Note

Click here to download the full example code

# Basic history¶

In this example, we illustrate the use of the `BasicHistory`

plot
on the Sobieski’s SSBJ problem.

```
from __future__ import division, unicode_literals
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.

```
from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
configure_logger()
```

Out:

```
<RootLogger root (INFO)>
```

## Description¶

The `BasicHistory`

post-processing
plots any of the constraint or objective functions
w.r.t. the optimization iterations or sampling snapshots.

## 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().read_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.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
```

Out:

```
INFO - 14:41:48:
INFO - 14:41:48: *** Start MDO Scenario execution ***
INFO - 14:41:48: MDOScenario
INFO - 14:41:48: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
INFO - 14:41:48: MDOFormulation: MDF
INFO - 14:41:48: Algorithm: SLSQP
INFO - 14:41:48: Optimization problem:
INFO - 14:41:48: Minimize: -y_4(x_shared, x_1, x_2, x_3)
INFO - 14:41:48: With respect to: x_shared, x_1, x_2, x_3
INFO - 14:41:48: Subject to constraints:
INFO - 14:41:48: g_1(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:41:48: g_2(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:41:48: g_3(x_shared, x_1, x_2, x_3) <= 0.0
INFO - 14:41:48: Design space:
INFO - 14:41:48: +----------+-------------+-------+-------------+-------+
INFO - 14:41:48: | name | lower_bound | value | upper_bound | type |
INFO - 14:41:48: +----------+-------------+-------+-------------+-------+
INFO - 14:41:48: | x_shared | 0.01 | 0.05 | 0.09 | float |
INFO - 14:41:48: | x_shared | 30000 | 45000 | 60000 | float |
INFO - 14:41:48: | x_shared | 1.4 | 1.6 | 1.8 | float |
INFO - 14:41:48: | x_shared | 2.5 | 5.5 | 8.5 | float |
INFO - 14:41:48: | x_shared | 40 | 55 | 70 | float |
INFO - 14:41:48: | x_shared | 500 | 1000 | 1500 | float |
INFO - 14:41:48: | x_1 | 0.1 | 0.25 | 0.4 | float |
INFO - 14:41:48: | x_1 | 0.75 | 1 | 1.25 | float |
INFO - 14:41:48: | x_2 | 0.75 | 1 | 1.25 | float |
INFO - 14:41:48: | x_3 | 0.1 | 0.5 | 1 | float |
INFO - 14:41:48: +----------+-------------+-------+-------------+-------+
INFO - 14:41:48: Optimization: 0%| | 0/10 [00:00<?, ?it]
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.2.2/lib/python3.8/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:407: SparseEfficiencyWarning: splu requires CSC matrix format
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
INFO - 14:41:48: Optimization: 20%|██ | 2/10 [00:00<00:00, 53.21 it/sec, obj=2.12e+3]
INFO - 14:41:48: Optimization: 40%|████ | 4/10 [00:00<00:00, 21.30 it/sec, obj=3.97e+3]
INFO - 14:41:48: Optimization: 50%|█████ | 5/10 [00:00<00:00, 16.62 it/sec, obj=3.96e+3]
INFO - 14:41:48: Optimization: 60%|██████ | 6/10 [00:00<00:00, 13.63 it/sec, obj=3.96e+3]
INFO - 14:41:49: Optimization: 70%|███████ | 7/10 [00:00<00:00, 11.54 it/sec, obj=3.96e+3]
INFO - 14:41:49: Optimization: 90%|█████████ | 9/10 [00:01<00:00, 9.85 it/sec, obj=3.96e+3]
INFO - 14:41:49: Optimization: 100%|██████████| 10/10 [00:01<00:00, 9.16 it/sec, obj=3.96e+3]
INFO - 14:41:49: Optimization result:
INFO - 14:41:49: Objective value = 3963.595455433326
INFO - 14:41:49: The result is feasible.
INFO - 14:41:49: Status: None
INFO - 14:41:49: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 14:41:49: Number of calls to the objective function by the optimizer: 12
INFO - 14:41:49: Constraints values:
INFO - 14:41:49: g_1 = [-0.01814919 -0.03340982 -0.04429875 -0.05187486 -0.05736009 -0.13720854
INFO - 14:41:49: -0.10279146]
INFO - 14:41:49: g_2 = 3.236261671801799e-05
INFO - 14:41:49: g_3 = [-7.67067574e-01 -2.32932426e-01 -9.19662628e-05 -1.83255000e-01]
INFO - 14:41:49: Design space:
INFO - 14:41:49: +----------+-------------+--------------------+-------------+-------+
INFO - 14:41:49: | name | lower_bound | value | upper_bound | type |
INFO - 14:41:49: +----------+-------------+--------------------+-------------+-------+
INFO - 14:41:49: | x_shared | 0.01 | 0.0600080906541795 | 0.09 | float |
INFO - 14:41:49: | x_shared | 30000 | 60000 | 60000 | float |
INFO - 14:41:49: | x_shared | 1.4 | 1.4 | 1.8 | float |
INFO - 14:41:49: | x_shared | 2.5 | 2.5 | 8.5 | float |
INFO - 14:41:49: | x_shared | 40 | 70 | 70 | float |
INFO - 14:41:49: | x_shared | 500 | 1500 | 1500 | float |
INFO - 14:41:49: | x_1 | 0.1 | 0.3999993439500847 | 0.4 | float |
INFO - 14:41:49: | x_1 | 0.75 | 0.75 | 1.25 | float |
INFO - 14:41:49: | x_2 | 0.75 | 0.75 | 1.25 | float |
INFO - 14:41:49: | x_3 | 0.1 | 0.156230376400943 | 1 | float |
INFO - 14:41:49: +----------+-------------+--------------------+-------------+-------+
INFO - 14:41:49: *** MDO Scenario run terminated in 0:00:01.101392 ***
{'algo': 'SLSQP', 'max_iter': 10}
```

## Post-process scenario¶

Lastly, we post-process the scenario by means of the `BasicHistory`

plot which plots any of the constraint or objective functions
w.r.t. optimization iterations or sampling snapshots.

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:
Options for Post-processing algorithms.

```
scenario.post_process(
"BasicHistory", data_list=["g_1", "g_2", "g_3"], save=False, show=False
)
```

Out:

```
<gemseo.post.basic_history.BasicHistory object at 0x7fcaac2ea820>
```

Warning

In the `Database`

, when the aim of the
optimization problem is to maximize the objective function,
the objective function name is preceded by a “-” and the stored values are
the opposite of the objective function.

```
scenario.post_process("BasicHistory", data_list=["-y_4"], save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
```

**Total running time of the script:** ( 0 minutes 1.529 seconds)