.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/optimization_problem/plot_simple_opt_2.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_optimization_problem_plot_simple_opt_2.py: Analytical test case # 2 ======================== .. GENERATED FROM PYTHON SOURCE LINES 24-29 In this example, we consider a simple optimization problem to illustrate algorithms interfaces and optimization libraries integration. Imports ------- .. GENERATED FROM PYTHON SOURCE LINES 29-46 .. code-block:: Python from __future__ import annotations from numpy import cos from numpy import exp from numpy import sin from gemseo import configure_logger from gemseo import execute_algo from gemseo import execute_post from gemseo import get_available_opt_algorithms from gemseo.algos.design_space import DesignSpace from gemseo.algos.optimization_problem import OptimizationProblem from gemseo.core.mdo_functions.mdo_function import MDOFunction configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 47-51 Define the objective function ----------------------------- We define the objective function :math:`f(x)=\sin(x)-\exp(x)` using an :class:`.MDOFunction` defined by the sum of :class:`.MDOFunction` objects. .. GENERATED FROM PYTHON SOURCE LINES 51-55 .. code-block:: Python f_1 = MDOFunction(sin, name="f_1", jac=cos, expr="sin(x)") f_2 = MDOFunction(exp, name="f_2", jac=exp, expr="exp(x)") objective = f_1 - f_2 .. GENERATED FROM PYTHON SOURCE LINES 56-64 .. seealso:: The following operators are implemented: addition, subtraction and multiplication. The minus operator is also defined. Define the design space ----------------------- Then, we define the :class:`.DesignSpace` with |g|. .. GENERATED FROM PYTHON SOURCE LINES 64-67 .. code-block:: Python design_space = DesignSpace() design_space.add_variable("x", lower_bound=-2.0, upper_bound=2.0, value=-0.5) .. GENERATED FROM PYTHON SOURCE LINES 68-71 Define the optimization problem ------------------------------- Then, we define the :class:`.OptimizationProblem` with |g|. .. GENERATED FROM PYTHON SOURCE LINES 71-74 .. code-block:: Python problem = OptimizationProblem(design_space) problem.objective = objective .. GENERATED FROM PYTHON SOURCE LINES 75-81 Solve the optimization problem using an optimization algorithm -------------------------------------------------------------- Finally, we solve the optimization problems with |g| interface. Solve the problem ^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 81-84 .. code-block:: Python optimization_result = execute_algo(problem, algo_name="L-BFGS-B") optimization_result .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 08:35:46: Optimization problem: INFO - 08:35:46: minimize [f_1-f_2] = sin(x)-exp(x) INFO - 08:35:46: with respect to x INFO - 08:35:46: over the design space: INFO - 08:35:46: +------+-------------+-------+-------------+-------+ INFO - 08:35:46: | Name | Lower bound | Value | Upper bound | Type | INFO - 08:35:46: +------+-------------+-------+-------------+-------+ INFO - 08:35:46: | x | -2 | -0.5 | 2 | float | INFO - 08:35:46: +------+-------------+-------+-------------+-------+ INFO - 08:35:46: Solving optimization problem with algorithm L-BFGS-B: INFO - 08:35:46: 1%| | 6/1000 [00:00<00:00, 1270.30 it/sec, obj=-1.24] INFO - 08:35:46: 1%| | 7/1000 [00:00<00:00, 1211.83 it/sec, obj=-1.24] INFO - 08:35:46: Optimization result: INFO - 08:35:46: Optimizer info: INFO - 08:35:46: Status: 0 INFO - 08:35:46: Message: CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL INFO - 08:35:46: Number of calls to the objective function by the optimizer: 8 INFO - 08:35:46: Solution: INFO - 08:35:46: Objective: -1.2361083418592416 INFO - 08:35:46: Design space: INFO - 08:35:46: +------+-------------+--------------------+-------------+-------+ INFO - 08:35:46: | Name | Lower bound | Value | Upper bound | Type | INFO - 08:35:46: +------+-------------+--------------------+-------------+-------+ INFO - 08:35:46: | x | -2 | -1.292695718944152 | 2 | float | INFO - 08:35:46: +------+-------------+--------------------+-------------+-------+ .. raw:: html
Optimization result:
  • Design variables: [-1.29269572]
  • Objective function: -1.2361083418592416
  • Feasible solution: True


.. GENERATED FROM PYTHON SOURCE LINES 85-86 Note that you can get all the optimization algorithms names: .. GENERATED FROM PYTHON SOURCE LINES 86-88 .. code-block:: Python get_available_opt_algorithms() .. rst-class:: sphx-glr-script-out .. code-block:: none ['Augmented_Lagrangian_order_0', 'Augmented_Lagrangian_order_1', 'MNBI', 'MultiStart', 'NLOPT_MMA', 'NLOPT_COBYLA', 'NLOPT_SLSQP', 'NLOPT_BOBYQA', 'NLOPT_BFGS', 'NLOPT_NEWUOA', 'DUAL_ANNEALING', 'SHGO', 'DIFFERENTIAL_EVOLUTION', 'INTERIOR_POINT', 'DUAL_SIMPLEX', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'NELDER-MEAD'] .. GENERATED FROM PYTHON SOURCE LINES 89-92 Save the optimization results ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ We can serialize the results for further exploitation. .. GENERATED FROM PYTHON SOURCE LINES 92-94 .. code-block:: Python problem.to_hdf("my_optim.hdf5") .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 08:35:46: Exporting the optimization problem to the file my_optim.hdf5 at node .. GENERATED FROM PYTHON SOURCE LINES 95-97 Post-process the results ^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 97-99 .. code-block:: Python execute_post(problem, post_name="OptHistoryView", save=False, show=True) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_001.png :alt: Evolution of the optimization variables :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_001.png :class: sphx-glr-multi-img * .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_002.png :alt: Evolution of the objective value :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_002.png :class: sphx-glr-multi-img * .. image-sg:: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_003.png :alt: Evolution of the distance to the optimum :srcset: /examples/optimization_problem/images/sphx_glr_plot_simple_opt_2_003.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 100-104 .. note:: We can also save this plot using the arguments ``save=False`` and ``file_path='file_path'``. .. GENERATED FROM PYTHON SOURCE LINES 106-110 Solve the optimization problem using a DOE algorithm ---------------------------------------------------- We can also see this optimization problem as a trade-off problem and solve it by means of a design of experiments (DOE). .. GENERATED FROM PYTHON SOURCE LINES 110-115 .. code-block:: Python problem.reset() optimization_result = execute_algo( problem, algo_name="PYDOE_LHS", n_samples=10, algo_type="doe" ) optimization_result .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 08:35:47: Optimization problem: INFO - 08:35:47: minimize [f_1-f_2] = sin(x)-exp(x) INFO - 08:35:47: with respect to x INFO - 08:35:47: over the design space: INFO - 08:35:47: +------+-------------+-------+-------------+-------+ INFO - 08:35:47: | Name | Lower bound | Value | Upper bound | Type | INFO - 08:35:47: +------+-------------+-------+-------------+-------+ INFO - 08:35:47: | x | -2 | -0.5 | 2 | float | INFO - 08:35:47: +------+-------------+-------+-------------+-------+ INFO - 08:35:47: Solving optimization problem with algorithm PYDOE_LHS: INFO - 08:35:47: 10%|█ | 1/10 [00:00<00:00, 5090.17 it/sec, obj=-5.17] INFO - 08:35:47: 20%|██ | 2/10 [00:00<00:00, 3951.30 it/sec, obj=-1.15] INFO - 08:35:47: 30%|███ | 3/10 [00:00<00:00, 3960.63 it/sec, obj=-1.24] INFO - 08:35:47: 40%|████ | 4/10 [00:00<00:00, 3963.43 it/sec, obj=-1.13] INFO - 08:35:47: 50%|█████ | 5/10 [00:00<00:00, 3973.38 it/sec, obj=-2.91] INFO - 08:35:47: 60%|██████ | 6/10 [00:00<00:00, 3992.04 it/sec, obj=-1.75] INFO - 08:35:47: 70%|███████ | 7/10 [00:00<00:00, 4020.83 it/sec, obj=-1.14] INFO - 08:35:47: 80%|████████ | 8/10 [00:00<00:00, 4043.19 it/sec, obj=-1.05] INFO - 08:35:47: 90%|█████████ | 9/10 [00:00<00:00, 4019.24 it/sec, obj=-1.23] INFO - 08:35:47: 100%|██████████| 10/10 [00:00<00:00, 4035.31 it/sec, obj=-1] INFO - 08:35:47: Optimization result: INFO - 08:35:47: Optimizer info: INFO - 08:35:47: Status: None INFO - 08:35:47: Message: None INFO - 08:35:47: Number of calls to the objective function by the optimizer: 10 INFO - 08:35:47: Solution: INFO - 08:35:47: Objective: -5.174108803965849 INFO - 08:35:47: Design space: INFO - 08:35:47: +------+-------------+-------------------+-------------+-------+ INFO - 08:35:47: | Name | Lower bound | Value | Upper bound | Type | INFO - 08:35:47: +------+-------------+-------------------+-------------+-------+ INFO - 08:35:47: | x | -2 | 1.815526693601343 | 2 | float | INFO - 08:35:47: +------+-------------+-------------------+-------------+-------+ .. raw:: html
Optimization result:
  • Design variables: [1.81552669]
  • Objective function: -5.174108803965849
  • Feasible solution: True


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