Note
Click here to download the full example code
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 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 matplotlib import pyplot as plt
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)
Out:
INFO - 10:06:11: Optimization problem:
INFO - 10:06:11: minimize f = sum(x)
INFO - 10:06:11: with respect to x
INFO - 10:06:11: over the design space:
INFO - 10:06:11: +------+-------------+-------+-------------+---------+
INFO - 10:06:11: | name | lower_bound | value | upper_bound | type |
INFO - 10:06:11: +------+-------------+-------+-------------+---------+
INFO - 10:06:11: | x | -5 | None | 5 | integer |
INFO - 10:06:11: | x | -5 | None | 5 | integer |
INFO - 10:06:11: +------+-------------+-------+-------------+---------+
INFO - 10:06:11: Solving optimization problem with algorithm fullfact:
INFO - 10:06:11: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 121 samples: 11
INFO - 10:06:11: Final number of samples for DOE = 121 vs 121 requested
INFO - 10:06:11: ... 0%| | 0/121 [00:00<?, ?it]
INFO - 10:06:11: ... 100%|██████████| 121/121 [00:00<00:00, 10772.66 it/sec, obj=10]
INFO - 10:06:11: Optimization result:
INFO - 10:06:11: Optimizer info:
INFO - 10:06:11: Status: None
INFO - 10:06:11: Message: None
INFO - 10:06:11: Number of calls to the objective function by the optimizer: 121
INFO - 10:06:11: Solution:
INFO - 10:06:11: Objective: -10.0
INFO - 10:06:11: Design space:
INFO - 10:06:11: +------+-------------+-------+-------------+---------+
INFO - 10:06:11: | name | lower_bound | value | upper_bound | type |
INFO - 10:06:11: +------+-------------+-------+-------------+---------+
INFO - 10:06:11: | x | -5 | -5 | 5 | integer |
INFO - 10:06:11: | x | -5 | -5 | 5 | integer |
INFO - 10:06:11: +------+-------------+-------+-------------+---------+
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=False
)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
Note that you can get all the optimization algorithms names:
algo_list = DOEFactory().algorithms
print("Available algorithms ", algo_list)
Out:
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 0.597 seconds)