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 numpy import sum as np_sum

from gemseo import configure_logger
from gemseo import execute_algo
from gemseo import execute_post
from gemseo import get_available_doe_algorithms
from gemseo import get_available_opt_algorithms
from gemseo.algos.design_space import DesignSpace
from gemseo.algos.optimization_problem import OptimizationProblem
from gemseo.core.mdo_functions.mdo_function import MDOFunction

LOGGER = configure_logger()

Define the objective function#

We define the objective function \(f(x)=\sum_{i=1}^dx_i\) using an 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, lower_bound=-5, upper_bound=5, 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

execute_algo(problem, algo_name="PYDOE_FULLFACT", n_samples=11**2, algo_type="doe")

INFO - 08:35:47: Optimization problem:
INFO - 08:35:47:    minimize f = sum(x)
INFO - 08:35:47:    with respect to x
INFO - 08:35:47:    over the design space:
INFO - 08:35:47:       +------+-------------+-------+-------------+---------+
INFO - 08:35:47:       | Name | Lower bound | Value | Upper bound | Type    |
INFO - 08:35:47:       +------+-------------+-------+-------------+---------+
INFO - 08:35:47:       | x[0] |      -5     |  None |      5      | integer |
INFO - 08:35:47:       | x[1] |      -5     |  None |      5      | integer |
INFO - 08:35:47:       +------+-------------+-------+-------------+---------+
INFO - 08:35:47: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 08:35:47:      1%|          | 1/121 [00:00<00:00, 4957.81 it/sec, obj=-10]
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INFO - 08:35:47:     94%|█████████▍| 114/121 [00:00<00:00, 3832.26 it/sec, obj=3]
INFO - 08:35:47:     95%|█████████▌| 115/121 [00:00<00:00, 3833.31 it/sec, obj=4]
INFO - 08:35:47:     96%|█████████▌| 116/121 [00:00<00:00, 3833.80 it/sec, obj=5]
INFO - 08:35:47:     97%|█████████▋| 117/121 [00:00<00:00, 3834.22 it/sec, obj=6]
INFO - 08:35:47:     98%|█████████▊| 118/121 [00:00<00:00, 3834.69 it/sec, obj=7]
INFO - 08:35:47:     98%|█████████▊| 119/121 [00:00<00:00, 3833.36 it/sec, obj=8]
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INFO - 08:35:47:    100%|██████████| 121/121 [00:00<00:00, 3840.24 it/sec, obj=10]
INFO - 08:35:47: Optimization result:
INFO - 08:35:47:    Optimizer info:
INFO - 08:35:47:       Status: None
INFO - 08:35:47:       Message: None
INFO - 08:35:47:       Number of calls to the objective function by the optimizer: 121
INFO - 08:35:47:    Solution:
INFO - 08:35:47:       Objective: -10.0
INFO - 08:35:47:       Design space:
INFO - 08:35:47:          +------+-------------+-------+-------------+---------+
INFO - 08:35:47:          | Name | Lower bound | Value | Upper bound | Type    |
INFO - 08:35:47:          +------+-------------+-------+-------------+---------+
INFO - 08:35:47:          | x[0] |      -5     |   -5  |      5      | integer |
INFO - 08:35:47:          | x[1] |      -5     |   -5  |      5      | integer |
INFO - 08:35:47:          +------+-------------+-------+-------------+---------+
Optimization result:
  • Design variables: [-5. -5.]
  • Objective function: -10.0
  • Feasible solution: True


Post-process the results#

execute_post(
    problem,
    post_name="ScatterPlotMatrix",
    variable_names=["x", "f"],
    save=False,
    show=True,
)
plot simple opt 3
<gemseo.post.scatter_plot_matrix.ScatterPlotMatrix object at 0x7f2514ea8310>

Note that you can get all the optimization algorithms names:

get_available_opt_algorithms()

['Augmented_Lagrangian_order_0', 'Augmented_Lagrangian_order_1', 'MNBI', 'MultiStart', 'NLOPT_MMA', 'NLOPT_COBYLA', 'NLOPT_SLSQP', 'NLOPT_BOBYQA', 'NLOPT_BFGS', 'NLOPT_NEWUOA', 'DUAL_ANNEALING', 'SHGO', 'DIFFERENTIAL_EVOLUTION', 'INTERIOR_POINT', 'DUAL_SIMPLEX', 'Scipy_MILP', 'SLSQP', 'L-BFGS-B', 'TNC', 'NELDER-MEAD']

and all the DOE algorithms names:

get_available_doe_algorithms()

['CustomDOE', 'DiagonalDOE', 'MorrisDOE', 'OATDOE', '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', 'PYDOE_BBDESIGN', 'PYDOE_CCDESIGN', 'PYDOE_FF2N', 'PYDOE_FULLFACT', 'PYDOE_LHS', 'PYDOE_PBDESIGN', 'Halton', 'LHS', 'MC', 'PoissonDisk', 'Sobol']

Total running time of the script: (0 minutes 0.715 seconds)

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