.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/formulations/plot_sobieski_mdf_example.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_formulations_plot_sobieski_mdf_example.py: MDF-based MDO on the Sobieski SSBJ test case ============================================ .. GENERATED FROM PYTHON SOURCE LINES 24-32 .. code-block:: default from gemseo.api import configure_logger from gemseo.api import create_discipline from gemseo.api import create_scenario from gemseo.problems.sobieski.core.problem import SobieskiProblem from matplotlib import pyplot as plt configure_logger() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 33-40 Instantiate the disciplines ---------------------------- First, we instantiate the four disciplines of the use case: :class:`~gemseo.problems.sobieski.disciplines.SobieskiPropulsion`, :class:`~gemseo.problems.sobieski.disciplines.SobieskiAerodynamics`, :class:`~gemseo.problems.sobieski.disciplines.SobieskiMission` and :class:`~gemseo.problems.sobieski.disciplines.SobieskiStructure`. .. GENERATED FROM PYTHON SOURCE LINES 40-49 .. code-block:: default disciplines = create_discipline( [ "SobieskiPropulsion", "SobieskiAerodynamics", "SobieskiMission", "SobieskiStructure", ] ) .. GENERATED FROM PYTHON SOURCE LINES 50-61 Build, execute and post-process the scenario -------------------------------------------- Then, we build the scenario which links the disciplines with the formulation and the optimization algorithm. Here, we use the :class:`.MDF` formulation. We tell the scenario to minimize -y_4 instead of minimizing y_4 (range), which is the default option. Instantiate the scenario ^^^^^^^^^^^^^^^^^^^^^^^^ During the instantiation of the scenario, we provide some options for the MDF formulations: .. GENERATED FROM PYTHON SOURCE LINES 61-68 .. code-block:: default formulation_options = { "tolerance": 1e-10, "max_mda_iter": 50, "warm_start": True, "use_lu_fact": True, "linear_solver_tolerance": 1e-15, } .. GENERATED FROM PYTHON SOURCE LINES 69-78 - :code:`'warm_start`: warm starts MDA, - :code:`'warm_start`: optimize the adjoints resolution by storing the Jacobian matrix LU factorization for the multiple RHS (objective + constraints). This saves CPU time if you can pay for the memory and have the full Jacobians available, not just matrix vector products. - :code:`'linear_solver_tolerance'`: set the linear solver tolerance, idem we need full convergence .. GENERATED FROM PYTHON SOURCE LINES 79-89 .. code-block:: default design_space = SobieskiProblem().design_space scenario = create_scenario( disciplines, "MDF", objective_name="y_4", design_space=design_space, maximize_objective=True, **formulation_options, ) .. GENERATED FROM PYTHON SOURCE LINES 90-92 Set the design constraints ^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 92-95 .. code-block:: default for c_name in ["g_1", "g_2", "g_3"]: scenario.add_constraint(c_name, "ineq") .. GENERATED FROM PYTHON SOURCE LINES 96-102 XDSMIZE the scenario ^^^^^^^^^^^^^^^^^^^^ Generate the XDSM file on the fly, setting print_statuses=true will print the status in the console html_output (default True), will generate a self contained html file, that can be automatically open using open_browser=True .. GENERATED FROM PYTHON SOURCE LINES 102-104 .. code-block:: default scenario.xdsmize(html_output=True, print_statuses=False, open_browser=False) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 10:05:51: Generating HTML XDSM file in : xdsm.html .. GENERATED FROM PYTHON SOURCE LINES 105-116 Define the algorithm inputs ^^^^^^^^^^^^^^^^^^^^^^^^^^^ We set the maximum number of iterations, the optimizer and the optimizer options. Algorithm specific options are passed there. Use :meth:`~gemseo.api.get_algorithm_options_schema` API function for more information or read the documentation. Here ftol_rel option is a stop criteria based on the relative difference in the objective between two iterates ineq_tolerance the tolerance determination of the optimum; this is specific to the |g| wrapping and not in the solver. .. GENERATED FROM PYTHON SOURCE LINES 116-123 .. code-block:: default algo_options = { "ftol_rel": 1e-10, "ineq_tolerance": 2e-3, "normalize_design_space": True, } scn_inputs = {"max_iter": 10, "algo": "SLSQP", "algo_options": algo_options} .. GENERATED FROM PYTHON SOURCE LINES 124-138 .. seealso:: We can also generates a backup file for the optimization, as well as plots on the fly of the optimization history if option :code:`generate_opt_plot` is :code:`True`. This slows down a lot the process, here since SSBJ is very light .. code:: scenario.set_optimization_history_backup(file_path="mdf_backup.h5", each_new_iter=True, each_store=False, erase=True, pre_load=False, generate_opt_plot=True) .. GENERATED FROM PYTHON SOURCE LINES 140-142 Execute the scenario ^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 142-144 .. code-block:: default scenario.execute(scn_inputs) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 10:05:51: INFO - 10:05:51: *** Start MDOScenario execution *** INFO - 10:05:51: MDOScenario INFO - 10:05:51: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure INFO - 10:05:51: MDO formulation: MDF INFO - 10:05:51: Optimization problem: INFO - 10:05:51: minimize -y_4(x_shared, x_1, x_2, x_3) INFO - 10:05:51: with respect to x_1, x_2, x_3, x_shared INFO - 10:05:51: subject to constraints: INFO - 10:05:51: g_1(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:05:51: g_2(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:05:51: g_3(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:05:51: over the design space: INFO - 10:05:51: +----------+-------------+-------+-------------+-------+ INFO - 10:05:51: | name | lower_bound | value | upper_bound | type | INFO - 10:05:51: +----------+-------------+-------+-------------+-------+ INFO - 10:05:51: | x_shared | 0.01 | 0.05 | 0.09 | float | INFO - 10:05:51: | x_shared | 30000 | 45000 | 60000 | float | INFO - 10:05:51: | x_shared | 1.4 | 1.6 | 1.8 | float | INFO - 10:05:51: | x_shared | 2.5 | 5.5 | 8.5 | float | INFO - 10:05:51: | x_shared | 40 | 55 | 70 | float | INFO - 10:05:51: | x_shared | 500 | 1000 | 1500 | float | INFO - 10:05:51: | x_1 | 0.1 | 0.25 | 0.4 | float | INFO - 10:05:51: | x_1 | 0.75 | 1 | 1.25 | float | INFO - 10:05:51: | x_2 | 0.75 | 1 | 1.25 | float | INFO - 10:05:51: | x_3 | 0.1 | 0.5 | 1 | float | INFO - 10:05:51: +----------+-------------+-------+-------------+-------+ INFO - 10:05:51: Solving optimization problem with algorithm SLSQP: INFO - 10:05:51: ... 0%| | 0/10 [00:00 .. GENERATED FROM PYTHON SOURCE LINES 168-170 Plot the basic history view ^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 170-174 .. code-block:: default scenario.post_process( "BasicHistory", variable_names=["x_shared"], save=False, show=False ) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png :alt: History plot :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 175-177 Plot the constraints and objective history ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 177-179 .. code-block:: default scenario.post_process("ObjConstrHist", save=False, show=False) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_007.png :alt: Evolution of the objective value and maximal constraint :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_007.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 180-182 Plot the constraints history ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 182-186 .. code-block:: default scenario.post_process( "ConstraintsHistory", save=False, show=False, constraint_names=["g_1", "g_2", "g_3"] ) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_008.png :alt: Evolution of the constraints w.r.t. iterations, g_1 (0), g_1 (1), g_1 (2), g_1 (3), g_1 (4), g_1 (5), g_1 (6), g_2, g_3 (0), g_3 (1), g_3 (2), g_3 (3) :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_008.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 187-189 Plot the constraints history using a radar chart ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 189-193 .. code-block:: default scenario.post_process( "RadarChart", save=False, show=False, constraint_names=["g_1", "g_2", "g_3"] ) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_009.png :alt: Constraints at iteration 4 (optimum) :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_009.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 194-196 Plot the quadratic approximation of the objective ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 196-198 .. code-block:: default scenario.post_process("QuadApprox", function="-y_4", save=False, show=False) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png :alt: Hessian matrix SR1 approximation of -y_4 :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png :class: sphx-glr-multi-img * .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png :alt: plot sobieski mdf example :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 199-201 Plot the functions using a SOM ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 201-203 .. code-block:: default scenario.post_process("SOM", save=False, show=False) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png :alt: Self Organizing Maps of the design space, -y_4, g_1_6, g_2, g_3_3 :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 10:05:55: Building Self Organizing Map from optimization history: INFO - 10:05:55: Number of neurons in x direction = 4 INFO - 10:05:55: Number of neurons in y direction = 4 .. GENERATED FROM PYTHON SOURCE LINES 204-206 Plot the scatter matrix of variables of interest ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 206-214 .. code-block:: default scenario.post_process( "ScatterPlotMatrix", save=False, show=False, variable_names=["-y_4", "g_1"], fig_size=(14, 14), ) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_013.png :alt: plot sobieski mdf example :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_013.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 215-217 Plot the variables using the parallel coordinates ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 217-219 .. code-block:: default scenario.post_process("ParallelCoordinates", save=False, show=False) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_014.png :alt: Design variables history colored by '-y_4' value :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_014.png :class: sphx-glr-multi-img * .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_015.png :alt: Objective function and constraints history colored by '-y_4' value. :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_015.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 220-222 Plot the robustness of the solution ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 222-224 .. code-block:: default scenario.post_process("Robustness", save=False, show=False) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png :alt: Boxplot of the optimization functions with normalized stddev 0.01 :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 225-227 Plot the influence of the design variables ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 227-230 .. code-block:: default scenario.post_process("VariableInfluence", save=False, show=False, fig_size=(14, 14)) # Workaround for HTML rendering, instead of ``show=True`` plt.show() .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_017.png :alt: Partial variation of the functions wrt design variables, 9 variables required to explain 99% of -y_4 variations, 5 variables required to explain 99% of g_1_0 variations, 5 variables required to explain 99% of g_1_1 variations, 5 variables required to explain 99% of g_1_2 variations, 5 variables required to explain 99% of g_1_3 variations, 5 variables required to explain 99% of g_1_4 variations, 4 variables required to explain 99% of g_1_5 variations, 4 variables required to explain 99% of g_1_6 variations, 1 variables required to explain 99% of g_2 variations, 7 variables required to explain 99% of g_3_0 variations, 7 variables required to explain 99% of g_3_1 variations, 3 variables required to explain 99% of g_3_2 variations, 3 variables required to explain 99% of g_3_3 variations :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_017.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 10:06:00: VariableInfluence for function -y_4 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [1 4 3 2 5 9 7 8 0] /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/4.0.1/lib/python3.9/site-packages/gemseo/post/variable_influence.py:234: UserWarning: FixedFormatter should only be used together with FixedLocator axe.set_xticklabels(x_labels, fontsize=font_size, rotation=rotation) INFO - 10:06:00: VariableInfluence for function g_1_0 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [0 7 3 5 6] INFO - 10:06:00: VariableInfluence for function g_1_1 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [7 0 3 5 6] INFO - 10:06:00: VariableInfluence for function g_1_2 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [7 0 3 5 6] INFO - 10:06:00: VariableInfluence for function g_1_3 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [7 0 3 5 6] INFO - 10:06:00: VariableInfluence for function g_1_4 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [7 0 3 5 6] INFO - 10:06:00: VariableInfluence for function g_1_5 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [3 7 5 6] INFO - 10:06:00: VariableInfluence for function g_1_6 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [3 7 5 6] INFO - 10:06:00: VariableInfluence for function g_2 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [0] INFO - 10:06:00: VariableInfluence for function g_3_0 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [1 9 5 2 4 0 8] INFO - 10:06:00: VariableInfluence for function g_3_1 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [1 9 5 2 4 0 8] INFO - 10:06:00: VariableInfluence for function g_3_2 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [1 9 2] INFO - 10:06:00: VariableInfluence for function g_3_3 INFO - 10:06:00: Most influential variables indices to explain % of the function variation: 99 INFO - 10:06:00: [9 1 2] .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 10.142 seconds) .. _sphx_glr_download_examples_formulations_plot_sobieski_mdf_example.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_sobieski_mdf_example.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sobieski_mdf_example.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_