.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/post_process/algorithms/plot_robustness.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_robustness.py: Robustness ========== In this example, we illustrate the use of the :class:`.Robustness` plot on the Sobieski's SSBJ problem. .. GENERATED FROM PYTHON SOURCE LINES 28-36 .. code-block:: Python from __future__ import annotations from gemseo import configure_logger from gemseo import create_discipline from gemseo import create_scenario from gemseo.problems.sobieski.core.design_space import SobieskiDesignSpace .. GENERATED FROM PYTHON SOURCE LINES 37-41 Import ------ The first step is to import some high-level functions and a method to get the design space. .. GENERATED FROM PYTHON SOURCE LINES 41-44 .. code-block:: Python configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 45-60 Description ----------- In the :class:`.Robustness` post-processing, the robustness of the optimum is represented by a box plot. Using the quadratic approximations of all the output functions, we propagate analytically a normal distribution with 1% standard deviation on all the design variables, assuming no cross-correlations of inputs, to obtain the mean and standard deviation of the resulting normal distribution. A series of samples are randomly generated from the resulting distribution, whose quartiles are plotted, relatively to the values of the function at the optimum. For each function (in abscissa), the plot shows the extreme values encountered in the samples (top and bottom bars). Then, 95% of the values are within the blue boxes. The average is given by the red bar. .. GENERATED FROM PYTHON SOURCE LINES 62-66 Create disciplines ------------------ At this point, we instantiate the disciplines of Sobieski's SSBJ problem: Propulsion, Aerodynamics, Structure and Mission .. GENERATED FROM PYTHON SOURCE LINES 66-73 .. code-block:: Python disciplines = create_discipline([ "SobieskiPropulsion", "SobieskiAerodynamics", "SobieskiStructure", "SobieskiMission", ]) .. GENERATED FROM PYTHON SOURCE LINES 74-77 Create design space ------------------- We also create the :class:`.SobieskiDesignSpace`. .. GENERATED FROM PYTHON SOURCE LINES 77-79 .. code-block:: Python design_space = SobieskiDesignSpace() .. GENERATED FROM PYTHON SOURCE LINES 80-87 Create and execute scenario --------------------------- The next step is to build an MDO scenario in order to maximize the range, encoded 'y_4', with respect to the design parameters, while satisfying the inequality constraints 'g_1', 'g_2' and 'g_3'. We can use the MDF formulation, the SLSQP optimization algorithm and a maximum number of iterations equal to 100. .. GENERATED FROM PYTHON SOURCE LINES 87-99 .. code-block:: Python scenario = create_scenario( disciplines, formulation="MDF", objective_name="y_4", maximize_objective=True, design_space=design_space, ) scenario.set_differentiation_method() for constraint in ["g_1", "g_2", "g_3"]: scenario.add_constraint(constraint, "ineq") scenario.execute({"algo": "SLSQP", "max_iter": 10}) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:55:42: INFO - 10:55:42: *** Start MDOScenario execution *** INFO - 10:55:42: MDOScenario INFO - 10:55:42: Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure INFO - 10:55:42: MDO formulation: MDF INFO - 10:55:42: Optimization problem: INFO - 10:55:42: minimize -y_4(x_shared, x_1, x_2, x_3) INFO - 10:55:42: with respect to x_1, x_2, x_3, x_shared INFO - 10:55:42: subject to constraints: INFO - 10:55:42: g_1(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:55:42: g_2(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:55:42: g_3(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:55:42: over the design space: INFO - 10:55:42: +-------------+-------------+-------+-------------+-------+ INFO - 10:55:42: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:55:42: +-------------+-------------+-------+-------------+-------+ INFO - 10:55:42: | x_shared[0] | 0.01 | 0.05 | 0.09 | float | INFO - 10:55:42: | x_shared[1] | 30000 | 45000 | 60000 | float | INFO - 10:55:42: | x_shared[2] | 1.4 | 1.6 | 1.8 | float | INFO - 10:55:42: | x_shared[3] | 2.5 | 5.5 | 8.5 | float | INFO - 10:55:42: | x_shared[4] | 40 | 55 | 70 | float | INFO - 10:55:42: | x_shared[5] | 500 | 1000 | 1500 | float | INFO - 10:55:42: | x_1[0] | 0.1 | 0.25 | 0.4 | float | INFO - 10:55:42: | x_1[1] | 0.75 | 1 | 1.25 | float | INFO - 10:55:42: | x_2 | 0.75 | 1 | 1.25 | float | INFO - 10:55:42: | x_3 | 0.1 | 0.5 | 1 | float | INFO - 10:55:42: +-------------+-------------+-------+-------------+-------+ INFO - 10:55:42: Solving optimization problem with algorithm SLSQP: INFO - 10:55:42: 10%|█ | 1/10 [00:00<00:00, 9.28 it/sec, obj=-536] INFO - 10:55:42: 20%|██ | 2/10 [00:00<00:01, 6.63 it/sec, obj=-2.12e+3] WARNING - 10:55:43: MDAJacobi has reached its maximum number of iterations but the normed residual 1.7130677857005655e-05 is still above the tolerance 1e-06. INFO - 10:55:43: 30%|███ | 3/10 [00:00<00:01, 5.62 it/sec, obj=-3.75e+3] INFO - 10:55:43: 40%|████ | 4/10 [00:00<00:01, 5.36 it/sec, obj=-3.96e+3] INFO - 10:55:43: 50%|█████ | 5/10 [00:00<00:00, 5.22 it/sec, obj=-3.96e+3] INFO - 10:55:43: Optimization result: INFO - 10:55:43: Optimizer info: INFO - 10:55:43: Status: 8 INFO - 10:55:43: Message: Positive directional derivative for linesearch INFO - 10:55:43: Number of calls to the objective function by the optimizer: 6 INFO - 10:55:43: Solution: INFO - 10:55:43: The solution is feasible. INFO - 10:55:43: Objective: -3963.408265187933 INFO - 10:55:43: Standardized constraints: INFO - 10:55:43: g_1 = [-0.01806104 -0.03334642 -0.04424946 -0.0518346 -0.05732607 -0.13720865 INFO - 10:55:43: -0.10279135] INFO - 10:55:43: g_2 = 3.333278582928756e-06 INFO - 10:55:43: g_3 = [-7.67181773e-01 -2.32818227e-01 8.30379541e-07 -1.83255000e-01] INFO - 10:55:43: Design space: INFO - 10:55:43: +-------------+-------------+---------------------+-------------+-------+ INFO - 10:55:43: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:55:43: +-------------+-------------+---------------------+-------------+-------+ INFO - 10:55:43: | x_shared[0] | 0.01 | 0.06000083331964572 | 0.09 | float | INFO - 10:55:43: | x_shared[1] | 30000 | 60000 | 60000 | float | INFO - 10:55:43: | x_shared[2] | 1.4 | 1.4 | 1.8 | float | INFO - 10:55:43: | x_shared[3] | 2.5 | 2.5 | 8.5 | float | INFO - 10:55:43: | x_shared[4] | 40 | 70 | 70 | float | INFO - 10:55:43: | x_shared[5] | 500 | 1500 | 1500 | float | INFO - 10:55:43: | x_1[0] | 0.1 | 0.4 | 0.4 | float | INFO - 10:55:43: | x_1[1] | 0.75 | 0.75 | 1.25 | float | INFO - 10:55:43: | x_2 | 0.75 | 0.75 | 1.25 | float | INFO - 10:55:43: | x_3 | 0.1 | 0.1562448753887276 | 1 | float | INFO - 10:55:43: +-------------+-------------+---------------------+-------------+-------+ INFO - 10:55:43: *** End MDOScenario execution (time: 0:00:01.095196) *** {'max_iter': 10, 'algo': 'SLSQP'} .. GENERATED FROM PYTHON SOURCE LINES 100-105 Post-process scenario --------------------- Lastly, we post-process the scenario by means of the :class:`.Robustness` which plots any of the constraint or objective functions w.r.t. the optimization iterations or sampling snapshots. .. GENERATED FROM PYTHON SOURCE LINES 107-115 .. tip:: Each post-processing method requires different inputs and offers a variety of customization options. Use the high-level function :func:`.get_post_processing_options_schema` to print a table with the options for any post-processing algorithm. Or refer to our dedicated page: :ref:`gen_post_algos`. .. GENERATED FROM PYTHON SOURCE LINES 115-117 .. code-block:: Python scenario.post_process("Robustness", save=False, show=True) .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_robustness_001.png :alt: Boxplot of the optimization functions with normalized stddev 0.01 :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_robustness_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.325 seconds) .. _sphx_glr_download_examples_post_process_algorithms_plot_robustness.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_robustness.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_robustness.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_