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.. "examples/post_process/plot_opt_hist_view.py"
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.. _sphx_glr_examples_post_process_plot_opt_hist_view.py:
Optimization History View
=========================
In this example, we illustrate the use of the :class:`.OptHistoryView` plot
on the Sobieski's SSBJ problem.
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.. code-block:: default
from __future__ import division, unicode_literals
from matplotlib import pyplot as plt
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Import
------
The first step is to import some functions from the API
and a method to get the design space.
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.. code-block:: default
from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
configure_logger()
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Description
-----------
The **OptHistoryView** post-processing
creates a series of plots:
- The design variables history - This graph shows the normalized values of the
design variables, the :math:`y` axis is the index of the inputs in the vector;
and the :math:`x` axis represents the iterations.
- The objective function history - It shows the evolution of the objective
value during the optimization.
- The distance to the best design variables - Plots the vector
:math:`log( ||x-x^*|| )` in log scale.
- The history of the Hessian approximation of the objective - Plots an approximation
of the second order derivatives of the objective function
:math:`\frac{\partial^2 f(x)}{\partial x^2}`, which is a measure of
the sensitivity of the function with respect to the design variables,
and of the anisotropy of the problem (differences of curvatures in the
design space).
- The inequality constraint history - Portrays the evolution of the values of the
:term:`constraints`. The inequality constraints must be non-positive, that is why
the plot must be green or white for satisfied constraints (white = active,
red = violated). For an :ref:`IDF formulation `, an additional
plot is created to track the equality constraint history.
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Create disciplines
------------------
At this point we instantiate the disciplines of Sobieski's SSBJ problem:
Propulsion, Aerodynamics, Structure and Mission
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.. code-block:: default
disciplines = create_discipline(
[
"SobieskiPropulsion",
"SobieskiAerodynamics",
"SobieskiStructure",
"SobieskiMission",
]
)
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Create design space
-------------------
We also read the design space from the :class:`.SobieskiProblem`.
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design_space = SobieskiProblem().read_design_space()
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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.
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.. code-block:: default
scenario = create_scenario(
disciplines,
formulation="MDF",
objective_name="y_4",
maximize_objective=True,
design_space=design_space,
)
scenario.set_differentiation_method("user")
for constraint in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
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INFO - 14:42:16:
INFO - 14:42:16: *** Start MDO Scenario execution ***
INFO - 14:42:16: MDOScenario
INFO - 14:42:16: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 14:42:16: MDOFormulation: MDF
INFO - 14:42:16: Algorithm: SLSQP
INFO - 14:42:16: Optimization problem:
INFO - 14:42:16: Minimize: -y_4(x_shared, x_1, x_2, x_3)
INFO - 14:42:16: With respect to: x_shared, x_1, x_2, x_3
INFO - 14:42:16: Subject to constraints:
INFO - 14:42:16: g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:42:16: g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:42:16: g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:42:16: Design space:
INFO - 14:42:16: +----------+-------------+-------+-------------+-------+
INFO - 14:42:16: | name | lower_bound | value | upper_bound | type |
INFO - 14:42:16: +----------+-------------+-------+-------------+-------+
INFO - 14:42:16: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 14:42:16: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 14:42:16: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 14:42:16: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 14:42:16: | x_shared | 40 | 55 | 70 | float |
INFO - 14:42:16: | x_shared | 500 | 1000 | 1500 | float |
INFO - 14:42:16: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 14:42:16: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 14:42:16: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 14:42:16: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 14:42:16: +----------+-------------+-------+-------------+-------+
INFO - 14:42:16: Optimization: 0%| | 0/10 [00:00`
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