Note
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Analytical test case # 3¶
In this example, we consider a simple optimization problem to illustrate algorithms interfaces and DOE libraries integration. Integer variables are used
Imports¶
from __future__ import annotations
from gemseo.algos.design_space import DesignSpace
from gemseo.algos.doe.doe_factory import DOEFactory
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.api import configure_logger
from gemseo.api import execute_post
from gemseo.core.mdofunctions.mdo_function import MDOFunction
from numpy import sum as np_sum
LOGGER = configure_logger()
Define the objective function¶
We define the objective function \(f(x)=\sum_{i=1}^dx_i\)
using a MDOFunction.
objective = MDOFunction(np_sum, name="f", expr="sum(x)")
Define the design space¶
Then, we define the DesignSpace with GEMSEO.
design_space = DesignSpace()
design_space.add_variable("x", 2, l_b=-5, u_b=5, var_type="integer")
Define the optimization problem¶
Then, we define the OptimizationProblem with GEMSEO.
problem = OptimizationProblem(design_space)
problem.objective = objective
Solve the optimization problem using a DOE algorithm¶
We can see this optimization problem as a trade-off and solve it by means of a design of experiments (DOE), e.g. full factorial design
DOEFactory().execute(problem, "fullfact", n_samples=11**2)
INFO - 13:29:07: Optimization problem:
INFO - 13:29:07: minimize f = sum(x)
INFO - 13:29:07: with respect to x
INFO - 13:29:07: over the design space:
INFO - 13:29:07: +------+-------------+-------+-------------+---------+
INFO - 13:29:07: | name | lower_bound | value | upper_bound | type |
INFO - 13:29:07: +------+-------------+-------+-------------+---------+
INFO - 13:29:07: | x[0] | -5 | None | 5 | integer |
INFO - 13:29:07: | x[1] | -5 | None | 5 | integer |
INFO - 13:29:07: +------+-------------+-------+-------------+---------+
INFO - 13:29:07: Solving optimization problem with algorithm fullfact:
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INFO - 13:29:07: Optimization result:
INFO - 13:29:07: Optimizer info:
INFO - 13:29:07: Status: None
INFO - 13:29:07: Message: None
INFO - 13:29:07: Number of calls to the objective function by the optimizer: 121
INFO - 13:29:07: Solution:
INFO - 13:29:07: Objective: -10.0
INFO - 13:29:07: Design space:
INFO - 13:29:07: +------+-------------+-------+-------------+---------+
INFO - 13:29:07: | name | lower_bound | value | upper_bound | type |
INFO - 13:29:07: +------+-------------+-------+-------------+---------+
INFO - 13:29:07: | x[0] | -5 | -5 | 5 | integer |
INFO - 13:29:07: | x[1] | -5 | -5 | 5 | integer |
INFO - 13:29:07: +------+-------------+-------+-------------+---------+
Optimization result:
Design variables: [-5. -5.]
Objective function: -10.0
Feasible solution: True
Post-process the results¶
execute_post(
problem,
"ScatterPlotMatrix",
variable_names=["x", "f"],
save=False,
show=True,
)
<gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7f67b124f9d0>
Note that you can get all the optimization algorithms names:
algo_list = DOEFactory().algorithms
print("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']
Total running time of the script: ( 0 minutes 0.665 seconds)