:01: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 11:43:01:    100%|██████████| 50/50 [00:01<00:00, 47.50 it/sec, obj=100]
        INFO - 11:43:01: Optimization result:
        INFO - 11:43:01:    Optimizer info:
        INFO - 11:43:01:       Status: None
        INFO - 11:43:01:       Message: None
        INFO - 11:43:01:       Number of calls to the objective function by the optimizer: 50
        INFO - 11:43:01:    Solution:
        INFO - 11:43:01:       The solution is feasible.
        INFO - 11:43:01:       Objective: 0.10832777706440924
        INFO - 11:43:01:       Standardized constraints:
        INFO - 11:43:01:          cstr3 = 0.008327777064409236
        INFO - 11:43:01:       Design space:
        INFO - 11:43:01:          +-------------+-------------+-------+-------------+-------+
        INFO - 11:43:01:          | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 11:43:01:          +-------------+-------------+-------+-------------+-------+
        INFO - 11:43:01:          | obj1_target |     0.1     |  0.1  |     100     | float |
        INFO - 11:43:01:          +-------------+-------------+-------+-------------+-------+
        INFO - 11:43:01: *** End DOEScenario execution (time: 0:00:01.055850) ***

    <gemseo.post.pareto_front.ParetoFront object at 0x70492a4ee3c0>



.. GENERATED FROM PYTHON SOURCE LINES 192-200

Plot the sub-scenario histories of the 2 first system iterations
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The code below will not work if you ran the system scenario with ``n_processes`` > 1.
Indeed, parallel execution of sub-scenarios prevents us to save the databases from
each sub-process to the main process. If you ran the system scenario with many
processes, you can still save the databases to the disk with
``save_opt_history=True`` and ``naming="UUID"``. Refer to the formulation settings for
more information.

.. GENERATED FROM PYTHON SOURCE LINES 200-205

.. code-block:: Python

    sub_scenario_databases = system_scenario.formulation.scenario_adapters[0].databases
    for database in sub_scenario_databases[:2]:
        opt_problem = deepcopy(sub_scenario.formulation.optimization_problem)
        opt_problem.database = database
        execute_post(opt_problem, post_name="OptHistoryView", save=False, show=True)



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_004.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_005.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_006.png
         :alt: Evolution of the equality constraints
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_006.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_007.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_008.png
         :alt: Evolution of the objective value
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_009.png
         :alt: Evolution of the distance to the optimum
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_009.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_010.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_010.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_011.png
         :alt: Evolution of the equality constraints
         :srcset: /examples/multi_objective/images/sphx_glr_plot_pareto_front_binhkorn_bilevel_011.png
         :class: sphx-glr-multi-img






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

   **Total running time of the script:** (0 minutes 3.370 seconds)


.. _sphx_glr_download_examples_multi_objective_plot_pareto_front_binhkorn_bilevel.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_pareto_front_binhkorn_bilevel.ipynb <plot_pareto_front_binhkorn_bilevel.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_pareto_front_binhkorn_bilevel.py <plot_pareto_front_binhkorn_bilevel.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_pareto_front_binhkorn_bilevel.zip <plot_pareto_front_binhkorn_bilevel.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_