Note

Go to the end to download the full example code.

Create a DOE Scenario#

from __future__ import annotations

from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import get_available_doe_algorithms
from gemseo import get_available_post_processings

Let \((P)\) be a simple optimization problem:

\[\begin{split}(P) = \left\{ \begin{aligned} & \underset{x\in\mathbb{N}^2}{\text{minimize}} & & f(x) = x_1 + x_2 \\ & \text{subject to} & & -5 \leq x \leq 5 \end{aligned} \right.\end{split}\]

In this example, we will see how to use GEMSEO to solve this problem \((P)\) by means of a Design Of Experiments (DOE)

Define the discipline#

Firstly, by means of the create_discipline() API function, we create an Discipline of AnalyticDiscipline type from a Python function:

expressions = {"y": "x1+x2"}
discipline = create_discipline("AnalyticDiscipline", expressions=expressions)

Now, we want to minimize this Discipline over a design of experiments (DOE).

Define the design space#

For that, by means of the create_design_space() API function, we define the DesignSpace \([-5, 5]\times[-5, 5]\) by using its DesignSpace.add_variable() method.

design_space = create_design_space()
design_space.add_variable("x1", lower_bound=-5, upper_bound=5, type_="integer")
design_space.add_variable("x2", lower_bound=-5, upper_bound=5, type_="integer")

Define the DOE scenario#

Then, by means of the create_scenario() API function, we define a DOEScenario from the Discipline and the DesignSpace defined above:

scenario = create_scenario(
    discipline,
    "y",
    design_space,
    scenario_type="DOE",
    formulation_name="DisciplinaryOpt",
)

Note that the formulation settings passed to create_scenario() can be provided via a Pydantic model. For more information, see Formulation Settings.

Execute the DOE scenario#

Lastly, we solve the OptimizationProblem included in the DOEScenario defined above by minimizing the objective function over a design of experiments included in the DesignSpace. Precisely, we choose a full factorial design of size \(11^2\):

scenario.execute(algo_name="PYDOE_FULLFACT", n_samples=11**2)

INFO - 16:25:11: *** Start DOEScenario execution ***
INFO - 16:25:11: DOEScenario
INFO - 16:25:11:    Disciplines: AnalyticDiscipline
INFO - 16:25:11:    MDO formulation: DisciplinaryOpt
INFO - 16:25:11: Optimization problem:
INFO - 16:25:11:    minimize y(x1, x2)
INFO - 16:25:11:    with respect to x1, x2
INFO - 16:25:11:    over the design space:
INFO - 16:25:11:       +------+-------------+-------+-------------+---------+
INFO - 16:25:11:       | Name | Lower bound | Value | Upper bound | Type    |
INFO - 16:25:11:       +------+-------------+-------+-------------+---------+
INFO - 16:25:11:       | x1   |      -5     |  None |      5      | integer |
INFO - 16:25:11:       | x2   |      -5     |  None |      5      | integer |
INFO - 16:25:11:       +------+-------------+-------+-------------+---------+
INFO - 16:25:11: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:25:11:      1%|          | 1/121 [00:00<00:00, 545.07 it/sec, feas=True, obj=-10]
INFO - 16:25:11:      2%|▏         | 2/121 [00:00<00:00, 926.00 it/sec, feas=True, obj=-9]
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INFO - 16:25:11:     91%|█████████ | 110/121 [00:00<00:00, 4372.13 it/sec, feas=True, obj=9]
INFO - 16:25:11:     92%|█████████▏| 111/121 [00:00<00:00, 4376.87 it/sec, feas=True, obj=0]
INFO - 16:25:11:     93%|█████████▎| 112/121 [00:00<00:00, 4382.23 it/sec, feas=True, obj=1]
INFO - 16:25:11:     93%|█████████▎| 113/121 [00:00<00:00, 4383.13 it/sec, feas=True, obj=2]
INFO - 16:25:11:     94%|█████████▍| 114/121 [00:00<00:00, 4387.87 it/sec, feas=True, obj=3]
INFO - 16:25:11:     95%|█████████▌| 115/121 [00:00<00:00, 4392.06 it/sec, feas=True, obj=4]
INFO - 16:25:11:     96%|█████████▌| 116/121 [00:00<00:00, 4396.43 it/sec, feas=True, obj=5]
INFO - 16:25:11:     97%|█████████▋| 117/121 [00:00<00:00, 4401.00 it/sec, feas=True, obj=6]
INFO - 16:25:11:     98%|█████████▊| 118/121 [00:00<00:00, 4401.78 it/sec, feas=True, obj=7]
INFO - 16:25:11:     98%|█████████▊| 119/121 [00:00<00:00, 4405.82 it/sec, feas=True, obj=8]
INFO - 16:25:11:     99%|█████████▉| 120/121 [00:00<00:00, 4410.22 it/sec, feas=True, obj=9]
INFO - 16:25:11:    100%|██████████| 121/121 [00:00<00:00, 4370.95 it/sec, feas=True, obj=10]
INFO - 16:25:11: Optimization result:
INFO - 16:25:11:    Optimizer info:
INFO - 16:25:11:       Status: None
INFO - 16:25:11:       Message: None
INFO - 16:25:11:    Solution:
INFO - 16:25:11:       Objective: -10.0
INFO - 16:25:11:       Design space:
INFO - 16:25:11:          +------+-------------+-------+-------------+---------+
INFO - 16:25:11:          | Name | Lower bound | Value | Upper bound | Type    |
INFO - 16:25:11:          +------+-------------+-------+-------------+---------+
INFO - 16:25:11:          | x1   |      -5     |   -5  |      5      | integer |
INFO - 16:25:11:          | x2   |      -5     |   -5  |      5      | integer |
INFO - 16:25:11:          +------+-------------+-------+-------------+---------+
INFO - 16:25:11: *** End DOEScenario execution ***

Note that the algorithm settings passed to execute() can be provided via a Pydantic model. For more information, see Algorithm Settings.

The optimum results can be found in the execution log. It is also possible to access them with Scenario.optimization_result:

optimization_result = scenario.optimization_result
f"The solution of P is (x*, f(x*)) = ({optimization_result.x_opt}, {optimization_result.f_opt})"

'The solution of P is (x*, f(x*)) = ([-5. -5.], -10.0)'

Available DOE algorithms#

In order to get the list of available DOE algorithms, use:

get_available_doe_algorithms()

['CustomDOE', 'DiagonalDOE', 'MorrisDOE', 'OATDOE', 'OT_SOBOL', 'OT_RANDOM', 'OT_HASELGROVE', 'OT_REVERSE_HALTON', 'OT_HALTON', 'OT_FAURE', 'OT_MONTE_CARLO', 'OT_FACTORIAL', 'OT_COMPOSITE', 'OT_AXIAL', 'OT_OPT_LHS', 'OT_LHS', 'OT_LHSC', 'OT_FULLFACT', 'OT_SOBOL_INDICES', 'PYDOE_BBDESIGN', 'PYDOE_CCDESIGN', 'PYDOE_FF2N', 'PYDOE_FULLFACT', 'PYDOE_LHS', 'PYDOE_PBDESIGN', 'Halton', 'LHS', 'MC', 'PoissonDisk', 'Sobol']

Available post-processing#

In order to get the list of available post-processing algorithms, use:

get_available_post_processings()

['Animation', 'BasicHistory', 'ConstraintsHistory', 'Correlations', 'DataVersusModel', 'GradientSensitivity', 'HessianHistory', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'QuadApprox', 'RadarChart', 'Robustness', 'SOM', 'ScatterPlotMatrix', 'TopologyView', 'VariableInfluence']

You can also look at the examples:

Total running time of the script: (0 minutes 0.036 seconds)

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