Optimization History View

In this example, we illustrate the use of the OptHistoryView plot on the Sobieski's SSBJ problem.

from __future__ import annotations

from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace

Import

The first step is to import some high-level functions and a method to get the design space.

configure_logger()

<RootLogger root (INFO)>

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 \(y\) axis is the index of the inputs in the vector; and the \(x\) 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 \(log( ||x-x^*|| )\) in log scale.

• The history of the Hessian approximation of the objective - Plots an approximation of the second order derivatives of the objective function \(\frac{\partial^2 f(x)}{\partial x^2}\), 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 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 IDF formulation, an additional plot is created to track the equality constraint history.

Create disciplines

At this point we instantiate the disciplines of Sobieski's SSBJ problem: Propulsion, Aerodynamics, Structure and Mission

disciplines = create_discipline([
    "SobieskiPropulsion",
    "SobieskiAerodynamics",
    "SobieskiStructure",
    "SobieskiMission",
])

Create design space

We also create the SobieskiDesignSpace.

design_space = SobieskiDesignSpace()

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.

scenario = create_scenario(
    disciplines,
    "y_4",
    design_space,
    formulation_name="MDF",
    maximize_objective=True,
)
scenario.set_differentiation_method()
for constraint in ["g_1", "g_2", "g_3"]:
    scenario.add_constraint(constraint, constraint_type="ineq")
scenario.execute(algo_name="SLSQP", max_iter=100)

WARNING - 08:38:42: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
WARNING - 08:38:42: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
   INFO - 08:38:42:
   INFO - 08:38:42: *** Start MDOScenario execution ***
   INFO - 08:38:42: MDOScenario
   INFO - 08:38:42:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
   INFO - 08:38:42:    MDO formulation: MDF
   INFO - 08:38:42: Optimization problem:
   INFO - 08:38:42:    minimize -y_4(x_shared, x_1, x_2, x_3)
   INFO - 08:38:42:    with respect to x_1, x_2, x_3, x_shared
   INFO - 08:38:42:    subject to constraints:
   INFO - 08:38:42:       g_1(x_shared, x_1, x_2, x_3) <= 0
   INFO - 08:38:42:       g_2(x_shared, x_1, x_2, x_3) <= 0
   INFO - 08:38:42:       g_3(x_shared, x_1, x_2, x_3) <= 0
   INFO - 08:38:42:    over the design space:
   INFO - 08:38:42:       +-------------+-------------+-------+-------------+-------+
   INFO - 08:38:42:       | Name        | Lower bound | Value | Upper bound | Type  |
   INFO - 08:38:42:       +-------------+-------------+-------+-------------+-------+
   INFO - 08:38:42:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
   INFO - 08:38:42:       | x_shared[1] |    30000    | 45000 |    60000    | float |
   INFO - 08:38:42:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
   INFO - 08:38:42:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
   INFO - 08:38:42:       | x_shared[4] |      40     |   55  |      70     | float |
   INFO - 08:38:42:       | x_shared[5] |     500     |  1000 |     1500    | float |
   INFO - 08:38:42:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
   INFO - 08:38:42:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
   INFO - 08:38:42:       | x_2         |     0.75    |   1   |     1.25    | float |
   INFO - 08:38:42:       | x_3         |     0.1     |  0.5  |      1      | float |
   INFO - 08:38:42:       +-------------+-------------+-------+-------------+-------+
   INFO - 08:38:42: Solving optimization problem with algorithm SLSQP:
   INFO - 08:38:42:      1%|          | 1/100 [00:00<00:05, 18.52 it/sec, obj=-536]
   INFO - 08:38:42:      2%|▏         | 2/100 [00:00<00:07, 13.74 it/sec, obj=-2.12e+3]
WARNING - 08:38:42: MDAJacobi has reached its maximum number of iterations but the normed residual 5.741449586530469e-06 is still above the tolerance 1e-06.
   INFO - 08:38:42:      3%|▎         | 3/100 [00:00<00:08, 11.06 it/sec, obj=-3.46e+3]
   INFO - 08:38:42:      4%|▍         | 4/100 [00:00<00:09, 10.63 it/sec, obj=-3.96e+3]
   INFO - 08:38:42:      5%|▌         | 5/100 [00:00<00:08, 10.84 it/sec, obj=-4.61e+3]
   INFO - 08:38:42:      6%|▌         | 6/100 [00:00<00:08, 11.55 it/sec, obj=-4.5e+3]
   INFO - 08:38:42:      7%|▋         | 7/100 [00:00<00:07, 11.94 it/sec, obj=-4.26e+3]
   INFO - 08:38:42:      8%|▊         | 8/100 [00:00<00:07, 12.27 it/sec, obj=-4.11e+3]
   INFO - 08:38:42:      9%|▉         | 9/100 [00:00<00:07, 12.54 it/sec, obj=-4.02e+3]
   INFO - 08:38:43:     10%|█         | 10/100 [00:00<00:07, 12.77 it/sec, obj=-3.99e+3]
   INFO - 08:38:43:     11%|█         | 11/100 [00:00<00:06, 12.89 it/sec, obj=-3.97e+3]
   INFO - 08:38:43:     12%|█▏        | 12/100 [00:00<00:06, 12.99 it/sec, obj=-3.97e+3]
   INFO - 08:38:43:     13%|█▎        | 13/100 [00:00<00:06, 13.08 it/sec, obj=-3.97e+3]
   INFO - 08:38:43:     14%|█▍        | 14/100 [00:01<00:06, 13.17 it/sec, obj=-3.96e+3]
   INFO - 08:38:43:     15%|█▌        | 15/100 [00:01<00:06, 13.24 it/sec, obj=-3.96e+3]
   INFO - 08:38:43:     16%|█▌        | 16/100 [00:01<00:06, 12.93 it/sec, obj=-3.96e+3]
   INFO - 08:38:43: Optimization result:
   INFO - 08:38:43:    Optimizer info:
   INFO - 08:38:43:       Status: 8
   INFO - 08:38:43:       Message: Positive directional derivative for linesearch
   INFO - 08:38:43:       Number of calls to the objective function by the optimizer: 17
   INFO - 08:38:43:    Solution:
   INFO - 08:38:43:       The solution is feasible.
   INFO - 08:38:43:       Objective: -3463.120411437138
   INFO - 08:38:43:       Standardized constraints:
   INFO - 08:38:43:          g_1 = [-0.01112145 -0.02847064 -0.04049911 -0.04878943 -0.05476349 -0.14014207
   INFO - 08:38:43:  -0.09985793]
   INFO - 08:38:43:          g_2 = -0.0020925663903177405
   INFO - 08:38:43:          g_3 = [-0.71359843 -0.28640157 -0.05926796 -0.183255  ]
   INFO - 08:38:43:       Design space:
   INFO - 08:38:43:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 08:38:43:          | Name        | Lower bound |        Value        | Upper bound | Type  |
   INFO - 08:38:43:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 08:38:43:          | x_shared[0] |     0.01    | 0.05947685840242058 |     0.09    | float |
   INFO - 08:38:43:          | x_shared[1] |    30000    |   59246.692998739   |    60000    | float |
   INFO - 08:38:43:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
   INFO - 08:38:43:          | x_shared[3] |     2.5     |   2.64097355362077  |     8.5     | float |
   INFO - 08:38:43:          | x_shared[4] |      40     |  69.32144380869019  |      70     | float |
   INFO - 08:38:43:          | x_shared[5] |     500     |  1478.031626737187  |     1500    | float |
   INFO - 08:38:43:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
   INFO - 08:38:43:          | x_1[1]      |     0.75    |  0.7608797907508461 |     1.25    | float |
   INFO - 08:38:43:          | x_2         |     0.75    |  0.7607584987262048 |     1.25    | float |
   INFO - 08:38:43:          | x_3         |     0.1     |  0.1514057659459843 |      1      | float |
   INFO - 08:38:43:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 08:38:43: *** End MDOScenario execution (time: 0:00:01.282304) ***

Post-process scenario

Lastly, we post-process the scenario by means of the OptHistoryView plot which plots the history of optimization for both objective function, constraints, design parameters and distance to the optimum.

Tip

Each post-processing method requires different inputs and offers a variety of customization options. Use the high-level function get_post_processing_options_schema() to print a table with the options for any post-processing algorithm. Or refer to our dedicated page: Post-processing algorithms.

scenario.post_process(
    post_name="OptHistoryView", save=False, show=True, variable_names=["x_2", "x_1"]
)

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<gemseo.post.opt_history_view.OptHistoryView object at 0x7f6dc8c09b80>