Note
Click here to download the full example code
Create a DOE Scenario¶
from __future__ import annotations
from gemseo.api import configure_logger
from gemseo.api import create_design_space
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.api import get_available_doe_algorithms
from gemseo.api 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 - 17:23:05:
INFO - 17:23:05: *** Start DOEScenario execution ***
INFO - 17:23:05: DOEScenario
INFO - 17:23:05: Disciplines: AnalyticDiscipline
INFO - 17:23:05: MDO formulation: DisciplinaryOpt
INFO - 17:23:05: Optimization problem:
INFO - 17:23:05: minimize y(x1, x2)
INFO - 17:23:05: with respect to x1, x2
INFO - 17:23:05: over the design space:
INFO - 17:23:05: +------+-------------+-------+-------------+---------+
INFO - 17:23:05: | name | lower_bound | value | upper_bound | type |
INFO - 17:23:05: +------+-------------+-------+-------------+---------+
INFO - 17:23:05: | x1 | -5 | None | 5 | integer |
INFO - 17:23:05: | x2 | -5 | None | 5 | integer |
INFO - 17:23:05: +------+-------------+-------+-------------+---------+
INFO - 17:23:05: Solving optimization problem with algorithm fullfact:
INFO - 17:23:05: ... 0%| | 0/121 [00:00<?, ?it]
INFO - 17:23:05: ... 1%| | 1/121 [00:00<00:00, 219.98 it/sec, obj=-10]
INFO - 17:23:05: ... 2%|▏ | 2/121 [00:00<00:00, 359.67 it/sec, obj=-9]
INFO - 17:23:05: ... 2%|▏ | 3/121 [00:00<00:00, 453.57 it/sec, obj=-8]
INFO - 17:23:05: ... 3%|▎ | 4/121 [00:00<00:00, 526.56 it/sec, obj=-7]
INFO - 17:23:05: ... 4%|▍ | 5/121 [00:00<00:00, 584.00 it/sec, obj=-6]
INFO - 17:23:05: ... 5%|▍ | 6/121 [00:00<00:00, 630.06 it/sec, obj=-5]
INFO - 17:23:05: ... 6%|▌ | 7/121 [00:00<00:00, 661.65 it/sec, obj=-4]
INFO - 17:23:05: ... 7%|▋ | 8/121 [00:00<00:00, 691.87 it/sec, obj=-3]
INFO - 17:23:05: ... 7%|▋ | 9/121 [00:00<00:00, 718.26 it/sec, obj=-2]
INFO - 17:23:05: ... 8%|▊ | 10/121 [00:00<00:00, 741.29 it/sec, obj=-1]
INFO - 17:23:05: ... 9%|▉ | 11/121 [00:00<00:00, 756.92 it/sec, obj=0]
INFO - 17:23:05: ... 10%|▉ | 12/121 [00:00<00:00, 773.77 it/sec, obj=-9]
INFO - 17:23:05: ... 11%|█ | 13/121 [00:00<00:00, 789.58 it/sec, obj=-8]
INFO - 17:23:05: ... 12%|█▏ | 14/121 [00:00<00:00, 803.51 it/sec, obj=-7]
INFO - 17:23:05: ... 12%|█▏ | 15/121 [00:00<00:00, 812.63 it/sec, obj=-6]
INFO - 17:23:05: ... 13%|█▎ | 16/121 [00:00<00:00, 823.06 it/sec, obj=-5]
INFO - 17:23:05: ... 14%|█▍ | 17/121 [00:00<00:00, 833.38 it/sec, obj=-4]
INFO - 17:23:05: ... 15%|█▍ | 18/121 [00:00<00:00, 842.60 it/sec, obj=-3]
INFO - 17:23:05: ... 16%|█▌ | 19/121 [00:00<00:00, 845.99 it/sec, obj=-2]
INFO - 17:23:05: ... 17%|█▋ | 20/121 [00:00<00:00, 853.06 it/sec, obj=-1]
INFO - 17:23:05: ... 17%|█▋ | 21/121 [00:00<00:00, 860.57 it/sec, obj=0]
INFO - 17:23:05: ... 18%|█▊ | 22/121 [00:00<00:00, 867.48 it/sec, obj=1]
INFO - 17:23:05: ... 19%|█▉ | 23/121 [00:00<00:00, 871.43 it/sec, obj=-8]
INFO - 17:23:05: ... 20%|█▉ | 24/121 [00:00<00:00, 876.71 it/sec, obj=-7]
INFO - 17:23:05: ... 21%|██ | 25/121 [00:00<00:00, 882.31 it/sec, obj=-6]
INFO - 17:23:05: ... 21%|██▏ | 26/121 [00:00<00:00, 887.65 it/sec, obj=-5]
INFO - 17:23:05: ... 22%|██▏ | 27/121 [00:00<00:00, 890.36 it/sec, obj=-4]
INFO - 17:23:05: ... 23%|██▎ | 28/121 [00:00<00:00, 894.53 it/sec, obj=-3]
INFO - 17:23:05: ... 24%|██▍ | 29/121 [00:00<00:00, 899.03 it/sec, obj=-2]
INFO - 17:23:05: ... 25%|██▍ | 30/121 [00:00<00:00, 903.16 it/sec, obj=-1]
INFO - 17:23:05: ... 26%|██▌ | 31/121 [00:00<00:00, 905.06 it/sec, obj=0]
INFO - 17:23:05: ... 26%|██▋ | 32/121 [00:00<00:00, 908.13 it/sec, obj=1]
INFO - 17:23:05: ... 27%|██▋ | 33/121 [00:00<00:00, 911.81 it/sec, obj=2]
INFO - 17:23:05: ... 28%|██▊ | 34/121 [00:00<00:00, 915.16 it/sec, obj=-7]
INFO - 17:23:05: ... 29%|██▉ | 35/121 [00:00<00:00, 916.19 it/sec, obj=-6]
INFO - 17:23:05: ... 30%|██▉ | 36/121 [00:00<00:00, 918.62 it/sec, obj=-5]
INFO - 17:23:05: ... 31%|███ | 37/121 [00:00<00:00, 921.60 it/sec, obj=-4]
INFO - 17:23:05: ... 31%|███▏ | 38/121 [00:00<00:00, 924.41 it/sec, obj=-3]
INFO - 17:23:05: ... 32%|███▏ | 39/121 [00:00<00:00, 925.52 it/sec, obj=-2]
INFO - 17:23:05: ... 33%|███▎ | 40/121 [00:00<00:00, 927.38 it/sec, obj=-1]
INFO - 17:23:05: ... 34%|███▍ | 41/121 [00:00<00:00, 929.83 it/sec, obj=0]
INFO - 17:23:05: ... 35%|███▍ | 42/121 [00:00<00:00, 932.18 it/sec, obj=1]
INFO - 17:23:05: ... 36%|███▌ | 43/121 [00:00<00:00, 932.78 it/sec, obj=2]
INFO - 17:23:05: ... 36%|███▋ | 44/121 [00:00<00:00, 932.91 it/sec, obj=3]
INFO - 17:23:05: ... 37%|███▋ | 45/121 [00:00<00:00, 933.47 it/sec, obj=-6]
INFO - 17:23:05: ... 38%|███▊ | 46/121 [00:00<00:00, 935.84 it/sec, obj=-5]
INFO - 17:23:05: ... 39%|███▉ | 47/121 [00:00<00:00, 936.42 it/sec, obj=-4]
INFO - 17:23:05: ... 40%|███▉ | 48/121 [00:00<00:00, 937.91 it/sec, obj=-3]
INFO - 17:23:05: ... 40%|████ | 49/121 [00:00<00:00, 939.82 it/sec, obj=-2]
INFO - 17:23:05: ... 41%|████▏ | 50/121 [00:00<00:00, 941.64 it/sec, obj=-1]
INFO - 17:23:05: ... 42%|████▏ | 51/121 [00:00<00:00, 942.13 it/sec, obj=0]
INFO - 17:23:05: ... 43%|████▎ | 52/121 [00:00<00:00, 943.43 it/sec, obj=1]
INFO - 17:23:05: ... 44%|████▍ | 53/121 [00:00<00:00, 945.19 it/sec, obj=2]
INFO - 17:23:05: ... 45%|████▍ | 54/121 [00:00<00:00, 946.91 it/sec, obj=3]
INFO - 17:23:05: ... 45%|████▌ | 55/121 [00:00<00:00, 947.15 it/sec, obj=4]
INFO - 17:23:05: ... 46%|████▋ | 56/121 [00:00<00:00, 948.21 it/sec, obj=-5]
INFO - 17:23:05: ... 47%|████▋ | 57/121 [00:00<00:00, 949.80 it/sec, obj=-4]
INFO - 17:23:05: ... 48%|████▊ | 58/121 [00:00<00:00, 951.38 it/sec, obj=-3]
INFO - 17:23:05: ... 49%|████▉ | 59/121 [00:00<00:00, 951.72 it/sec, obj=-2]
INFO - 17:23:05: ... 50%|████▉ | 60/121 [00:00<00:00, 952.55 it/sec, obj=-1]
INFO - 17:23:05: ... 50%|█████ | 61/121 [00:00<00:00, 953.88 it/sec, obj=0]
INFO - 17:23:05: ... 51%|█████ | 62/121 [00:00<00:00, 955.19 it/sec, obj=1]
INFO - 17:23:05: ... 52%|█████▏ | 63/121 [00:00<00:00, 955.47 it/sec, obj=2]
INFO - 17:23:05: ... 53%|█████▎ | 64/121 [00:00<00:00, 956.25 it/sec, obj=3]
INFO - 17:23:05: ... 54%|█████▎ | 65/121 [00:00<00:00, 957.53 it/sec, obj=4]
INFO - 17:23:05: ... 55%|█████▍ | 66/121 [00:00<00:00, 958.73 it/sec, obj=5]
INFO - 17:23:05: ... 55%|█████▌ | 67/121 [00:00<00:00, 959.07 it/sec, obj=-4]
INFO - 17:23:05: ... 56%|█████▌ | 68/121 [00:00<00:00, 959.94 it/sec, obj=-3]
INFO - 17:23:05: ... 57%|█████▋ | 69/121 [00:00<00:00, 960.88 it/sec, obj=-2]
INFO - 17:23:05: ... 58%|█████▊ | 70/121 [00:00<00:00, 962.00 it/sec, obj=-1]
INFO - 17:23:05: ... 59%|█████▊ | 71/121 [00:00<00:00, 960.19 it/sec, obj=0]
INFO - 17:23:05: ... 60%|█████▉ | 72/121 [00:00<00:00, 960.99 it/sec, obj=1]
INFO - 17:23:05: ... 60%|██████ | 73/121 [00:00<00:00, 961.92 it/sec, obj=2]
INFO - 17:23:05: ... 61%|██████ | 74/121 [00:00<00:00, 962.11 it/sec, obj=3]
INFO - 17:23:05: ... 62%|██████▏ | 75/121 [00:00<00:00, 962.33 it/sec, obj=4]
INFO - 17:23:05: ... 63%|██████▎ | 76/121 [00:00<00:00, 962.81 it/sec, obj=5]
INFO - 17:23:05: ... 64%|██████▎ | 77/121 [00:00<00:00, 963.80 it/sec, obj=6]
INFO - 17:23:05: ... 64%|██████▍ | 78/121 [00:00<00:00, 964.74 it/sec, obj=-3]
INFO - 17:23:05: ... 65%|██████▌ | 79/121 [00:00<00:00, 964.54 it/sec, obj=-2]
INFO - 17:23:05: ... 66%|██████▌ | 80/121 [00:00<00:00, 965.63 it/sec, obj=-1]
INFO - 17:23:05: ... 67%|██████▋ | 81/121 [00:00<00:00, 966.23 it/sec, obj=0]
INFO - 17:23:05: ... 68%|██████▊ | 82/121 [00:00<00:00, 967.07 it/sec, obj=1]
INFO - 17:23:05: ... 69%|██████▊ | 83/121 [00:00<00:00, 967.21 it/sec, obj=2]
INFO - 17:23:05: ... 69%|██████▉ | 84/121 [00:00<00:00, 967.71 it/sec, obj=3]
INFO - 17:23:05: ... 70%|███████ | 85/121 [00:00<00:00, 968.35 it/sec, obj=4]
INFO - 17:23:05: ... 71%|███████ | 86/121 [00:00<00:00, 969.08 it/sec, obj=5]
INFO - 17:23:05: ... 72%|███████▏ | 87/121 [00:00<00:00, 969.75 it/sec, obj=6]
INFO - 17:23:05: ... 73%|███████▎ | 88/121 [00:00<00:00, 969.71 it/sec, obj=7]
INFO - 17:23:05: ... 74%|███████▎ | 89/121 [00:00<00:00, 970.34 it/sec, obj=-2]
INFO - 17:23:05: ... 74%|███████▍ | 90/121 [00:00<00:00, 971.04 it/sec, obj=-1]
INFO - 17:23:05: ... 75%|███████▌ | 91/121 [00:00<00:00, 971.80 it/sec, obj=0]
INFO - 17:23:05: ... 76%|███████▌ | 92/121 [00:00<00:00, 971.64 it/sec, obj=1]
INFO - 17:23:05: ... 77%|███████▋ | 93/121 [00:00<00:00, 972.12 it/sec, obj=2]
INFO - 17:23:05: ... 78%|███████▊ | 94/121 [00:00<00:00, 972.80 it/sec, obj=3]
INFO - 17:23:05: ... 79%|███████▊ | 95/121 [00:00<00:00, 973.47 it/sec, obj=4]
INFO - 17:23:05: ... 79%|███████▉ | 96/121 [00:00<00:00, 973.35 it/sec, obj=5]
INFO - 17:23:05: ... 80%|████████ | 97/121 [00:00<00:00, 973.75 it/sec, obj=6]
INFO - 17:23:05: ... 81%|████████ | 98/121 [00:00<00:00, 974.27 it/sec, obj=7]
INFO - 17:23:05: ... 82%|████████▏ | 99/121 [00:00<00:00, 974.89 it/sec, obj=8]
INFO - 17:23:05: ... 83%|████████▎ | 100/121 [00:00<00:00, 974.71 it/sec, obj=-1]
INFO - 17:23:05: ... 83%|████████▎ | 101/121 [00:00<00:00, 975.17 it/sec, obj=0]
INFO - 17:23:05: ... 84%|████████▍ | 102/121 [00:00<00:00, 975.76 it/sec, obj=1]
INFO - 17:23:05: ... 85%|████████▌ | 103/121 [00:00<00:00, 976.31 it/sec, obj=2]
INFO - 17:23:05: ... 86%|████████▌ | 104/121 [00:00<00:00, 976.15 it/sec, obj=3]
INFO - 17:23:05: ... 87%|████████▋ | 105/121 [00:00<00:00, 976.57 it/sec, obj=4]
INFO - 17:23:05: ... 88%|████████▊ | 106/121 [00:00<00:00, 976.49 it/sec, obj=5]
INFO - 17:23:05: ... 88%|████████▊ | 107/121 [00:00<00:00, 976.08 it/sec, obj=6]
INFO - 17:23:05: ... 89%|████████▉ | 108/121 [00:00<00:00, 976.09 it/sec, obj=7]
INFO - 17:23:05: ... 90%|█████████ | 109/121 [00:00<00:00, 976.41 it/sec, obj=8]
INFO - 17:23:05: ... 91%|█████████ | 110/121 [00:00<00:00, 976.94 it/sec, obj=9]
INFO - 17:23:05: ... 92%|█████████▏| 111/121 [00:00<00:00, 977.54 it/sec, obj=0]
INFO - 17:23:05: ... 93%|█████████▎| 112/121 [00:00<00:00, 977.37 it/sec, obj=1]
INFO - 17:23:05: ... 93%|█████████▎| 113/121 [00:00<00:00, 977.58 it/sec, obj=2]
INFO - 17:23:05: ... 94%|█████████▍| 114/121 [00:00<00:00, 978.10 it/sec, obj=3]
INFO - 17:23:05: ... 95%|█████████▌| 115/121 [00:00<00:00, 978.53 it/sec, obj=4]
INFO - 17:23:05: ... 96%|█████████▌| 116/121 [00:00<00:00, 978.36 it/sec, obj=5]
INFO - 17:23:05: ... 97%|█████████▋| 117/121 [00:00<00:00, 978.67 it/sec, obj=6]
INFO - 17:23:05: ... 98%|█████████▊| 118/121 [00:00<00:00, 979.16 it/sec, obj=7]
INFO - 17:23:05: ... 98%|█████████▊| 119/121 [00:00<00:00, 979.64 it/sec, obj=8]
INFO - 17:23:05: ... 99%|█████████▉| 120/121 [00:00<00:00, 979.25 it/sec, obj=9]
INFO - 17:23:05: ... 100%|██████████| 121/121 [00:00<00:00, 979.52 it/sec, obj=10]
INFO - 17:23:05: Optimization result:
INFO - 17:23:05: Optimizer info:
INFO - 17:23:05: Status: None
INFO - 17:23:05: Message: None
INFO - 17:23:05: Number of calls to the objective function by the optimizer: 121
INFO - 17:23:05: Solution:
INFO - 17:23:05: Objective: -10.0
INFO - 17:23:05: Design space:
INFO - 17:23:05: +------+-------------+-------+-------------+---------+
INFO - 17:23:05: | name | lower_bound | value | upper_bound | type |
INFO - 17:23:05: +------+-------------+-------+-------------+---------+
INFO - 17:23:05: | x1 | -5 | -5 | 5 | integer |
INFO - 17:23:05: | x2 | -5 | -5 | 5 | integer |
INFO - 17:23:05: +------+-------------+-------+-------------+---------+
INFO - 17:23:05: *** End DOEScenario execution (time: 0:00:00.139840) ***
{'eval_jac': False, 'algo': 'fullfact', 'n_samples': 121}
The optimum results can be found in the execution log. It is also possible to
extract them by invoking the Scenario.get_optimum() method. It
returns a dictionary containing the optimum results for the
scenario under consideration:
opt_results = scenario.get_optimum()
print(
"The solution of P is (x*,f(x*)) = ({}, {})".format(
opt_results.x_opt, opt_results.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:
algo_list = get_available_doe_algorithms()
print(f"Available algorithms: {algo_list}")
Available 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']
Available post-processing¶
In order to get the list of available post-processing algorithms, use:
post_list = get_available_post_processings()
print(f"Available algorithms: {post_list}")
Available algorithms: ['BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', 'GradientSensitivity', 'HighTradeOff', 'KMeans', 'MultiObjectiveDiagram', 'ObjConstrHist', 'OptHistoryView', 'ParallelCoordinates', 'ParetoFront', 'Petal', 'QuadApprox', 'Radar', 'RadarChart', 'Robustness', 'SOM', 'ScatterPareto', 'ScatterPlotMatrix', 'VariableInfluence']
You can also look at the examples:
Total running time of the script: ( 0 minutes 0.168 seconds)