.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/mdo/plot_sellar.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_mdo_plot_sellar.py: A from scratch example on the Sellar problem ============================================ .. _sellar_from_scratch: .. GENERATED FROM PYTHON SOURCE LINES 29-37 Introduction ------------ In this example, we will create an MDO scenario based on the Sellar's problem from scratch. Contrary to the :ref:`|g| in ten minutes tutorial `, all the disciplines will be implemented from scratch by sub-classing the :class:`.MDODiscipline` class for each discipline of the Sellar problem. .. GENERATED FROM PYTHON SOURCE LINES 39-44 The Sellar problem ------------------ We will consider in this example the Sellar problem: .. include:: /tutorials/_description/sellar_problem_definition.inc .. GENERATED FROM PYTHON SOURCE LINES 46-50 Imports ------- All the imports needed for the tutorials are performed here. Note that some of the imports are related to the Python 2/3 compatibility. .. GENERATED FROM PYTHON SOURCE LINES 50-65 .. code-block:: default from __future__ import division, unicode_literals from math import exp from matplotlib import pyplot as plt from numpy import array, ones from gemseo.algos.design_space import DesignSpace from gemseo.api import configure_logger, create_scenario from gemseo.core.discipline import MDODiscipline configure_logger() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 66-92 Create the disciplinary classes ------------------------------- In this section, we define the Sellar disciplines by sub-classing the :class:`.MDODiscipline` class. For each class, the constructor and the _run method are overriden: - In the constructor, the input and output grammar are created. They define which inputs and outputs variables are allowed at the discipline execution. The default inputs are also defined, in case of the user does not provide them at the discipline execution. - In the _run method is implemented the concrete computation of the discipline. The inputs data are fetch by using the :meth:`.MDODiscipline.get_inputs_by_name` method. The returned NumPy arrays can then be used to compute the output values. They can then be stored in the :attr:`!MDODiscipline.local_data` dictionary. If the discipline execution is successful. Note that we do not define the Jacobians in the disciplines. In this example, we will approximate the derivatives using the finite differences method. Create the SellarSystem class ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 92-119 .. code-block:: default class SellarSystem(MDODiscipline): def __init__(self): super(SellarSystem, self).__init__() # Initialize the grammars to define inputs and outputs self.input_grammar.initialize_from_data_names(["x", "z", "y_1", "y_2"]) self.output_grammar.initialize_from_data_names(["obj", "c_1", "c_2"]) # Default inputs define what data to use when the inputs are not # provided to the execute method self.default_inputs = { "x": ones(1), "z": array([4.0, 3.0]), "y_1": ones(1), "y_2": ones(1), } def _run(self): # The run method defines what happens at execution # ie how outputs are computed from inputs x, z, y_1, y_2 = self.get_inputs_by_name(["x", "z", "y_1", "y_2"]) # The ouputs are stored here self.local_data["obj"] = array([x[0] ** 2 + z[1] + y_1[0] ** 2 + exp(-y_2[0])]) self.local_data["c_1"] = array([3.16 - y_1[0] ** 2]) self.local_data["c_2"] = array([y_2[0] - 24.0]) .. GENERATED FROM PYTHON SOURCE LINES 120-122 Create the Sellar1 class ^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 122-143 .. code-block:: default class Sellar1(MDODiscipline): def __init__(self): super(Sellar1, self).__init__() self.input_grammar.initialize_from_data_names(["x", "z", "y_2"]) self.output_grammar.initialize_from_data_names(["y_1"]) self.default_inputs = { "x": ones(1), "z": array([4.0, 3.0]), "y_1": ones(1), "y_2": ones(1), } def _run(self): x, z, y_2 = self.get_inputs_by_name(["x", "z", "y_2"]) self.local_data["y_1"] = array( [(z[0] ** 2 + z[1] + x[0] - 0.2 * y_2[0]) ** 0.5] ) .. GENERATED FROM PYTHON SOURCE LINES 144-146 Create the Sellar2 class ^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 146-165 .. code-block:: default class Sellar2(MDODiscipline): def __init__(self): super(Sellar2, self).__init__() self.input_grammar.initialize_from_data_names(["z", "y_1"]) self.output_grammar.initialize_from_data_names(["y_2"]) self.default_inputs = { "x": ones(1), "z": array([4.0, 3.0]), "y_1": ones(1), "y_2": ones(1), } def _run(self): z, y_1 = self.get_inputs_by_name(["z", "y_1"]) self.local_data["y_2"] = array([abs(y_1[0]) + z[0] + z[1]]) .. GENERATED FROM PYTHON SOURCE LINES 166-173 Create and execute the scenario ------------------------------- Instantiate disciplines ^^^^^^^^^^^^^^^^^^^^^^^ We can now instantiate the disciplines and store the instances in a list which will be used below. .. GENERATED FROM PYTHON SOURCE LINES 173-176 .. code-block:: default disciplines = [Sellar1(), Sellar2(), SellarSystem()] .. GENERATED FROM PYTHON SOURCE LINES 177-189 Create the design space ^^^^^^^^^^^^^^^^^^^^^^^ In this section, we define the design space which will be used for the creation of the MDOScenario. Note that the coupling variables are defined in the design space. Indeed, as we are going to select the IDF formulation to solve the MDO scenario, the coupling variables will be unknowns of the optimization problem and consequently they have to be included in the design space. Conversely, it would not have been necessary to include them if we aimed to select an MDF formulation. .. GENERATED FROM PYTHON SOURCE LINES 189-198 .. code-block:: default design_space = DesignSpace() design_space.add_variable("x", 1, l_b=0.0, u_b=10.0, value=ones(1)) design_space.add_variable( "z", 2, l_b=(-10, 0.0), u_b=(10.0, 10.0), value=array([4.0, 3.0]) ) design_space.add_variable("y_1", 1, l_b=-100.0, u_b=100.0, value=ones(1)) design_space.add_variable("y_2", 1, l_b=-100.0, u_b=100.0, value=ones(1)) .. GENERATED FROM PYTHON SOURCE LINES 199-204 Create the scenario ^^^^^^^^^^^^^^^^^^^ In this section, we build the MDO scenario which links the disciplines with the formulation, the design space and the objective function. .. GENERATED FROM PYTHON SOURCE LINES 204-208 .. code-block:: default scenario = create_scenario( disciplines, formulation="IDF", objective_name="obj", design_space=design_space ) .. GENERATED FROM PYTHON SOURCE LINES 209-213 Add the constraints ^^^^^^^^^^^^^^^^^^^ Then, we have to set the design constraints .. GENERATED FROM PYTHON SOURCE LINES 213-216 .. code-block:: default scenario.add_constraint("c_1", "ineq") scenario.add_constraint("c_2", "ineq") .. GENERATED FROM PYTHON SOURCE LINES 217-220 As previously mentioned, we are going to use finite differences to approximate the derivatives since the disciplines do not provide them. .. GENERATED FROM PYTHON SOURCE LINES 220-222 .. code-block:: default scenario.set_differentiation_method("finite_differences", 1e-6) .. GENERATED FROM PYTHON SOURCE LINES 223-229 Execute the scenario ^^^^^^^^^^^^^^^^^^^^ Then, we execute the MDO scenario with the inputs of the MDO scenario as a dictionary. In this example, the gradient-based `SLSQP` optimizer is selected, with 10 iterations at maximum: .. GENERATED FROM PYTHON SOURCE LINES 229-231 .. code-block:: default scenario.execute(input_data={"max_iter": 10, "algo": "SLSQP"}) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 14:43:35: INFO - 14:43:35: *** Start MDO Scenario execution *** INFO - 14:43:35: MDOScenario INFO - 14:43:35: Disciplines: Sellar1 Sellar2 SellarSystem INFO - 14:43:35: MDOFormulation: IDF INFO - 14:43:35: Algorithm: SLSQP INFO - 14:43:35: Optimization problem: INFO - 14:43:35: Minimize: obj(x, z, y_1, y_2) INFO - 14:43:35: With respect to: x, z, y_1, y_2 INFO - 14:43:35: Subject to constraints: INFO - 14:43:35: c_1(x, z, y_1, y_2) <= 0.0 INFO - 14:43:35: c_2(x, z, y_1, y_2) <= 0.0 INFO - 14:43:35: y_1(x, z, y_2): y_1(x, z, y_2) - y_1 == 0.0 INFO - 14:43:35: y_2(z, y_1): y_2(z, y_1) - y_2 == 0.0 INFO - 14:43:35: Design space: INFO - 14:43:35: +------+-------------+-------+-------------+-------+ INFO - 14:43:35: | name | lower_bound | value | upper_bound | type | INFO - 14:43:35: +------+-------------+-------+-------------+-------+ INFO - 14:43:35: | x | 0 | 1 | 10 | float | INFO - 14:43:35: | z | -10 | 4 | 10 | float | INFO - 14:43:35: | z | 0 | 3 | 10 | float | INFO - 14:43:35: | y_1 | -100 | 1 | 100 | float | INFO - 14:43:35: | y_2 | -100 | 1 | 100 | float | INFO - 14:43:35: +------+-------------+-------+-------------+-------+ INFO - 14:43:35: Optimization: 0%| | 0/10 [00:00` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sellar.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_