# 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.api import configure_logger
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.problems.sobieski.core.problem import SobieskiProblem
from matplotlib import pyplot as plt


## Import¶

The first step is to import some functions from the API 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 read the design space from the SobieskiProblem.

design_space = SobieskiProblem().design_space


## 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,
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.execute({"algo": "SLSQP", "max_iter": 10})

    INFO - 14:43:34:
INFO - 14:43:34: *** Start MDOScenario execution ***
INFO - 14:43:34: MDOScenario
INFO - 14:43:34:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
INFO - 14:43:34:    MDO formulation: MDF
INFO - 14:43:34: Optimization problem:
INFO - 14:43:34:    minimize -y_4(x_shared, x_1, x_2, x_3)
INFO - 14:43:34:    with respect to x_1, x_2, x_3, x_shared
INFO - 14:43:34:    subject to constraints:
INFO - 14:43:34:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:43:34:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:43:34:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:43:34:    over the design space:
INFO - 14:43:34:    +-------------+-------------+-------+-------------+-------+
INFO - 14:43:34:    | name        | lower_bound | value | upper_bound | type  |
INFO - 14:43:34:    +-------------+-------------+-------+-------------+-------+
INFO - 14:43:34:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
INFO - 14:43:34:    | x_shared[1] |    30000    | 45000 |    60000    | float |
INFO - 14:43:34:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
INFO - 14:43:34:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
INFO - 14:43:34:    | x_shared[4] |      40     |   55  |      70     | float |
INFO - 14:43:34:    | x_shared[5] |     500     |  1000 |     1500    | float |
INFO - 14:43:34:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
INFO - 14:43:34:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
INFO - 14:43:34:    | x_2         |     0.75    |   1   |     1.25    | float |
INFO - 14:43:34:    | x_3         |     0.1     |  0.5  |      1      | float |
INFO - 14:43:34:    +-------------+-------------+-------+-------------+-------+
INFO - 14:43:34: Solving optimization problem with algorithm SLSQP:
INFO - 14:43:34: ...   0%|          | 0/10 [00:00<?, ?it]
INFO - 14:43:34: ...  20%|██        | 2/10 [00:00<00:00, 40.93 it/sec, obj=-2.12e+3]
WARNING - 14:43:34: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
INFO - 14:43:34: ...  30%|███       | 3/10 [00:00<00:00, 23.58 it/sec, obj=-3.75e+3]
INFO - 14:43:34: ...  40%|████      | 4/10 [00:00<00:00, 17.20 it/sec, obj=-4.01e+3]
WARNING - 14:43:35: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
INFO - 14:43:35: ...  50%|█████     | 5/10 [00:00<00:00, 13.09 it/sec, obj=-4.49e+3]
INFO - 14:43:35: ...  60%|██████    | 6/10 [00:00<00:00, 11.10 it/sec, obj=-3.4e+3]
INFO - 14:43:35: ...  80%|████████  | 8/10 [00:01<00:00,  9.45 it/sec, obj=-4.76e+3]
INFO - 14:43:35: ... 100%|██████████| 10/10 [00:01<00:00,  8.23 it/sec, obj=-4.56e+3]
INFO - 14:43:35: ... 100%|██████████| 10/10 [00:01<00:00,  8.21 it/sec, obj=-4.56e+3]
INFO - 14:43:35: Optimization result:
INFO - 14:43:35:    Optimizer info:
INFO - 14:43:35:       Status: None
INFO - 14:43:35:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 14:43:35:       Number of calls to the objective function by the optimizer: 12
INFO - 14:43:35:    Solution:
INFO - 14:43:35:       The solution is feasible.
INFO - 14:43:35:       Objective: -3749.8868975554387
INFO - 14:43:35:       Standardized constraints:
INFO - 14:43:35:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
INFO - 14:43:35:  -0.10219342]
INFO - 14:43:35:          g_2 = -0.0004062839430756249
INFO - 14:43:35:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
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_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
INFO - 14:43:35:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
INFO - 14:43:35:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
INFO - 14:43:35:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
INFO - 14:43:35:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
INFO - 14:43:35:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
INFO - 14:43:35:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
INFO - 14:43:35:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
INFO - 14:43:35:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
INFO - 14:43:35:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
INFO - 14:43:35:       +-------------+-------------+---------------------+-------------+-------+
INFO - 14:43:35: *** End MDOScenario execution (time: 0:00:01.234570) ***

{'max_iter': 10, 'algo': 'SLSQP'}


## 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 API 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("OptHistoryView", save=False, show=False)
# Workaround for HTML rendering, instead of show=True
plt.show()


Total running time of the script: ( 0 minutes 2.688 seconds)

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