# Create a DOE Scenario¶

from __future__ import annotations

from gemseo import configure_logger
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

configure_logger()

<RootLogger root (INFO)>


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 MDODiscipline of AnalyticDiscipline type from a Python function:

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


Now, we want to minimize this MDODiscipline 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", l_b=-5, u_b=5, var_type="integer")
design_space.add_variable("x2", l_b=-5, u_b=5, var_type="integer")


## Define the DOE scenario¶

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

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


## 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": "fullfact", "n_samples": 11**2})

    INFO - 10:53:26:
INFO - 10:53:26: *** Start DOEScenario execution ***
INFO - 10:53:26: DOEScenario
INFO - 10:53:26:    Disciplines: AnalyticDiscipline
INFO - 10:53:26:    MDO formulation: DisciplinaryOpt
INFO - 10:53:26: Optimization problem:
INFO - 10:53:26:    minimize y(x1, x2)
INFO - 10:53:26:    with respect to x1, x2
INFO - 10:53:26:    over the design space:
INFO - 10:53:26:       +------+-------------+-------+-------------+---------+
INFO - 10:53:26:       | Name | Lower bound | Value | Upper bound | Type    |
INFO - 10:53:26:       +------+-------------+-------+-------------+---------+
INFO - 10:53:26:       | x1   |      -5     |  None |      5      | integer |
INFO - 10:53:26:       | x2   |      -5     |  None |      5      | integer |
INFO - 10:53:26:       +------+-------------+-------+-------------+---------+
INFO - 10:53:26: Solving optimization problem with algorithm fullfact:
INFO - 10:53:26:      1%|          | 1/121 [00:00<00:00, 345.44 it/sec, obj=-10]
INFO - 10:53:26:      2%|▏         | 2/121 [00:00<00:00, 546.81 it/sec, obj=-9]
INFO - 10:53:26:      2%|▏         | 3/121 [00:00<00:00, 696.73 it/sec, obj=-8]
INFO - 10:53:26:      3%|▎         | 4/121 [00:00<00:00, 810.69 it/sec, obj=-7]
INFO - 10:53:26:      4%|▍         | 5/121 [00:00<00:00, 897.06 it/sec, obj=-6]
INFO - 10:53:26:      5%|▍         | 6/121 [00:00<00:00, 961.56 it/sec, obj=-5]
INFO - 10:53:26:      6%|▌         | 7/121 [00:00<00:00, 1019.31 it/sec, obj=-4]
INFO - 10:53:26:      7%|▋         | 8/121 [00:00<00:00, 1067.76 it/sec, obj=-3]
INFO - 10:53:26:      7%|▋         | 9/121 [00:00<00:00, 1108.98 it/sec, obj=-2]
INFO - 10:53:26:      8%|▊         | 10/121 [00:00<00:00, 1144.64 it/sec, obj=-1]
INFO - 10:53:26:      9%|▉         | 11/121 [00:00<00:00, 1173.62 it/sec, obj=0]
INFO - 10:53:26:     10%|▉         | 12/121 [00:00<00:00, 1199.80 it/sec, obj=-9]
INFO - 10:53:26:     11%|█         | 13/121 [00:00<00:00, 1216.64 it/sec, obj=-8]
INFO - 10:53:26:     12%|█▏        | 14/121 [00:00<00:00, 1237.65 it/sec, obj=-7]
INFO - 10:53:26:     12%|█▏        | 15/121 [00:00<00:00, 1256.73 it/sec, obj=-6]
INFO - 10:53:26:     13%|█▎        | 16/121 [00:00<00:00, 1273.97 it/sec, obj=-5]
INFO - 10:53:26:     14%|█▍        | 17/121 [00:00<00:00, 1288.27 it/sec, obj=-4]
INFO - 10:53:26:     15%|█▍        | 18/121 [00:00<00:00, 1301.61 it/sec, obj=-3]
INFO - 10:53:26:     16%|█▌        | 19/121 [00:00<00:00, 1311.69 it/sec, obj=-2]
INFO - 10:53:26:     17%|█▋        | 20/121 [00:00<00:00, 1310.56 it/sec, obj=-1]
INFO - 10:53:26:     17%|█▋        | 21/121 [00:00<00:00, 1321.14 it/sec, obj=0]
INFO - 10:53:26:     18%|█▊        | 22/121 [00:00<00:00, 1331.22 it/sec, obj=1]
INFO - 10:53:26:     19%|█▉        | 23/121 [00:00<00:00, 1340.63 it/sec, obj=-8]
INFO - 10:53:26:     20%|█▉        | 24/121 [00:00<00:00, 1348.16 it/sec, obj=-7]
INFO - 10:53:26:     21%|██        | 25/121 [00:00<00:00, 1353.98 it/sec, obj=-6]
INFO - 10:53:26:     21%|██▏       | 26/121 [00:00<00:00, 1361.50 it/sec, obj=-5]
INFO - 10:53:26:     22%|██▏       | 27/121 [00:00<00:00, 1369.15 it/sec, obj=-4]
INFO - 10:53:26:     23%|██▎       | 28/121 [00:00<00:00, 1376.39 it/sec, obj=-3]
INFO - 10:53:26:     24%|██▍       | 29/121 [00:00<00:00, 1383.27 it/sec, obj=-2]
INFO - 10:53:26:     25%|██▍       | 30/121 [00:00<00:00, 1388.38 it/sec, obj=-1]
INFO - 10:53:26:     26%|██▌       | 31/121 [00:00<00:00, 1391.67 it/sec, obj=0]
INFO - 10:53:26:     26%|██▋       | 32/121 [00:00<00:00, 1397.05 it/sec, obj=1]
INFO - 10:53:26:     27%|██▋       | 33/121 [00:00<00:00, 1402.31 it/sec, obj=2]
INFO - 10:53:26:     28%|██▊       | 34/121 [00:00<00:00, 1399.87 it/sec, obj=-7]
INFO - 10:53:26:     29%|██▉       | 35/121 [00:00<00:00, 1391.81 it/sec, obj=-6]
INFO - 10:53:26:     30%|██▉       | 36/121 [00:00<00:00, 1394.47 it/sec, obj=-5]
INFO - 10:53:26:     31%|███       | 37/121 [00:00<00:00, 1397.35 it/sec, obj=-4]
INFO - 10:53:26:     31%|███▏      | 38/121 [00:00<00:00, 1401.57 it/sec, obj=-3]
INFO - 10:53:26:     32%|███▏      | 39/121 [00:00<00:00, 1405.89 it/sec, obj=-2]
INFO - 10:53:26:     33%|███▎      | 40/121 [00:00<00:00, 1410.12 it/sec, obj=-1]
INFO - 10:53:26:     34%|███▍      | 41/121 [00:00<00:00, 1414.33 it/sec, obj=0]
INFO - 10:53:26:     35%|███▍      | 42/121 [00:00<00:00, 1417.42 it/sec, obj=1]
INFO - 10:53:26:     36%|███▌      | 43/121 [00:00<00:00, 1419.71 it/sec, obj=2]
INFO - 10:53:26:     36%|███▋      | 44/121 [00:00<00:00, 1423.17 it/sec, obj=3]
INFO - 10:53:26:     37%|███▋      | 45/121 [00:00<00:00, 1426.54 it/sec, obj=-6]
INFO - 10:53:26:     38%|███▊      | 46/121 [00:00<00:00, 1417.20 it/sec, obj=-5]
INFO - 10:53:26:     39%|███▉      | 47/121 [00:00<00:00, 1417.89 it/sec, obj=-4]
INFO - 10:53:26:     40%|███▉      | 48/121 [00:00<00:00, 1420.10 it/sec, obj=-3]
INFO - 10:53:26:     40%|████      | 49/121 [00:00<00:00, 1422.00 it/sec, obj=-2]
INFO - 10:53:26:     41%|████▏     | 50/121 [00:00<00:00, 1424.96 it/sec, obj=-1]
INFO - 10:53:26:     42%|████▏     | 51/121 [00:00<00:00, 1428.18 it/sec, obj=0]
INFO - 10:53:26:     43%|████▎     | 52/121 [00:00<00:00, 1431.16 it/sec, obj=1]
INFO - 10:53:26:     44%|████▍     | 53/121 [00:00<00:00, 1434.07 it/sec, obj=2]
INFO - 10:53:26:     45%|████▍     | 54/121 [00:00<00:00, 1436.37 it/sec, obj=3]
INFO - 10:53:26:     45%|████▌     | 55/121 [00:00<00:00, 1437.88 it/sec, obj=4]
INFO - 10:53:26:     46%|████▋     | 56/121 [00:00<00:00, 1440.35 it/sec, obj=-5]
INFO - 10:53:26:     47%|████▋     | 57/121 [00:00<00:00, 1443.06 it/sec, obj=-4]
INFO - 10:53:26:     48%|████▊     | 58/121 [00:00<00:00, 1439.23 it/sec, obj=-3]
INFO - 10:53:26:     49%|████▉     | 59/121 [00:00<00:00, 1436.68 it/sec, obj=-2]
INFO - 10:53:26:     50%|████▉     | 60/121 [00:00<00:00, 1437.96 it/sec, obj=-1]
INFO - 10:53:26:     50%|█████     | 61/121 [00:00<00:00, 1439.02 it/sec, obj=0]
INFO - 10:53:26:     51%|█████     | 62/121 [00:00<00:00, 1441.15 it/sec, obj=1]
INFO - 10:53:26:     52%|█████▏    | 63/121 [00:00<00:00, 1443.48 it/sec, obj=2]
INFO - 10:53:26:     53%|█████▎    | 64/121 [00:00<00:00, 1445.92 it/sec, obj=3]
INFO - 10:53:26:     54%|█████▎    | 65/121 [00:00<00:00, 1448.18 it/sec, obj=4]
INFO - 10:53:26:     55%|█████▍    | 66/121 [00:00<00:00, 1449.74 it/sec, obj=5]
INFO - 10:53:26:     55%|█████▌    | 67/121 [00:00<00:00, 1450.94 it/sec, obj=-4]
INFO - 10:53:26:     56%|█████▌    | 68/121 [00:00<00:00, 1452.91 it/sec, obj=-3]
INFO - 10:53:26:     57%|█████▋    | 69/121 [00:00<00:00, 1454.99 it/sec, obj=-2]
INFO - 10:53:26:     58%|█████▊    | 70/121 [00:00<00:00, 1456.90 it/sec, obj=-1]
INFO - 10:53:26:     59%|█████▊    | 71/121 [00:00<00:00, 1458.90 it/sec, obj=0]
INFO - 10:53:26:     60%|█████▉    | 72/121 [00:00<00:00, 1460.38 it/sec, obj=1]
INFO - 10:53:26:     60%|██████    | 73/121 [00:00<00:00, 1462.20 it/sec, obj=2]
INFO - 10:53:26:     61%|██████    | 74/121 [00:00<00:00, 1455.58 it/sec, obj=3]
INFO - 10:53:26:     62%|██████▏   | 75/121 [00:00<00:00, 1453.50 it/sec, obj=4]
INFO - 10:53:26:     63%|██████▎   | 76/121 [00:00<00:00, 1454.99 it/sec, obj=5]
INFO - 10:53:26:     64%|██████▎   | 77/121 [00:00<00:00, 1456.60 it/sec, obj=6]
INFO - 10:53:26:     64%|██████▍   | 78/121 [00:00<00:00, 1457.62 it/sec, obj=-3]
INFO - 10:53:26:     65%|██████▌   | 79/121 [00:00<00:00, 1458.41 it/sec, obj=-2]
INFO - 10:53:26:     66%|██████▌   | 80/121 [00:00<00:00, 1459.93 it/sec, obj=-1]
INFO - 10:53:26:     67%|██████▋   | 81/121 [00:00<00:00, 1461.62 it/sec, obj=0]
INFO - 10:53:26:     68%|██████▊   | 82/121 [00:00<00:00, 1462.96 it/sec, obj=1]
INFO - 10:53:26:     69%|██████▊   | 83/121 [00:00<00:00, 1464.52 it/sec, obj=2]
INFO - 10:53:26:     69%|██████▉   | 84/121 [00:00<00:00, 1465.66 it/sec, obj=3]
INFO - 10:53:26:     70%|███████   | 85/121 [00:00<00:00, 1467.18 it/sec, obj=4]
INFO - 10:53:26:     71%|███████   | 86/121 [00:00<00:00, 1467.52 it/sec, obj=5]
INFO - 10:53:26:     72%|███████▏  | 87/121 [00:00<00:00, 1469.00 it/sec, obj=6]
INFO - 10:53:26:     73%|███████▎  | 88/121 [00:00<00:00, 1470.48 it/sec, obj=7]
INFO - 10:53:26:     74%|███████▎  | 89/121 [00:00<00:00, 1471.92 it/sec, obj=-2]
INFO - 10:53:26:     74%|███████▍  | 90/121 [00:00<00:00, 1473.28 it/sec, obj=-1]
INFO - 10:53:26:     75%|███████▌  | 91/121 [00:00<00:00, 1474.25 it/sec, obj=0]
INFO - 10:53:26:     76%|███████▌  | 92/121 [00:00<00:00, 1474.94 it/sec, obj=1]
INFO - 10:53:26:     77%|███████▋  | 93/121 [00:00<00:00, 1476.20 it/sec, obj=2]
INFO - 10:53:26:     78%|███████▊  | 94/121 [00:00<00:00, 1477.44 it/sec, obj=3]
INFO - 10:53:26:     79%|███████▊  | 95/121 [00:00<00:00, 1478.62 it/sec, obj=4]
INFO - 10:53:26:     79%|███████▉  | 96/121 [00:00<00:00, 1479.86 it/sec, obj=5]
INFO - 10:53:26:     80%|████████  | 97/121 [00:00<00:00, 1479.87 it/sec, obj=6]
INFO - 10:53:26:     81%|████████  | 98/121 [00:00<00:00, 1480.35 it/sec, obj=7]
INFO - 10:53:26:     82%|████████▏ | 99/121 [00:00<00:00, 1481.45 it/sec, obj=8]
INFO - 10:53:26:     83%|████████▎ | 100/121 [00:00<00:00, 1475.92 it/sec, obj=-1]
INFO - 10:53:26:     83%|████████▎ | 101/121 [00:00<00:00, 1476.06 it/sec, obj=0]
INFO - 10:53:26:     84%|████████▍ | 102/121 [00:00<00:00, 1477.11 it/sec, obj=1]
INFO - 10:53:26:     85%|████████▌ | 103/121 [00:00<00:00, 1477.76 it/sec, obj=2]
INFO - 10:53:26:     86%|████████▌ | 104/121 [00:00<00:00, 1478.16 it/sec, obj=3]
INFO - 10:53:26:     87%|████████▋ | 105/121 [00:00<00:00, 1479.21 it/sec, obj=4]
INFO - 10:53:26:     88%|████████▊ | 106/121 [00:00<00:00, 1480.29 it/sec, obj=5]
INFO - 10:53:26:     88%|████████▊ | 107/121 [00:00<00:00, 1481.39 it/sec, obj=6]
INFO - 10:53:26:     89%|████████▉ | 108/121 [00:00<00:00, 1482.58 it/sec, obj=7]
INFO - 10:53:26:     90%|█████████ | 109/121 [00:00<00:00, 1483.27 it/sec, obj=8]
INFO - 10:53:26:     91%|█████████ | 110/121 [00:00<00:00, 1483.82 it/sec, obj=9]
INFO - 10:53:26:     92%|█████████▏| 111/121 [00:00<00:00, 1484.80 it/sec, obj=0]
INFO - 10:53:26:     93%|█████████▎| 112/121 [00:00<00:00, 1485.83 it/sec, obj=1]
INFO - 10:53:26:     93%|█████████▎| 113/121 [00:00<00:00, 1486.82 it/sec, obj=2]
INFO - 10:53:26:     94%|█████████▍| 114/121 [00:00<00:00, 1485.19 it/sec, obj=3]
INFO - 10:53:26:     95%|█████████▌| 115/121 [00:00<00:00, 1485.78 it/sec, obj=4]
INFO - 10:53:26:     96%|█████████▌| 116/121 [00:00<00:00, 1486.72 it/sec, obj=5]
INFO - 10:53:26:     97%|█████████▋| 117/121 [00:00<00:00, 1487.18 it/sec, obj=6]
INFO - 10:53:26:     98%|█████████▊| 118/121 [00:00<00:00, 1488.18 it/sec, obj=7]
INFO - 10:53:26:     98%|█████████▊| 119/121 [00:00<00:00, 1489.09 it/sec, obj=8]
INFO - 10:53:26:     99%|█████████▉| 120/121 [00:00<00:00, 1490.05 it/sec, obj=9]
INFO - 10:53:26:    100%|██████████| 121/121 [00:00<00:00, 1490.96 it/sec, obj=10]
INFO - 10:53:26: Optimization result:
INFO - 10:53:26:    Optimizer info:
INFO - 10:53:26:       Status: None
INFO - 10:53:26:       Message: None
INFO - 10:53:26:       Number of calls to the objective function by the optimizer: 121
INFO - 10:53:26:    Solution:
INFO - 10:53:26:       Objective: -10.0
INFO - 10:53:26:       Design space:
INFO - 10:53:26:          +------+-------------+-------+-------------+---------+
INFO - 10:53:26:          | Name | Lower bound | Value | Upper bound | Type    |
INFO - 10:53:26:          +------+-------------+-------+-------------+---------+
INFO - 10:53:26:          | x1   |      -5     |   -5  |      5      | integer |
INFO - 10:53:26:          | x2   |      -5     |   -5  |      5      | integer |
INFO - 10:53:26:          +------+-------------+-------+-------------+---------+
INFO - 10:53:26: *** End DOEScenario execution (time: 0:00:00.094081) ***

{'eval_jac': False, 'n_samples': 121, 'algo': 'fullfact'}


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', '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', 'fullfact', 'ff2n', 'pbdesign', 'bbdesign', 'ccdesign', 'lhs', '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', 'Compromise', 'ConstraintsHistory', 'Correlations', 'DataVersusModel', 'GradientSensitivity', 'HighTradeOff', 'MultiObjectiveDiagram', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'Petal', 'QuadApprox', 'Radar', 'RadarChart', 'Robustness', 'SOM', 'ScatterPareto', 'ScatterPlotMatrix', 'TopologyView', 'VariableInfluence']


You can also look at the examples:

Total running time of the script: (0 minutes 0.108 seconds)

Gallery generated by Sphinx-Gallery