.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/scenario/plot_mdo_scenario.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_scenario_plot_mdo_scenario.py: Create an MDO Scenario ====================== .. GENERATED FROM PYTHON SOURCE LINES 26-41 .. code-block:: Python from __future__ import annotations from numpy import ones from gemseo import configure_logger from gemseo import create_design_space from gemseo import create_discipline from gemseo import create_scenario from gemseo import get_available_opt_algorithms from gemseo import get_available_post_processings configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 42-63 Let :math:`(P)` be a simple optimization problem: .. math:: (P) = \left\{ \begin{aligned} & \underset{x}{\text{minimize}} & & f(x) = \sin(x) - \exp(x) \\ & \text{subject to} & & -2 \leq x \leq 2 \end{aligned} \right. In this subsection, we will see how to use |g| to solve this problem :math:`(P)` by means of an optimization algorithm. Define the discipline --------------------- Firstly, by means of the high-level function :func:`.create_discipline`, we create an :class:`.MDODiscipline` of :class:`.AnalyticDiscipline` type from a Python function: .. GENERATED FROM PYTHON SOURCE LINES 63-67 .. code-block:: Python expressions = {"y": "sin(x)-exp(x)"} discipline = create_discipline("AnalyticDiscipline", expressions=expressions) .. GENERATED FROM PYTHON SOURCE LINES 68-71 We can quickly access the most relevant information of any discipline (name, inputs, and outputs) with their string representations. Moreover, we can get the default input values of a discipline with the attribute :attr:`.MDODiscipline.default_inputs` .. GENERATED FROM PYTHON SOURCE LINES 71-73 .. code-block:: Python discipline, discipline.default_inputs .. rst-class:: sphx-glr-script-out .. code-block:: none (AnalyticDiscipline Inputs: x Outputs: y, {'x': array([0.])}) .. GENERATED FROM PYTHON SOURCE LINES 74-82 Now, we can to minimize this :class:`.MDODiscipline` over a design space, by means of a quasi-Newton method from the initial point :math:`0.5`. Define the design space ----------------------- For that, by means of the high-level function :func:`.create_design_space`, we define the :class:`.DesignSpace` :math:`[-2, 2]` with initial value :math:`0.5` by using its :meth:`.DesignSpace.add_variable` method. .. GENERATED FROM PYTHON SOURCE LINES 82-86 .. code-block:: Python design_space = create_design_space() design_space.add_variable("x", l_b=-2.0, u_b=2.0, value=-0.5 * ones(1)) .. GENERATED FROM PYTHON SOURCE LINES 87-92 Define the MDO scenario ----------------------- Then, by means of the :func:`.create_scenario` API function, we define an :class:`.MDOScenario` from the :class:`.MDODiscipline` and the :class:`.DesignSpace` defined above: .. GENERATED FROM PYTHON SOURCE LINES 92-95 .. code-block:: Python scenario = create_scenario(discipline, "DisciplinaryOpt", "y", design_space) .. GENERATED FROM PYTHON SOURCE LINES 96-108 What about the differentiation method? -------------------------------------- The :class:`.AnalyticDiscipline` automatically differentiates the expressions to obtain the Jacobian matrices. Therefore, there is no need to define a differentiation method in this case. Keep in mind that for a generic discipline with no defined Jacobian function, you can use the :meth:`.Scenario.set_differentiation_method` method to define a numerical approximation of the gradients. .. code:: scenario.set_differentiation_method("finite_differences") .. GENERATED FROM PYTHON SOURCE LINES 110-117 Execute the MDO scenario ------------------------ Lastly, we solve the :class:`.OptimizationProblem` included in the :class:`.MDOScenario` defined above by minimizing the objective function over the :class:`.DesignSpace`. Precisely, we choose the `L-BFGS-B algorithm `_ implemented in the function ``scipy.optimize.fmin_l_bfgs_b``. .. GENERATED FROM PYTHON SOURCE LINES 117-120 .. code-block:: Python scenario.execute({"algo": "L-BFGS-B", "max_iter": 100}) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:51:22: INFO - 10:51:22: *** Start MDOScenario execution *** INFO - 10:51:22: MDOScenario INFO - 10:51:22: Disciplines: AnalyticDiscipline INFO - 10:51:22: MDO formulation: DisciplinaryOpt INFO - 10:51:22: Optimization problem: INFO - 10:51:22: minimize y(x) INFO - 10:51:22: with respect to x INFO - 10:51:22: over the design space: INFO - 10:51:22: +------+-------------+-------+-------------+-------+ INFO - 10:51:22: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:51:22: +------+-------------+-------+-------------+-------+ INFO - 10:51:22: | x | -2 | -0.5 | 2 | float | INFO - 10:51:22: +------+-------------+-------+-------------+-------+ INFO - 10:51:22: Solving optimization problem with algorithm L-BFGS-B: INFO - 10:51:22: 1%| | 1/100 [00:00<00:00, 361.02 it/sec, obj=-1.09] INFO - 10:51:22: 2%|▏ | 2/100 [00:00<00:00, 430.58 it/sec, obj=-1.04] INFO - 10:51:22: 3%|▎ | 3/100 [00:00<00:00, 525.89 it/sec, obj=-1.24] INFO - 10:51:22: 4%|▍ | 4/100 [00:00<00:00, 546.38 it/sec, obj=-1.23] INFO - 10:51:22: 5%|▌ | 5/100 [00:00<00:00, 566.06 it/sec, obj=-1.24] INFO - 10:51:22: 6%|▌ | 6/100 [00:00<00:00, 577.38 it/sec, obj=-1.24] INFO - 10:51:22: 7%|▋ | 7/100 [00:00<00:00, 588.12 it/sec, obj=-1.24] INFO - 10:51:22: Optimization result: INFO - 10:51:22: Optimizer info: INFO - 10:51:22: Status: 0 INFO - 10:51:22: Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL INFO - 10:51:22: Number of calls to the objective function by the optimizer: 8 INFO - 10:51:22: Solution: INFO - 10:51:22: Objective: -1.2361083418592416 INFO - 10:51:22: Design space: INFO - 10:51:22: +------+-------------+--------------------+-------------+-------+ INFO - 10:51:22: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:51:22: +------+-------------+--------------------+-------------+-------+ INFO - 10:51:22: | x | -2 | -1.292695718944152 | 2 | float | INFO - 10:51:22: +------+-------------+--------------------+-------------+-------+ INFO - 10:51:22: *** End MDOScenario execution (time: 0:00:00.025802) *** {'max_iter': 100, 'algo': 'L-BFGS-B'} .. GENERATED FROM PYTHON SOURCE LINES 121-123 The optimum results can be found in the execution log. It is also possible to access them with :attr:`.Scenario.optimization_result`: .. GENERATED FROM PYTHON SOURCE LINES 123-127 .. code-block:: Python optimization_result = scenario.optimization_result f"The solution of P is (x*, f(x*)) = ({optimization_result.x_opt}, {optimization_result.f_opt})" .. rst-class:: sphx-glr-script-out .. code-block:: none 'The solution of P is (x*, f(x*)) = ([-1.29269572], -1.2361083418592416)' .. GENERATED FROM PYTHON SOURCE LINES 128-138 .. seealso:: You can find the `SciPy `_ implementation of the `L-BFGS-B algorithm `_ algorithm `by clicking here `_. # noqa Available algorithms -------------------- In order to get the list of available optimization algorithms, use: .. GENERATED FROM PYTHON SOURCE LINES 138-140 .. code-block:: Python get_available_opt_algorithms() .. rst-class:: sphx-glr-script-out .. code-block:: none ['Augmented_Lagrangian_order_0', 'Augmented_Lagrangian_order_1', 'MMA', 'NLOPT_MMA', 'NLOPT_COBYLA', 'NLOPT_SLSQP', 'NLOPT_BOBYQA', 'NLOPT_BFGS', 'NLOPT_NEWUOA', 'PDFO_COBYLA', 'PDFO_BOBYQA', 'PDFO_NEWUOA', 'PSEVEN', 'PSEVEN_FD', 'PSEVEN_MOM', 'PSEVEN_NCG', 'PSEVEN_NLS', 'PSEVEN_POWELL', 'PSEVEN_QP', 'PSEVEN_SQP', 'PSEVEN_SQ2P', 'PYMOO_GA', 'PYMOO_NSGA2', 'PYMOO_NSGA3', 'PYMOO_UNSGA3', 'PYMOO_RNSGA3', 'DUAL_ANNEALING', 'SHGO', 'DIFFERENTIAL_EVOLUTION', 'LINEAR_INTERIOR_POINT', 'REVISED_SIMPLEX', 'SIMPLEX', 'HIGHS_INTERIOR_POINT', 'HIGHS_DUAL_SIMPLEX', 'HIGHS', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'SBO'] .. GENERATED FROM PYTHON SOURCE LINES 141-144 Available post-processing ------------------------- In order to get the list of available post-processing algorithms, use: .. GENERATED FROM PYTHON SOURCE LINES 144-146 .. code-block:: Python get_available_post_processings() .. rst-class:: sphx-glr-script-out .. code-block:: none ['Animation', 'BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', 'DataVersusModel', 'GradientSensitivity', 'HighTradeOff', 'MultiObjectiveDiagram', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'Petal', 'QuadApprox', 'Radar', 'RadarChart', 'Robustness', 'SOM', 'ScatterPareto', 'ScatterPlotMatrix', 'TopologyView', 'VariableInfluence'] .. GENERATED FROM PYTHON SOURCE LINES 147-152 Exporting the problem data. --------------------------- After the execution of the scenario, you may want to export your data to use it elsewhere. The :meth:`.Scenario.to_dataset` will allow you to export your results to a :class:`.Dataset`, the basic |g| class to store data. .. GENERATED FROM PYTHON SOURCE LINES 152-154 .. code-block:: Python dataset = scenario.to_dataset("a_name_for_my_dataset") .. GENERATED FROM PYTHON SOURCE LINES 155-161 You can also look at the examples: .. raw:: html .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.046 seconds) .. _sphx_glr_download_examples_scenario_plot_mdo_scenario.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_mdo_scenario.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_mdo_scenario.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_