.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/post_process/algorithms/plot_pareto_front_binhkorn.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_post_process_algorithms_plot_pareto_front_binhkorn.py: Pareto front on Binh and Korn problem ===================================== In this example, we illustrate the use of the :class:`.ParetoFront` plot on the Binh and Korn multi-objective problem. .. GENERATED FROM PYTHON SOURCE LINES 28-36 .. code-block:: Python from __future__ import annotations from gemseo import configure_logger from gemseo.algos.doe.doe_factory import DOEFactory from gemseo.post.post_factory import PostFactory from gemseo.problems.analytical.binh_korn import BinhKorn .. GENERATED FROM PYTHON SOURCE LINES 37-40 Import ------ The first step is to import a high-level function for logging. .. GENERATED FROM PYTHON SOURCE LINES 40-44 .. code-block:: Python configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 45-48 Import the optimization problem ------------------------------- Then, we instantiate the Binh and Korn optimization problem (see :class:`.BinhKorn`). .. GENERATED FROM PYTHON SOURCE LINES 48-51 .. code-block:: Python problem = BinhKorn() .. GENERATED FROM PYTHON SOURCE LINES 52-57 Create and execute scenario --------------------------- Then, we instantiate the design of experiment factory, and we request the execution of a 100-length LHS optimized by simulated annealing. .. GENERATED FROM PYTHON SOURCE LINES 57-60 .. code-block:: Python doe_factory = DOEFactory() doe_factory.execute(problem, algo_name="OT_OPT_LHS", n_samples=100) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:55:30: Optimization problem: INFO - 10:55:30: minimize compute_binhkorn(x, y) = (4*x**2+ 4*y**2, (x-5.)**2 + (y-5.)**2) INFO - 10:55:30: with respect to x, y INFO - 10:55:30: subject to constraints: INFO - 10:55:30: ineq1(x, y): (x-5.)**2 + y**2 <= 25. <= 0.0 INFO - 10:55:30: ineq2(x, y): (x-8.)**2 + (y+3)**2 >= 7.7 <= 0.0 INFO - 10:55:30: over the design space: INFO - 10:55:30: +------+-------------+-------+-------------+-------+ INFO - 10:55:30: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:55:30: +------+-------------+-------+-------------+-------+ INFO - 10:55:30: | x | 0 | 1 | 5 | float | INFO - 10:55:30: | y | 0 | 1 | 3 | float | INFO - 10:55:30: +------+-------------+-------+-------------+-------+ INFO - 10:55:30: Solving optimization problem with algorithm OT_OPT_LHS: INFO - 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10:55:30: 98%|█████████▊| 98/100 [00:00<00:00, 1884.29 it/sec, obj=[81.61206359 10.43246637]] INFO - 10:55:30: 99%|█████████▉| 99/100 [00:00<00:00, 1884.64 it/sec, obj=[40.83406128 15.59204339]] INFO - 10:55:30: 100%|██████████| 100/100 [00:00<00:00, 1885.17 it/sec, obj=[52.02690192 12.02601654]] INFO - 10:55:30: Optimization result: INFO - 10:55:30: Optimizer info: INFO - 10:55:30: Status: None INFO - 10:55:30: Message: None INFO - 10:55:30: Number of calls to the objective function by the optimizer: 100 INFO - 10:55:30: Solution: INFO - 10:55:30: The solution is feasible. INFO - 10:55:30: Objective: 30.39964825035985 INFO - 10:55:30: Standardized constraints: INFO - 10:55:30: ineq1 = [-11.77907222] INFO - 10:55:30: ineq2 = [-38.26307397] INFO - 10:55:30: Design space: INFO - 10:55:30: +------+-------------+-------------------+-------------+-------+ INFO - 10:55:30: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:55:30: +------+-------------+-------------------+-------------+-------+ INFO - 10:55:30: | x | 0 | 1.542975634014225 | 5 | float | INFO - 10:55:30: | y | 0 | 1.269910308585573 | 3 | float | INFO - 10:55:30: +------+-------------+-------------------+-------------+-------+ .. raw:: html
Optimization result:
  • Design variables: [1.54297563 1.26991031]
  • Objective function: 30.39964825035985
  • Feasible solution: True


.. GENERATED FROM PYTHON SOURCE LINES 61-69 Post-process scenario --------------------- Lastly, we post-process the scenario by means of the :class:`.ParetoFront` plot which generates a plot or a matrix of plots if there are more than 2 objectives, plots in blue the locally non dominated points for the current two objectives, plots in green the globally (all objectives) Pareto optimal points. The plots in green denote non-feasible points. Note that the user can avoid the display of the non-feasible points. .. GENERATED FROM PYTHON SOURCE LINES 69-88 .. code-block:: Python PostFactory().execute( problem, "ParetoFront", show_non_feasible=False, objectives=["compute_binhkorn"], objectives_labels=["f1", "f2"], save=False, show=True, ) PostFactory().execute( problem, "ParetoFront", objectives=["compute_binhkorn"], objectives_labels=["f1", "f2"], save=False, show=True, ) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_pareto_front_binhkorn_001.png :alt: Pareto front :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_pareto_front_binhkorn_001.png :class: sphx-glr-multi-img * .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_pareto_front_binhkorn_002.png :alt: Pareto front :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_pareto_front_binhkorn_002.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.496 seconds) .. _sphx_glr_download_examples_post_process_algorithms_plot_pareto_front_binhkorn.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.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_pareto_front_binhkorn.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_