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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 - 08:23:29:
INFO - 08:23:29: *** Start DOEScenario execution ***
INFO - 08:23:29: DOEScenario
INFO - 08:23:29: Disciplines: AnalyticDiscipline
INFO - 08:23:29: MDO formulation: DisciplinaryOpt
INFO - 08:23:29: Optimization problem:
INFO - 08:23:29: minimize y(x1, x2)
INFO - 08:23:29: with respect to x1, x2
INFO - 08:23:29: over the design space:
INFO - 08:23:29: +------+-------------+-------+-------------+---------+
INFO - 08:23:29: | name | lower_bound | value | upper_bound | type |
INFO - 08:23:29: +------+-------------+-------+-------------+---------+
INFO - 08:23:29: | x1 | -5 | None | 5 | integer |
INFO - 08:23:29: | x2 | -5 | None | 5 | integer |
INFO - 08:23:29: +------+-------------+-------+-------------+---------+
INFO - 08:23:29: Solving optimization problem with algorithm fullfact:
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INFO - 08:23:29: Optimization result:
INFO - 08:23:29: Optimizer info:
INFO - 08:23:29: Status: None
INFO - 08:23:29: Message: None
INFO - 08:23:29: Number of calls to the objective function by the optimizer: 121
INFO - 08:23:29: Solution:
INFO - 08:23:29: Objective: -10.0
INFO - 08:23:29: Design space:
INFO - 08:23:29: +------+-------------+-------+-------------+---------+
INFO - 08:23:29: | name | lower_bound | value | upper_bound | type |
INFO - 08:23:29: +------+-------------+-------+-------------+---------+
INFO - 08:23:29: | x1 | -5 | -5 | 5 | integer |
INFO - 08:23:29: | x2 | -5 | -5 | 5 | integer |
INFO - 08:23:29: +------+-------------+-------+-------------+---------+
INFO - 08:23:29: *** End DOEScenario execution (time: 0:00:00.094239) ***
{'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']
Available post-processing¶
In order to get the list of available post-processing algorithms, use:
get_available_post_processings()
['Animation', 'BasicHistory', 'Compromise', 'ConstraintsHistory', 'Correlations', '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 0.106 seconds)