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 - 16:24:38: *** Start DOEScenario execution ***
INFO - 16:24:38: DOEScenario
INFO - 16:24:38:    Disciplines: AnalyticDiscipline
INFO - 16:24:38:    MDO formulation: DisciplinaryOpt
INFO - 16:24:38: Optimization problem:
INFO - 16:24:38:    minimize y(x1, x2)
INFO - 16:24:38:    with respect to x1, x2
INFO - 16:24:38:    over the design space:
INFO - 16:24:38:       +------+-------------+-------+-------------+---------+
INFO - 16:24:38:       | Name | Lower bound | Value | Upper bound | Type    |
INFO - 16:24:38:       +------+-------------+-------+-------------+---------+
INFO - 16:24:38:       | x1   |      -5     |  None |      5      | integer |
INFO - 16:24:38:       | x2   |      -5     |  None |      5      | integer |
INFO - 16:24:38:       +------+-------------+-------+-------------+---------+
INFO - 16:24:38: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 16:24:38:      1%|          | 1/121 [00:00<00:00, 555.68 it/sec, feas=True, obj=-10]
INFO - 16:24:38:      2%|▏         | 2/121 [00:00<00:00, 939.48 it/sec, feas=True, obj=-9]
INFO - 16:24:38:      2%|▏         | 3/121 [00:00<00:00, 1245.34 it/sec, feas=True, obj=-8]
INFO - 16:24:38:      3%|▎         | 4/121 [00:00<00:00, 1508.47 it/sec, feas=True, obj=-7]
INFO - 16:24:38:      4%|▍         | 5/121 [00:00<00:00, 1733.47 it/sec, feas=True, obj=-6]
INFO - 16:24:38:      5%|▍         | 6/121 [00:00<00:00, 1930.49 it/sec, feas=True, obj=-5]
INFO - 16:24:38:      6%|▌         | 7/121 [00:00<00:00, 2092.07 it/sec, feas=True, obj=-4]
INFO - 16:24:38:      7%|▋         | 8/121 [00:00<00:00, 2237.26 it/sec, feas=True, obj=-3]
INFO - 16:24:38:      7%|▋         | 9/121 [00:00<00:00, 2370.41 it/sec, feas=True, obj=-2]
INFO - 16:24:38:      8%|▊         | 10/121 [00:00<00:00, 2490.24 it/sec, feas=True, obj=-1]
INFO - 16:24:38:      9%|▉         | 11/121 [00:00<00:00, 2600.75 it/sec, feas=True, obj=0]
INFO - 16:24:38:     10%|▉         | 12/121 [00:00<00:00, 2688.80 it/sec, feas=True, obj=-9]
INFO - 16:24:38:     11%|█         | 13/121 [00:00<00:00, 2773.87 it/sec, feas=True, obj=-8]
INFO - 16:24:38:     12%|█▏        | 14/121 [00:00<00:00, 2856.88 it/sec, feas=True, obj=-7]
INFO - 16:24:38:     12%|█▏        | 15/121 [00:00<00:00, 2935.27 it/sec, feas=True, obj=-6]
INFO - 16:24:38:     13%|█▎        | 16/121 [00:00<00:00, 2998.74 it/sec, feas=True, obj=-5]
INFO - 16:24:38:     14%|█▍        | 17/121 [00:00<00:00, 3060.75 it/sec, feas=True, obj=-4]
INFO - 16:24:38:     15%|█▍        | 18/121 [00:00<00:00, 3123.73 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     16%|█▌        | 19/121 [00:00<00:00, 3176.11 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     17%|█▋        | 20/121 [00:00<00:00, 3228.13 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     17%|█▋        | 21/121 [00:00<00:00, 3268.17 it/sec, feas=True, obj=0]
INFO - 16:24:38:     18%|█▊        | 22/121 [00:00<00:00, 3312.92 it/sec, feas=True, obj=1]
INFO - 16:24:38:     19%|█▉        | 23/121 [00:00<00:00, 3358.83 it/sec, feas=True, obj=-8]
INFO - 16:24:38:     20%|█▉        | 24/121 [00:00<00:00, 3403.66 it/sec, feas=True, obj=-7]
INFO - 16:24:38:     21%|██        | 25/121 [00:00<00:00, 3444.50 it/sec, feas=True, obj=-6]
INFO - 16:24:38:     21%|██▏       | 26/121 [00:00<00:00, 3471.33 it/sec, feas=True, obj=-5]
INFO - 16:24:38:     22%|██▏       | 27/121 [00:00<00:00, 3505.42 it/sec, feas=True, obj=-4]
INFO - 16:24:38:     23%|██▎       | 28/121 [00:00<00:00, 3540.03 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     24%|██▍       | 29/121 [00:00<00:00, 3571.93 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     25%|██▍       | 30/121 [00:00<00:00, 3595.84 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     26%|██▌       | 31/121 [00:00<00:00, 3622.02 it/sec, feas=True, obj=0]
INFO - 16:24:38:     26%|██▋       | 32/121 [00:00<00:00, 3650.40 it/sec, feas=True, obj=1]
INFO - 16:24:38:     27%|██▋       | 33/121 [00:00<00:00, 3677.75 it/sec, feas=True, obj=2]
INFO - 16:24:38:     28%|██▊       | 34/121 [00:00<00:00, 3703.68 it/sec, feas=True, obj=-7]
INFO - 16:24:38:     29%|██▉       | 35/121 [00:00<00:00, 3722.03 it/sec, feas=True, obj=-6]
INFO - 16:24:38:     30%|██▉       | 36/121 [00:00<00:00, 3742.69 it/sec, feas=True, obj=-5]
INFO - 16:24:38:     31%|███       | 37/121 [00:00<00:00, 3764.81 it/sec, feas=True, obj=-4]
INFO - 16:24:38:     31%|███▏      | 38/121 [00:00<00:00, 3781.16 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     32%|███▏      | 39/121 [00:00<00:00, 3802.37 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     33%|███▎      | 40/121 [00:00<00:00, 3813.18 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     34%|███▍      | 41/121 [00:00<00:00, 3830.59 it/sec, feas=True, obj=0]
INFO - 16:24:38:     35%|███▍      | 42/121 [00:00<00:00, 3849.50 it/sec, feas=True, obj=1]
INFO - 16:24:38:     36%|███▌      | 43/121 [00:00<00:00, 3866.55 it/sec, feas=True, obj=2]
INFO - 16:24:38:     36%|███▋      | 44/121 [00:00<00:00, 3878.15 it/sec, feas=True, obj=3]
INFO - 16:24:38:     37%|███▋      | 45/121 [00:00<00:00, 3890.98 it/sec, feas=True, obj=-6]
INFO - 16:24:38:     38%|███▊      | 46/121 [00:00<00:00, 3907.05 it/sec, feas=True, obj=-5]
INFO - 16:24:38:     39%|███▉      | 47/121 [00:00<00:00, 3920.69 it/sec, feas=True, obj=-4]
INFO - 16:24:38:     40%|███▉      | 48/121 [00:00<00:00, 3936.62 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     40%|████      | 49/121 [00:00<00:00, 3945.50 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     41%|████▏     | 50/121 [00:00<00:00, 3958.38 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     42%|████▏     | 51/121 [00:00<00:00, 3974.31 it/sec, feas=True, obj=0]
INFO - 16:24:38:     43%|████▎     | 52/121 [00:00<00:00, 3989.75 it/sec, feas=True, obj=1]
INFO - 16:24:38:     44%|████▍     | 53/121 [00:00<00:00, 4003.21 it/sec, feas=True, obj=2]
INFO - 16:24:38:     45%|████▍     | 54/121 [00:00<00:00, 4009.57 it/sec, feas=True, obj=3]
INFO - 16:24:38:     45%|████▌     | 55/121 [00:00<00:00, 4022.09 it/sec, feas=True, obj=4]
INFO - 16:24:38:     46%|████▋     | 56/121 [00:00<00:00, 4034.44 it/sec, feas=True, obj=-5]
INFO - 16:24:38:     47%|████▋     | 57/121 [00:00<00:00, 4047.46 it/sec, feas=True, obj=-4]
INFO - 16:24:38:     48%|████▊     | 58/121 [00:00<00:00, 4061.47 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     49%|████▉     | 59/121 [00:00<00:00, 4068.19 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     50%|████▉     | 60/121 [00:00<00:00, 4055.86 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     50%|█████     | 61/121 [00:00<00:00, 4064.89 it/sec, feas=True, obj=0]
INFO - 16:24:38:     51%|█████     | 62/121 [00:00<00:00, 4075.33 it/sec, feas=True, obj=1]
INFO - 16:24:38:     52%|█████▏    | 63/121 [00:00<00:00, 4080.82 it/sec, feas=True, obj=2]
INFO - 16:24:38:     53%|█████▎    | 64/121 [00:00<00:00, 4088.51 it/sec, feas=True, obj=3]
INFO - 16:24:38:     54%|█████▎    | 65/121 [00:00<00:00, 4096.98 it/sec, feas=True, obj=4]
INFO - 16:24:38:     55%|█████▍    | 66/121 [00:00<00:00, 4104.44 it/sec, feas=True, obj=5]
INFO - 16:24:38:     55%|█████▌    | 67/121 [00:00<00:00, 4112.12 it/sec, feas=True, obj=-4]
INFO - 16:24:38:     56%|█████▌    | 68/121 [00:00<00:00, 4115.56 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     57%|█████▋    | 69/121 [00:00<00:00, 4124.72 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     58%|█████▊    | 70/121 [00:00<00:00, 4133.54 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     59%|█████▊    | 71/121 [00:00<00:00, 4142.03 it/sec, feas=True, obj=0]
INFO - 16:24:38:     60%|█████▉    | 72/121 [00:00<00:00, 4146.62 it/sec, feas=True, obj=1]
INFO - 16:24:38:     60%|██████    | 73/121 [00:00<00:00, 4154.41 it/sec, feas=True, obj=2]
INFO - 16:24:38:     61%|██████    | 74/121 [00:00<00:00, 4163.64 it/sec, feas=True, obj=3]
INFO - 16:24:38:     62%|██████▏   | 75/121 [00:00<00:00, 4169.95 it/sec, feas=True, obj=4]
INFO - 16:24:38:     63%|██████▎   | 76/121 [00:00<00:00, 4178.42 it/sec, feas=True, obj=5]
INFO - 16:24:38:     64%|██████▎   | 77/121 [00:00<00:00, 4182.30 it/sec, feas=True, obj=6]
INFO - 16:24:38:     64%|██████▍   | 78/121 [00:00<00:00, 4190.01 it/sec, feas=True, obj=-3]
INFO - 16:24:38:     65%|██████▌   | 79/121 [00:00<00:00, 4198.02 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     66%|██████▌   | 80/121 [00:00<00:00, 4206.08 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     67%|██████▋   | 81/121 [00:00<00:00, 4212.77 it/sec, feas=True, obj=0]
INFO - 16:24:38:     68%|██████▊   | 82/121 [00:00<00:00, 4215.79 it/sec, feas=True, obj=1]
INFO - 16:24:38:     69%|██████▊   | 83/121 [00:00<00:00, 4223.31 it/sec, feas=True, obj=2]
INFO - 16:24:38:     69%|██████▉   | 84/121 [00:00<00:00, 4231.28 it/sec, feas=True, obj=3]
INFO - 16:24:38:     70%|███████   | 85/121 [00:00<00:00, 4239.04 it/sec, feas=True, obj=4]
INFO - 16:24:38:     71%|███████   | 86/121 [00:00<00:00, 4245.60 it/sec, feas=True, obj=5]
INFO - 16:24:38:     72%|███████▏  | 87/121 [00:00<00:00, 4247.37 it/sec, feas=True, obj=6]
INFO - 16:24:38:     73%|███████▎  | 88/121 [00:00<00:00, 4253.37 it/sec, feas=True, obj=7]
INFO - 16:24:38:     74%|███████▎  | 89/121 [00:00<00:00, 4259.44 it/sec, feas=True, obj=-2]
INFO - 16:24:38:     74%|███████▍  | 90/121 [00:00<00:00, 4265.35 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     75%|███████▌  | 91/121 [00:00<00:00, 4272.00 it/sec, feas=True, obj=0]
INFO - 16:24:38:     76%|███████▌  | 92/121 [00:00<00:00, 4273.55 it/sec, feas=True, obj=1]
INFO - 16:24:38:     77%|███████▋  | 93/121 [00:00<00:00, 4278.49 it/sec, feas=True, obj=2]
INFO - 16:24:38:     78%|███████▊  | 94/121 [00:00<00:00, 4281.71 it/sec, feas=True, obj=3]
INFO - 16:24:38:     79%|███████▊  | 95/121 [00:00<00:00, 4286.30 it/sec, feas=True, obj=4]
INFO - 16:24:38:     79%|███████▉  | 96/121 [00:00<00:00, 4287.92 it/sec, feas=True, obj=5]
INFO - 16:24:38:     80%|████████  | 97/121 [00:00<00:00, 4291.91 it/sec, feas=True, obj=6]
INFO - 16:24:38:     81%|████████  | 98/121 [00:00<00:00, 4297.35 it/sec, feas=True, obj=7]
INFO - 16:24:38:     82%|████████▏ | 99/121 [00:00<00:00, 4303.14 it/sec, feas=True, obj=8]
INFO - 16:24:38:     83%|████████▎ | 100/121 [00:00<00:00, 4308.92 it/sec, feas=True, obj=-1]
INFO - 16:24:38:     83%|████████▎ | 101/121 [00:00<00:00, 4311.13 it/sec, feas=True, obj=0]
INFO - 16:24:38:     84%|████████▍ | 102/121 [00:00<00:00, 4316.35 it/sec, feas=True, obj=1]
INFO - 16:24:38:     85%|████████▌ | 103/121 [00:00<00:00, 4322.25 it/sec, feas=True, obj=2]
INFO - 16:24:38:     86%|████████▌ | 104/121 [00:00<00:00, 4327.84 it/sec, feas=True, obj=3]
INFO - 16:24:38:     87%|████████▋ | 105/121 [00:00<00:00, 4333.00 it/sec, feas=True, obj=4]
INFO - 16:24:38:     88%|████████▊ | 106/121 [00:00<00:00, 4334.35 it/sec, feas=True, obj=5]
INFO - 16:24:38:     88%|████████▊ | 107/121 [00:00<00:00, 4338.87 it/sec, feas=True, obj=6]
INFO - 16:24:38:     89%|████████▉ | 108/121 [00:00<00:00, 4343.93 it/sec, feas=True, obj=7]
INFO - 16:24:38:     90%|█████████ | 109/121 [00:00<00:00, 4348.21 it/sec, feas=True, obj=8]
INFO - 16:24:38:     91%|█████████ | 110/121 [00:00<00:00, 4352.95 it/sec, feas=True, obj=9]
INFO - 16:24:38:     92%|█████████▏| 111/121 [00:00<00:00, 4353.83 it/sec, feas=True, obj=0]
INFO - 16:24:38:     93%|█████████▎| 112/121 [00:00<00:00, 4358.49 it/sec, feas=True, obj=1]
INFO - 16:24:38:     93%|█████████▎| 113/121 [00:00<00:00, 4356.30 it/sec, feas=True, obj=2]
INFO - 16:24:38:     94%|█████████▍| 114/121 [00:00<00:00, 4357.92 it/sec, feas=True, obj=3]
INFO - 16:24:38:     95%|█████████▌| 115/121 [00:00<00:00, 4357.78 it/sec, feas=True, obj=4]
INFO - 16:24:38:     96%|█████████▌| 116/121 [00:00<00:00, 4360.14 it/sec, feas=True, obj=5]
INFO - 16:24:38:     97%|█████████▋| 117/121 [00:00<00:00, 4363.36 it/sec, feas=True, obj=6]
INFO - 16:24:38:     98%|█████████▊| 118/121 [00:00<00:00, 4366.79 it/sec, feas=True, obj=7]
INFO - 16:24:38:     98%|█████████▊| 119/121 [00:00<00:00, 4370.33 it/sec, feas=True, obj=8]
INFO - 16:24:38:     99%|█████████▉| 120/121 [00:00<00:00, 4370.55 it/sec, feas=True, obj=9]
INFO - 16:24:38:    100%|██████████| 121/121 [00:00<00:00, 4332.96 it/sec, feas=True, obj=10]
INFO - 16:24:38: Optimization result:
INFO - 16:24:38:    Optimizer info:
INFO - 16:24:38:       Status: None
INFO - 16:24:38:       Message: None
INFO - 16:24:38:    Solution:
INFO - 16:24:38:       Objective: -10.0
INFO - 16:24:38:       Design space:
INFO - 16:24:38:          +------+-------------+-------+-------------+---------+
INFO - 16:24:38:          | Name | Lower bound | Value | Upper bound | Type    |
INFO - 16:24:38:          +------+-------------+-------+-------------+---------+
INFO - 16:24:38:          | x1   |      -5     |   -5  |      5      | integer |
INFO - 16:24:38:          | x2   |      -5     |   -5  |      5      | integer |
INFO - 16:24:38:          +------+-------------+-------+-------------+---------+
INFO - 16:24:38: *** 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)

Gallery generated by Sphinx-Gallery