.. 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 35-49

.. code-block:: Python

    from __future__ import annotations

    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

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 50-56

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 56-64

.. 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 65-67

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

.. GENERATED FROM PYTHON SOURCE LINES 67-70

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 71-75

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

Here, we create the disciplines from their expressions.

.. GENERATED FROM PYTHON SOURCE LINES 75-83

.. 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 84-86

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

.. GENERATED FROM PYTHON SOURCE LINES 86-96

.. code-block:: Python


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

    disciplines = [
        discipline_binh_korn,
        discipline_cstr_obj1,
    ]








.. GENERATED FROM PYTHON SOURCE LINES 97-100

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 100-110

.. code-block:: Python


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

    sub_scenario.default_inputs = {"algo": "NLOPT_SLSQP", "max_iter": 100}








.. GENERATED FROM PYTHON SOURCE LINES 111-112

We add the Binh and Korn problem constraints.

.. GENERATED FROM PYTHON SOURCE LINES 112-115

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 116-120

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 120-125

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 126-133

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 133-143

.. code-block:: Python


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





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

 .. code-block:: none

     WARNING - 13:53:14: No strongly coupled disciplines detected,  MDA1 is deactivated in the BiLevel formulation




.. GENERATED FROM PYTHON SOURCE LINES 144-153

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 153-156

.. code-block:: Python

    system_scenario.add_constraint("cstr3")
    system_scenario.add_observable("obj2")
    system_scenario.xdsmize()





.. 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": "Optimizer",
            "type": "optimization"
          },
          {
            "id": "Dis1",
            "name": "MDOScenario_scn-1-1",
            "type": "mdo",
            "subxdsm": "MDOScenario_scn-1-1"
          },
          {
            "id": "Dis2",
            "name": "AnalyticDiscipline",
            "type": "analysis"
          },
          {
            "id": "Dis3",
            "name": "AnalyticDiscipline",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "obj1_target^(0)"
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          {
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            "to": "_U_",
            "name": "obj1^*, cstr3^*, obj2^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "obj1, obj2"
          },
          {
            "from": "Opt",
            "to": "Dis3",
            "name": "obj1_target"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "cstr3"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "cstr1^*, cstr2^*"
          },
          {
            "from": "Dis2",
            "to": "Opt",
            "name": "obj1, obj2"
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          {
            "from": "Dis3",
            "to": "Opt",
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          {
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            "from": "Dis1",
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        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2",
              "Dis3"
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        ],
        "optpb": "Optimization problem:\n   minimize obj1(obj1_target)\n   with respect to obj1_target\n   subject to constraints:\n      cstr3(obj1_target) == 0.0"
      },
      "MDOScenario_scn-1-1": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization"
          },
          {
            "id": "Dis1",
            "name": "AnalyticDiscipline",
            "type": "analysis"
          },
          {
            "id": "Dis2",
            "name": "AnalyticDiscipline",
            "type": "analysis"
          }
        ],
        "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": "Optimization problem:\n   minimize obj2(x1, x2)\n   with respect to x1, x2\n   subject to constraints:\n      cstr1(x1, x2) <= 0.0\n      cstr2(x1, x2) <= 0.0\n      cstr3(x1, x2) == 0.0"
      }
    };
              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 157-160

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

.. GENERATED FROM PYTHON SOURCE LINES 160-165

.. code-block:: Python

    run_inputs = {"n_samples": 50, "algo": "fullfact"}
    system_scenario.execute(run_inputs)
    system_scenario.post_process(
        "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 - 13:53:14:  
        INFO - 13:53:14: *** Start DOEScenario execution ***
        INFO - 13:53:14: DOEScenario
        INFO - 13:53:14:    Disciplines: MDOScenario
        INFO - 13:53:14:    MDO formulation: BiLevel
        INFO - 13:53:14: Optimization problem:
        INFO - 13:53:14:    minimize obj1(obj1_target)
        INFO - 13:53:14:    with respect to obj1_target
        INFO - 13:53:14:    subject to constraints:
        INFO - 13:53:14:       cstr3(obj1_target) == 0.0
        INFO - 13:53:14:    over the design space:
        INFO - 13:53:14:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:53:14:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:14:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:53:14:       | obj1_target |     0.1     |   1   |     100     | float |
        INFO - 13:53:14:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:53:14: Solving optimization problem with algorithm fullfact:
        INFO - 13:53:14:      2%|▏         | 1/50 [00:00<00:07,  7.00 it/sec, obj=0.108]
        INFO - 13:53:14:      4%|▍         | 2/50 [00:00<00:05,  9.14 it/sec, obj=2.14]
        INFO - 13:53:14:      6%|▌         | 3/50 [00:00<00:04, 10.74 it/sec, obj=4.18]
        INFO - 13:53:14:      8%|▊         | 4/50 [00:00<00:03, 11.84 it/sec, obj=6.22]
        INFO - 13:53:14:     10%|█         | 5/50 [00:00<00:03, 12.50 it/sec, obj=8.26]
        INFO - 13:53:15:     12%|█▏        | 6/50 [00:00<00:03, 12.86 it/sec, obj=10.3]
        INFO - 13:53:15:     14%|█▍        | 7/50 [00:00<00:03, 13.04 it/sec, obj=12.3]
        INFO - 13:53:15:     16%|█▌        | 8/50 [00:00<00:03, 13.14 it/sec, obj=14.4]
        INFO - 13:53:15:     18%|█▊        | 9/50 [00:00<00:03, 13.27 it/sec, obj=16.4]
        INFO - 13:53:15:     20%|██        | 10/50 [00:00<00:02, 13.35 it/sec, obj=18.5]
        INFO - 13:53:15:     22%|██▏       | 11/50 [00:00<00:02, 13.58 it/sec, obj=20.5]
        INFO - 13:53:15:     24%|██▍       | 12/50 [00:00<00:02, 13.79 it/sec, obj=22.5]
        INFO - 13:53:15:     26%|██▌       | 13/50 [00:00<00:02, 13.96 it/sec, obj=24.6]
        INFO - 13:53:15:     28%|██▊       | 14/50 [00:00<00:02, 14.11 it/sec, obj=26.6]
        INFO - 13:53:15:     30%|███       | 15/50 [00:01<00:02, 14.22 it/sec, obj=28.6]
        INFO - 13:53:15:     32%|███▏      | 16/50 [00:01<00:02, 14.29 it/sec, obj=30.7]
        INFO - 13:53:15:     34%|███▍      | 17/50 [00:01<00:02, 14.34 it/sec, obj=32.7]
        INFO - 13:53:15:     36%|███▌      | 18/50 [00:01<00:02, 14.36 it/sec, obj=34.8]
        INFO - 13:53:15:     38%|███▊      | 19/50 [00:01<00:02, 14.40 it/sec, obj=36.8]
        INFO - 13:53:16:     40%|████      | 20/50 [00:01<00:02, 14.10 it/sec, obj=38.8]
        INFO - 13:53:16:     42%|████▏     | 21/50 [00:01<00:02, 14.13 it/sec, obj=40.9]
        INFO - 13:53:16:     44%|████▍     | 22/50 [00:01<00:01, 14.15 it/sec, obj=42.9]
        INFO - 13:53:16:     46%|████▌     | 23/50 [00:01<00:01, 14.07 it/sec, obj=45]
        INFO - 13:53:16:     48%|████▊     | 24/50 [00:01<00:01, 14.08 it/sec, obj=47]
        INFO - 13:53:16:     50%|█████     | 25/50 [00:01<00:01, 14.08 it/sec, obj=49]
        INFO - 13:53:16:     52%|█████▏    | 26/50 [00:01<00:01, 14.00 it/sec, obj=51.1]
        INFO - 13:53:16:     54%|█████▍    | 27/50 [00:01<00:01, 14.00 it/sec, obj=53.1]
        INFO - 13:53:16:     56%|█████▌    | 28/50 [00:02<00:01, 14.00 it/sec, obj=55.1]
        INFO - 13:53:16:     58%|█████▊    | 29/50 [00:02<00:01, 13.99 it/sec, obj=57.2]
        INFO - 13:53:16:     60%|██████    | 30/50 [00:02<00:01, 13.97 it/sec, obj=59.2]
        INFO - 13:53:16:     62%|██████▏   | 31/50 [00:02<00:01, 13.95 it/sec, obj=61.3]
        INFO - 13:53:16:     64%|██████▍   | 32/50 [00:02<00:01, 13.91 it/sec, obj=63.3]
       ERROR - 13:53:16: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:16:     66%|██████▌   | 33/50 [00:02<00:01, 13.89 it/sec, obj=65.3]
        INFO - 13:53:17:     68%|██████▊   | 34/50 [00:02<00:01, 13.86 it/sec, obj=67.4]
        INFO - 13:53:17:     70%|███████   | 35/50 [00:02<00:01, 13.83 it/sec, obj=69.4]
        INFO - 13:53:17:     72%|███████▏  | 36/50 [00:02<00:01, 13.82 it/sec, obj=71.5]
        INFO - 13:53:17:     74%|███████▍  | 37/50 [00:02<00:00, 13.86 it/sec, obj=73.5]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     76%|███████▌  | 38/50 [00:02<00:00, 13.89 it/sec, obj=75.5]
        INFO - 13:53:17:     78%|███████▊  | 39/50 [00:02<00:00, 13.91 it/sec, obj=77.6]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     80%|████████  | 40/50 [00:02<00:00, 13.95 it/sec, obj=79.6]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     82%|████████▏ | 41/50 [00:02<00:00, 13.99 it/sec, obj=81.7]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     84%|████████▍ | 42/50 [00:02<00:00, 14.02 it/sec, obj=83.7]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     86%|████████▌ | 43/50 [00:03<00:00, 14.04 it/sec, obj=85.7]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     88%|████████▊ | 44/50 [00:03<00:00, 14.07 it/sec, obj=87.8]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     90%|█████████ | 45/50 [00:03<00:00, 14.09 it/sec, obj=89.8]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     92%|█████████▏| 46/50 [00:03<00:00, 14.11 it/sec, obj=91.8]
        INFO - 13:53:17:     94%|█████████▍| 47/50 [00:03<00:00, 14.13 it/sec, obj=93.9]
       ERROR - 13:53:17: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:17:     96%|█████████▌| 48/50 [00:03<00:00, 14.14 it/sec, obj=95.9]
       ERROR - 13:53:18: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:18:     98%|█████████▊| 49/50 [00:03<00:00, 14.16 it/sec, obj=98]
       ERROR - 13:53:18: NLopt run failed: NLopt roundoff-limited, RoundoffLimited
    Traceback (most recent call last):
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/gemseo/algos/opt/lib_nlopt.py", line 498, in _run
        nlopt_problem.optimize(x_0.real)
      File "/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/stable/lib/python3.9/site-packages/nlopt/nlopt.py", line 335, in optimize
        return _nlopt.opt_optimize(self, *args)
    nlopt.RoundoffLimited: NLopt roundoff-limited
        INFO - 13:53:18:    100%|██████████| 50/50 [00:03<00:00, 14.17 it/sec, obj=100]
        INFO - 13:53:18: Optimization result:
        INFO - 13:53:18:    Optimizer info:
        INFO - 13:53:18:       Status: None
        INFO - 13:53:18:       Message: None
        INFO - 13:53:18:       Number of calls to the objective function by the optimizer: 50
        INFO - 13:53:18:    Solution:
        INFO - 13:53:18:       The solution is feasible.
        INFO - 13:53:18:       Objective: 0.10832777706440924
        INFO - 13:53:18:       Standardized constraints:
        INFO - 13:53:18:          cstr3 = 0.008327777064409236
        INFO - 13:53:18:       Design space:
        INFO - 13:53:18:          +-------------+-------------+-------+-------------+-------+
        INFO - 13:53:18:          | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 13:53:18:          +-------------+-------------+-------+-------------+-------+
        INFO - 13:53:18:          | obj1_target |     0.1     |  0.1  |     100     | float |
        INFO - 13:53:18:          +-------------+-------------+-------+-------------+-------+
        INFO - 13:53:18: *** End DOEScenario execution (time: 0:00:03.541989) ***

    <gemseo.post.pareto_front.ParetoFront object at 0x7f2d204133a0>




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

   **Total running time of the script:** (0 minutes 3.818 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>`


.. only:: html

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

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