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

.. only:: html

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

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

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

.. _sphx_glr_examples_topology_optimization_plot_topology_optimization_MBB.py:


Solve a 2D MBB topology optimization problem
============================================

.. GENERATED FROM PYTHON SOURCE LINES 23-33

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_scenario
    from gemseo.problems.topo_opt.topopt_initialize import (
        initialize_design_space_and_discipline_to,
    )

    configure_logger()




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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 34-36

Setup the topology optimization problem
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-39

Define the target volume fraction:

.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

    volume_fraction = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 42-43

Define the problem type:

.. GENERATED FROM PYTHON SOURCE LINES 43-45

.. code-block:: Python

    problem_name = "MBB"








.. GENERATED FROM PYTHON SOURCE LINES 46-47

Define the number of elements in x- and y- directions:

.. GENERATED FROM PYTHON SOURCE LINES 47-50

.. code-block:: Python

    n_x = 50
    n_y = 25








.. GENERATED FROM PYTHON SOURCE LINES 51-52

Define the full material Young's modulus and the Poisson's ratio:

.. GENERATED FROM PYTHON SOURCE LINES 52-55

.. code-block:: Python

    e0 = 1
    nu = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Define the penalty of the SIMP approach:

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: Python

    penalty = 3








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Define the minimum member size in the solution:

.. GENERATED FROM PYTHON SOURCE LINES 61-62

.. code-block:: Python

    min_member_size = 1.5







.. GENERATED FROM PYTHON SOURCE LINES 63-64

Instantiate the :class:`.DesignSpace` and the disciplines:

.. GENERATED FROM PYTHON SOURCE LINES 64-75

.. code-block:: Python


    design_space, disciplines = initialize_design_space_and_discipline_to(
        problem=problem_name,
        n_x=n_x,
        n_y=n_y,
        e0=e0,
        nu=nu,
        penalty=penalty,
        min_member_size=min_member_size,
        vf0=volume_fraction,
    )







.. GENERATED FROM PYTHON SOURCE LINES 76-79

Solve the topology optimization problem
---------------------------------------
Generate an :class:`.MDOScenario`

.. GENERATED FROM PYTHON SOURCE LINES 79-86

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "DisciplinaryOpt",
        "compliance",
        design_space,
    )








.. GENERATED FROM PYTHON SOURCE LINES 87-88

Add the volume fraction constraint to the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 88-92

.. code-block:: Python

    scenario.add_constraint(
        "volume fraction", constraint_type="ineq", value=volume_fraction
    )








.. GENERATED FROM PYTHON SOURCE LINES 93-94

Generate the XDSM

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: Python

    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": "DensityFilter",
            "type": "analysis"
          },
          {
            "id": "Dis2",
            "name": "MaterialModelInterpolation",
            "type": "analysis"
          },
          {
            "id": "Dis3",
            "name": "FininiteElementAnalysis",
            "type": "analysis"
          },
          {
            "id": "Dis4",
            "name": "VolumeFraction",
            "type": "analysis"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "compliance^*, [volume fraction-0.3]^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "compliance"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "volume fraction"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "xPhys^*"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "rho^*, E^*"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "compliance"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "volume fraction"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "xPhys"
          },
          {
            "from": "Dis2",
            "to": "Dis3",
            "name": "E"
          },
          {
            "from": "Dis2",
            "to": "Dis4",
            "name": "rho"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2",
              "Dis3",
              "Dis4"
            ]
          ]
        ],
        "optpb": "Optimization problem:\n   minimize compliance(x)\n   with respect to x\n   subject to constraints:\n      volume fraction(x) <= 0.3"
      }
    };
              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 97-98

Execute the scenario

.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: Python

    scenario.execute({"max_iter": 200, "algo": "NLOPT_MMA"})





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

 .. code-block:: none

        INFO - 13:57:26:  
        INFO - 13:57:26: *** Start MDOScenario execution ***
        INFO - 13:57:26: MDOScenario
        INFO - 13:57:26:    Disciplines: DensityFilter FininiteElementAnalysis MaterialModelInterpolation VolumeFraction
        INFO - 13:57:26:    MDO formulation: DisciplinaryOpt
        INFO - 13:57:26: Optimization problem:
        INFO - 13:57:26:    minimize compliance(x)
        INFO - 13:57:26:    with respect to x
        INFO - 13:57:26:    subject to constraints:
        INFO - 13:57:26:       volume fraction(x) <= 0.3
        INFO - 13:57:26: Solving optimization problem with algorithm NLOPT_MMA:
        INFO - 13:57:26:      1%|          | 2/200 [00:00<00:13, 14.71 it/sec, obj=1.79e+3]
        INFO - 13:57:26:      2%|▏         | 3/200 [00:00<00:11, 16.60 it/sec, obj=1.78e+3]
        INFO - 13:57:26:      2%|▏         | 4/200 [00:00<00:10, 17.82 it/sec, obj=1.77e+3]
        INFO - 13:57:26:      2%|▎         | 5/200 [00:00<00:10, 18.60 it/sec, obj=1.75e+3]
        INFO - 13:57:26:      3%|▎         | 6/200 [00:00<00:10, 19.13 it/sec, obj=1.71e+3]
        INFO - 13:57:26:      4%|▎         | 7/200 [00:00<00:09, 19.57 it/sec, obj=1.65e+3]
        INFO - 13:57:27:      4%|▍         | 8/200 [00:00<00:09, 19.97 it/sec, obj=1.41e+3]
        INFO - 13:57:27:      4%|▍         | 9/200 [00:00<00:09, 20.28 it/sec, obj=1.19e+3]
        INFO - 13:57:27:      5%|▌         | 10/200 [00:00<00:09, 20.31 it/sec, obj=903]
        INFO - 13:57:27:      6%|▌         | 11/200 [00:00<00:09, 20.53 it/sec, obj=724]
        INFO - 13:57:27:      6%|▌         | 12/200 [00:00<00:09, 20.56 it/sec, obj=612]
        INFO - 13:57:27:      6%|▋         | 13/200 [00:00<00:09, 20.40 it/sec, obj=534]
        INFO - 13:57:27:      7%|▋         | 14/200 [00:00<00:09, 20.40 it/sec, obj=474]
        INFO - 13:57:27:      8%|▊         | 15/200 [00:00<00:08, 20.58 it/sec, obj=444]
        INFO - 13:57:27:      8%|▊         | 16/200 [00:00<00:08, 20.73 it/sec, obj=419]
        INFO - 13:57:27:      8%|▊         | 17/200 [00:00<00:08, 20.90 it/sec, obj=405]
        INFO - 13:57:27:      9%|▉         | 18/200 [00:00<00:08, 21.05 it/sec, obj=387]
        INFO - 13:57:27:     10%|▉         | 19/200 [00:00<00:08, 21.17 it/sec, obj=364]
        INFO - 13:57:27:     10%|█         | 20/200 [00:00<00:08, 21.28 it/sec, obj=338]
        INFO - 13:57:27:     10%|█         | 21/200 [00:00<00:08, 21.37 it/sec, obj=306]
        INFO - 13:57:27:     11%|█         | 22/200 [00:01<00:08, 21.44 it/sec, obj=272]
        INFO - 13:57:27:     12%|█▏        | 23/200 [00:01<00:08, 21.55 it/sec, obj=253]
        INFO - 13:57:27:     12%|█▏        | 24/200 [00:01<00:08, 21.62 it/sec, obj=244]
        INFO - 13:57:27:     12%|█▎        | 25/200 [00:01<00:08, 21.70 it/sec, obj=234]
        INFO - 13:57:27:     13%|█▎        | 26/200 [00:01<00:07, 21.75 it/sec, obj=224]
        INFO - 13:57:27:     14%|█▎        | 27/200 [00:01<00:07, 21.83 it/sec, obj=213]
        INFO - 13:57:27:     14%|█▍        | 28/200 [00:01<00:07, 21.94 it/sec, obj=207]
        INFO - 13:57:27:     14%|█▍        | 29/200 [00:01<00:07, 22.02 it/sec, obj=202]
        INFO - 13:57:27:     15%|█▌        | 30/200 [00:01<00:07, 22.10 it/sec, obj=197]
        INFO - 13:57:28:     16%|█▌        | 31/200 [00:01<00:07, 22.16 it/sec, obj=193]
        INFO - 13:57:28:     16%|█▌        | 32/200 [00:01<00:07, 22.21 it/sec, obj=190]
        INFO - 13:57:28:     16%|█▋        | 33/200 [00:01<00:07, 22.28 it/sec, obj=188]
        INFO - 13:57:28:     17%|█▋        | 34/200 [00:01<00:07, 22.30 it/sec, obj=186]
        INFO - 13:57:28:     18%|█▊        | 35/200 [00:01<00:07, 22.35 it/sec, obj=185]
        INFO - 13:57:28:     18%|█▊        | 36/200 [00:01<00:07, 22.39 it/sec, obj=184]
        INFO - 13:57:28:     18%|█▊        | 37/200 [00:01<00:07, 22.41 it/sec, obj=183]
        INFO - 13:57:28:     19%|█▉        | 38/200 [00:01<00:07, 22.48 it/sec, obj=182]
        INFO - 13:57:28:     20%|█▉        | 39/200 [00:01<00:07, 22.51 it/sec, obj=181]
        INFO - 13:57:28:     20%|██        | 40/200 [00:01<00:07, 22.54 it/sec, obj=179]
        INFO - 13:57:28:     20%|██        | 41/200 [00:01<00:07, 22.59 it/sec, obj=177]
        INFO - 13:57:28:     21%|██        | 42/200 [00:01<00:06, 22.63 it/sec, obj=175]
        INFO - 13:57:28:     22%|██▏       | 43/200 [00:01<00:06, 22.65 it/sec, obj=174]
        INFO - 13:57:28:     22%|██▏       | 44/200 [00:01<00:06, 22.69 it/sec, obj=173]
        INFO - 13:57:28:     22%|██▎       | 45/200 [00:01<00:06, 22.72 it/sec, obj=172]
        INFO - 13:57:28:     23%|██▎       | 46/200 [00:02<00:06, 22.76 it/sec, obj=172]
        INFO - 13:57:28:     24%|██▎       | 47/200 [00:02<00:06, 22.79 it/sec, obj=172]
        INFO - 13:57:28:     24%|██▍       | 48/200 [00:02<00:06, 22.84 it/sec, obj=172]
        INFO - 13:57:28:     24%|██▍       | 49/200 [00:02<00:06, 22.87 it/sec, obj=172]
        INFO - 13:57:28:     25%|██▌       | 50/200 [00:02<00:06, 22.91 it/sec, obj=172]
        INFO - 13:57:28:     26%|██▌       | 51/200 [00:02<00:06, 22.94 it/sec, obj=172]
        INFO - 13:57:28:     26%|██▌       | 52/200 [00:02<00:06, 22.97 it/sec, obj=172]
        INFO - 13:57:28:     26%|██▋       | 53/200 [00:02<00:06, 23.00 it/sec, obj=172]
        INFO - 13:57:28:     27%|██▋       | 54/200 [00:02<00:06, 23.03 it/sec, obj=172]
        INFO - 13:57:29:     28%|██▊       | 55/200 [00:02<00:06, 23.06 it/sec, obj=172]
        INFO - 13:57:29:     28%|██▊       | 56/200 [00:02<00:06, 23.09 it/sec, obj=172]
        INFO - 13:57:29:     28%|██▊       | 57/200 [00:02<00:06, 23.13 it/sec, obj=172]
        INFO - 13:57:29:     29%|██▉       | 58/200 [00:02<00:06, 23.15 it/sec, obj=171]
        INFO - 13:57:29:     30%|██▉       | 59/200 [00:02<00:06, 23.17 it/sec, obj=171]
        INFO - 13:57:29:     30%|███       | 60/200 [00:02<00:06, 23.21 it/sec, obj=171]
        INFO - 13:57:29:     30%|███       | 61/200 [00:02<00:05, 23.23 it/sec, obj=171]
        INFO - 13:57:29:     31%|███       | 62/200 [00:02<00:05, 23.24 it/sec, obj=171]
        INFO - 13:57:29:     32%|███▏      | 63/200 [00:02<00:05, 23.27 it/sec, obj=171]
        INFO - 13:57:29:     32%|███▏      | 64/200 [00:02<00:05, 23.30 it/sec, obj=171]
        INFO - 13:57:29:     32%|███▎      | 65/200 [00:02<00:05, 23.32 it/sec, obj=171]
        INFO - 13:57:29:     33%|███▎      | 66/200 [00:02<00:05, 23.36 it/sec, obj=171]
        INFO - 13:57:29:     34%|███▎      | 67/200 [00:02<00:05, 23.38 it/sec, obj=171]
        INFO - 13:57:29:     34%|███▍      | 68/200 [00:02<00:05, 23.40 it/sec, obj=171]
        INFO - 13:57:29:     34%|███▍      | 69/200 [00:02<00:05, 23.42 it/sec, obj=171]
        INFO - 13:57:29:     35%|███▌      | 70/200 [00:02<00:05, 23.45 it/sec, obj=171]
        INFO - 13:57:29:     36%|███▌      | 71/200 [00:03<00:05, 23.47 it/sec, obj=171]
        INFO - 13:57:29:     36%|███▌      | 72/200 [00:03<00:05, 23.48 it/sec, obj=171]
        INFO - 13:57:29:     36%|███▋      | 73/200 [00:03<00:05, 23.50 it/sec, obj=171]
        INFO - 13:57:29:     37%|███▋      | 74/200 [00:03<00:05, 23.52 it/sec, obj=171]
        INFO - 13:57:29:     38%|███▊      | 75/200 [00:03<00:05, 23.54 it/sec, obj=171]
        INFO - 13:57:29:     38%|███▊      | 76/200 [00:03<00:05, 23.55 it/sec, obj=171]
        INFO - 13:57:29:     38%|███▊      | 77/200 [00:03<00:05, 23.57 it/sec, obj=171]
        INFO - 13:57:29:     39%|███▉      | 78/200 [00:03<00:05, 23.58 it/sec, obj=171]
        INFO - 13:57:29:     40%|███▉      | 79/200 [00:03<00:05, 23.60 it/sec, obj=171]
        INFO - 13:57:30:     40%|████      | 80/200 [00:03<00:05, 23.61 it/sec, obj=171]
        INFO - 13:57:30:     40%|████      | 81/200 [00:03<00:05, 23.63 it/sec, obj=171]
        INFO - 13:57:30:     41%|████      | 82/200 [00:03<00:04, 23.64 it/sec, obj=171]
        INFO - 13:57:30:     42%|████▏     | 83/200 [00:03<00:04, 23.64 it/sec, obj=171]
        INFO - 13:57:30:     42%|████▏     | 84/200 [00:03<00:04, 23.65 it/sec, obj=171]
        INFO - 13:57:30:     42%|████▎     | 85/200 [00:03<00:04, 23.66 it/sec, obj=171]
        INFO - 13:57:30:     43%|████▎     | 86/200 [00:03<00:04, 23.66 it/sec, obj=171]
        INFO - 13:57:30:     44%|████▎     | 87/200 [00:03<00:04, 23.67 it/sec, obj=171]
        INFO - 13:57:30:     44%|████▍     | 88/200 [00:03<00:04, 23.68 it/sec, obj=171]
        INFO - 13:57:30:     44%|████▍     | 89/200 [00:03<00:04, 23.68 it/sec, obj=171]
        INFO - 13:57:30:     45%|████▌     | 90/200 [00:03<00:04, 23.70 it/sec, obj=171]
        INFO - 13:57:30:     46%|████▌     | 91/200 [00:03<00:04, 23.70 it/sec, obj=171]
        INFO - 13:57:30:     46%|████▌     | 92/200 [00:03<00:04, 23.72 it/sec, obj=171]
        INFO - 13:57:30:     46%|████▋     | 93/200 [00:03<00:04, 23.73 it/sec, obj=171]
        INFO - 13:57:30:     47%|████▋     | 94/200 [00:03<00:04, 23.74 it/sec, obj=171]
        INFO - 13:57:30:     48%|████▊     | 95/200 [00:03<00:04, 23.76 it/sec, obj=171]
        INFO - 13:57:30:     48%|████▊     | 96/200 [00:04<00:04, 23.77 it/sec, obj=171]
        INFO - 13:57:30:     48%|████▊     | 97/200 [00:04<00:04, 23.78 it/sec, obj=171]
        INFO - 13:57:30:     49%|████▉     | 98/200 [00:04<00:04, 23.79 it/sec, obj=171]
        INFO - 13:57:30:     50%|████▉     | 99/200 [00:04<00:04, 23.80 it/sec, obj=171]
        INFO - 13:57:30:     50%|█████     | 100/200 [00:04<00:04, 23.82 it/sec, obj=171]
        INFO - 13:57:30:     50%|█████     | 101/200 [00:04<00:04, 23.83 it/sec, obj=171]
        INFO - 13:57:30:     51%|█████     | 102/200 [00:04<00:04, 23.84 it/sec, obj=171]
        INFO - 13:57:30:     52%|█████▏    | 103/200 [00:04<00:04, 23.85 it/sec, obj=171]
        INFO - 13:57:30:     52%|█████▏    | 104/200 [00:04<00:04, 23.86 it/sec, obj=171]
        INFO - 13:57:31:     52%|█████▎    | 105/200 [00:04<00:03, 23.87 it/sec, obj=171]
        INFO - 13:57:31:     53%|█████▎    | 106/200 [00:04<00:03, 23.88 it/sec, obj=171]
        INFO - 13:57:31:     54%|█████▎    | 107/200 [00:04<00:03, 23.89 it/sec, obj=171]
        INFO - 13:57:31:     54%|█████▍    | 108/200 [00:04<00:03, 23.89 it/sec, obj=171]
        INFO - 13:57:31:     55%|█████▍    | 109/200 [00:04<00:03, 23.90 it/sec, obj=171]
        INFO - 13:57:31:     55%|█████▌    | 110/200 [00:04<00:03, 23.90 it/sec, obj=171]
        INFO - 13:57:31:     56%|█████▌    | 111/200 [00:04<00:03, 23.91 it/sec, obj=171]
        INFO - 13:57:31:     56%|█████▌    | 112/200 [00:04<00:03, 23.91 it/sec, obj=171]
        INFO - 13:57:31:     56%|█████▋    | 113/200 [00:04<00:03, 23.92 it/sec, obj=171]
        INFO - 13:57:31:     57%|█████▋    | 114/200 [00:04<00:03, 23.93 it/sec, obj=171]
        INFO - 13:57:31:     57%|█████▊    | 115/200 [00:04<00:03, 23.94 it/sec, obj=172]
        INFO - 13:57:31:     58%|█████▊    | 116/200 [00:04<00:03, 23.95 it/sec, obj=172]
        INFO - 13:57:31:     58%|█████▊    | 117/200 [00:04<00:03, 23.96 it/sec, obj=172]
        INFO - 13:57:31:     59%|█████▉    | 118/200 [00:04<00:03, 23.97 it/sec, obj=172]
        INFO - 13:57:31:     60%|█████▉    | 119/200 [00:04<00:03, 23.99 it/sec, obj=171]
        INFO - 13:57:31:     60%|██████    | 120/200 [00:05<00:03, 23.99 it/sec, obj=171]
        INFO - 13:57:31:     60%|██████    | 121/200 [00:05<00:03, 24.00 it/sec, obj=171]
        INFO - 13:57:31:     61%|██████    | 122/200 [00:05<00:03, 24.00 it/sec, obj=170]
        INFO - 13:57:31:     62%|██████▏   | 123/200 [00:05<00:03, 24.00 it/sec, obj=170]
        INFO - 13:57:31:     62%|██████▏   | 124/200 [00:05<00:03, 24.01 it/sec, obj=170]
        INFO - 13:57:31:     62%|██████▎   | 125/200 [00:05<00:03, 24.02 it/sec, obj=170]
        INFO - 13:57:31:     63%|██████▎   | 126/200 [00:05<00:03, 24.03 it/sec, obj=170]
        INFO - 13:57:31:     64%|██████▎   | 127/200 [00:05<00:03, 24.04 it/sec, obj=170]
        INFO - 13:57:31:     64%|██████▍   | 128/200 [00:05<00:02, 24.05 it/sec, obj=170]
        INFO - 13:57:31:     64%|██████▍   | 129/200 [00:05<00:02, 24.05 it/sec, obj=170]
        INFO - 13:57:32:     65%|██████▌   | 130/200 [00:05<00:02, 24.06 it/sec, obj=170]
        INFO - 13:57:32:     66%|██████▌   | 131/200 [00:05<00:02, 24.06 it/sec, obj=170]
        INFO - 13:57:32:     66%|██████▌   | 132/200 [00:05<00:02, 24.07 it/sec, obj=170]
        INFO - 13:57:32:     66%|██████▋   | 133/200 [00:05<00:02, 24.07 it/sec, obj=170]
        INFO - 13:57:32:     67%|██████▋   | 134/200 [00:05<00:02, 24.07 it/sec, obj=170]
        INFO - 13:57:32:     68%|██████▊   | 135/200 [00:05<00:02, 24.08 it/sec, obj=170]
        INFO - 13:57:32:     68%|██████▊   | 136/200 [00:05<00:02, 24.08 it/sec, obj=170]
        INFO - 13:57:32:     68%|██████▊   | 137/200 [00:05<00:02, 24.09 it/sec, obj=170]
        INFO - 13:57:32:     69%|██████▉   | 138/200 [00:05<00:02, 24.09 it/sec, obj=170]
        INFO - 13:57:32:     70%|██████▉   | 139/200 [00:05<00:02, 24.09 it/sec, obj=170]
        INFO - 13:57:32:     70%|███████   | 140/200 [00:05<00:02, 24.09 it/sec, obj=170]
        INFO - 13:57:32:     70%|███████   | 141/200 [00:05<00:02, 24.09 it/sec, obj=170]
        INFO - 13:57:32:     71%|███████   | 142/200 [00:05<00:02, 24.09 it/sec, obj=170]
        INFO - 13:57:32:     72%|███████▏  | 143/200 [00:05<00:02, 24.10 it/sec, obj=170]
        INFO - 13:57:32:     72%|███████▏  | 144/200 [00:05<00:02, 24.10 it/sec, obj=170]
        INFO - 13:57:32:     72%|███████▎  | 145/200 [00:06<00:02, 24.10 it/sec, obj=170]
        INFO - 13:57:32:     73%|███████▎  | 146/200 [00:06<00:02, 24.11 it/sec, obj=170]
        INFO - 13:57:32:     74%|███████▎  | 147/200 [00:06<00:02, 24.11 it/sec, obj=170]
        INFO - 13:57:32:     74%|███████▍  | 148/200 [00:06<00:02, 24.12 it/sec, obj=170]
        INFO - 13:57:32:     74%|███████▍  | 149/200 [00:06<00:02, 24.12 it/sec, obj=170]
        INFO - 13:57:32:     75%|███████▌  | 150/200 [00:06<00:02, 24.13 it/sec, obj=170]
        INFO - 13:57:32:     76%|███████▌  | 151/200 [00:06<00:02, 24.13 it/sec, obj=170]
        INFO - 13:57:32:     76%|███████▌  | 152/200 [00:06<00:01, 24.14 it/sec, obj=170]
        INFO - 13:57:32:     76%|███████▋  | 153/200 [00:06<00:01, 24.14 it/sec, obj=170]
        INFO - 13:57:33:     77%|███████▋  | 154/200 [00:06<00:01, 24.15 it/sec, obj=170]
        INFO - 13:57:33:     78%|███████▊  | 155/200 [00:06<00:01, 24.15 it/sec, obj=170]
        INFO - 13:57:33:     78%|███████▊  | 156/200 [00:06<00:01, 24.15 it/sec, obj=170]
        INFO - 13:57:33:     78%|███████▊  | 157/200 [00:06<00:01, 24.16 it/sec, obj=170]
        INFO - 13:57:33:     79%|███████▉  | 158/200 [00:06<00:01, 24.17 it/sec, obj=170]
        INFO - 13:57:33:     80%|███████▉  | 159/200 [00:06<00:01, 24.17 it/sec, obj=170]
        INFO - 13:57:33:     80%|████████  | 160/200 [00:06<00:01, 24.17 it/sec, obj=170]
        INFO - 13:57:33:     80%|████████  | 161/200 [00:06<00:01, 24.17 it/sec, obj=170]
        INFO - 13:57:33:     81%|████████  | 162/200 [00:06<00:01, 24.18 it/sec, obj=170]
        INFO - 13:57:33:     82%|████████▏ | 163/200 [00:06<00:01, 24.18 it/sec, obj=170]
        INFO - 13:57:33:     82%|████████▏ | 164/200 [00:06<00:01, 24.19 it/sec, obj=170]
        INFO - 13:57:33:     82%|████████▎ | 165/200 [00:06<00:01, 24.20 it/sec, obj=170]
        INFO - 13:57:33:     83%|████████▎ | 166/200 [00:06<00:01, 24.21 it/sec, obj=170]
        INFO - 13:57:33:     84%|████████▎ | 167/200 [00:06<00:01, 24.21 it/sec, obj=170]
        INFO - 13:57:33:     84%|████████▍ | 168/200 [00:06<00:01, 24.22 it/sec, obj=170]
        INFO - 13:57:33:     84%|████████▍ | 169/200 [00:06<00:01, 24.22 it/sec, obj=170]
        INFO - 13:57:33:     85%|████████▌ | 170/200 [00:07<00:01, 24.23 it/sec, obj=170]
        INFO - 13:57:33:     86%|████████▌ | 171/200 [00:07<00:01, 24.23 it/sec, obj=170]
        INFO - 13:57:33:     86%|████████▌ | 172/200 [00:07<00:01, 24.23 it/sec, obj=170]
        INFO - 13:57:33:     86%|████████▋ | 173/200 [00:07<00:01, 24.23 it/sec, obj=170]
        INFO - 13:57:33:     87%|████████▋ | 174/200 [00:07<00:01, 24.24 it/sec, obj=170]
        INFO - 13:57:33:     88%|████████▊ | 175/200 [00:07<00:01, 24.25 it/sec, obj=170]
        INFO - 13:57:33:     88%|████████▊ | 176/200 [00:07<00:00, 24.25 it/sec, obj=170]
        INFO - 13:57:33:     88%|████████▊ | 177/200 [00:07<00:00, 24.25 it/sec, obj=170]
        INFO - 13:57:33:     89%|████████▉ | 178/200 [00:07<00:00, 24.25 it/sec, obj=170]
        INFO - 13:57:34:     90%|████████▉ | 179/200 [00:07<00:00, 24.26 it/sec, obj=170]
        INFO - 13:57:34:     90%|█████████ | 180/200 [00:07<00:00, 24.26 it/sec, obj=170]
        INFO - 13:57:34:     90%|█████████ | 181/200 [00:07<00:00, 24.26 it/sec, obj=170]
        INFO - 13:57:34:     91%|█████████ | 182/200 [00:07<00:00, 24.26 it/sec, obj=170]
        INFO - 13:57:34:     92%|█████████▏| 183/200 [00:07<00:00, 24.26 it/sec, obj=170]
        INFO - 13:57:34:     92%|█████████▏| 184/200 [00:07<00:00, 24.26 it/sec, obj=170]
        INFO - 13:57:34:     92%|█████████▎| 185/200 [00:07<00:00, 24.27 it/sec, obj=170]
        INFO - 13:57:34:     93%|█████████▎| 186/200 [00:07<00:00, 24.27 it/sec, obj=170]
        INFO - 13:57:34:     94%|█████████▎| 187/200 [00:07<00:00, 24.28 it/sec, obj=170]
        INFO - 13:57:34:     94%|█████████▍| 188/200 [00:07<00:00, 24.28 it/sec, obj=170]
        INFO - 13:57:34:     94%|█████████▍| 189/200 [00:07<00:00, 24.28 it/sec, obj=170]
        INFO - 13:57:34:     95%|█████████▌| 190/200 [00:07<00:00, 24.29 it/sec, obj=170]
        INFO - 13:57:34:     96%|█████████▌| 191/200 [00:07<00:00, 24.29 it/sec, obj=170]
        INFO - 13:57:34:     96%|█████████▌| 192/200 [00:07<00:00, 24.30 it/sec, obj=170]
        INFO - 13:57:34:     96%|█████████▋| 193/200 [00:07<00:00, 24.30 it/sec, obj=170]
        INFO - 13:57:34:     97%|█████████▋| 194/200 [00:07<00:00, 24.30 it/sec, obj=170]
        INFO - 13:57:34:     98%|█████████▊| 195/200 [00:08<00:00, 24.30 it/sec, obj=170]
        INFO - 13:57:34:     98%|█████████▊| 196/200 [00:08<00:00, 24.30 it/sec, obj=170]
        INFO - 13:57:34:     98%|█████████▊| 197/200 [00:08<00:00, 24.31 it/sec, obj=170]
        INFO - 13:57:34:     99%|█████████▉| 198/200 [00:08<00:00, 24.31 it/sec, obj=170]
        INFO - 13:57:34:    100%|█████████▉| 199/200 [00:08<00:00, 24.32 it/sec, obj=170]
        INFO - 13:57:34:    100%|██████████| 200/200 [00:08<00:00, 24.41 it/sec, obj=170]
        INFO - 13:57:34: Optimization result:
        INFO - 13:57:34:    Optimizer info:
        INFO - 13:57:34:       Status: None
        INFO - 13:57:34:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 13:57:34:       Number of calls to the objective function by the optimizer: 201
        INFO - 13:57:34:    Solution:
        INFO - 13:57:34:       The solution is feasible.
        INFO - 13:57:34:       Objective: 169.89161468983534
        INFO - 13:57:34:       Standardized constraints:
        INFO - 13:57:34:          [volume fraction-0.3] = -4.312432086428508e-07
        INFO - 13:57:34: *** End MDOScenario execution (time: 0:00:08.212408) ***

    {'max_iter': 200, 'algo': 'NLOPT_MMA'}



.. GENERATED FROM PYTHON SOURCE LINES 101-104

Results
-------
Post-process the optimization history:

.. GENERATED FROM PYTHON SOURCE LINES 104-108

.. code-block:: Python

    scenario.post_process(
        "BasicHistory", variable_names=["compliance"], show=True, save=False
    )




.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_001.png
   :alt: History plot
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7f28d00f14f0>



.. GENERATED FROM PYTHON SOURCE LINES 109-110

Plot the solution

.. GENERATED FROM PYTHON SOURCE LINES 110-111

.. code-block:: Python

    scenario.post_process("TopologyView", n_x=n_x, n_y=n_y, show=True, save=False)



.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_002.png
   :alt: plot topology optimization MBB
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.topology_view.TopologyView object at 0x7f28cf641dc0>




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

   **Total running time of the script:** (0 minutes 8.554 seconds)


.. _sphx_glr_download_examples_topology_optimization_plot_topology_optimization_MBB.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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