Note
Go to the end to download the full example code
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:
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)