Binary Optimization via Stochastic Learning#

References:#

  1. Ahmed Attia, Sven Leyffer, and Todd S. Munson. “Stochastic learning approach for binary optimization: Application to Bayesian optimal design of experiments.” SIAM Journal on Scientific Computing 44, no. 2 (2022): B395-B427.

[1]:

from pyoed.optimization.binary_optimization import BinaryReinforceOptimizer
from pyoed.optimization.test_functions.binary_test_functions import AlternatingSignOptimizationFunction
import matplotlib.pyplot as plt

Maximization problem#

Create the optimizer, solve maximization problem, and then plot results

[2]:

## Settings
# Objective function (Define your own)
fun = AlternatingSignOptimizationFunction(10)
# Dimension of the optimization variable
size = 10

# Create the optimizer
optimizer = BinaryReinforceOptimizer(
    configs=dict(
        fun=fun,
        size=size,
        maxiter=500,
        maximize=True,
        random_seed=1011,  # for reproducibility
    )
)

[3]:

# Solve
maximization_results = optimizer.solve()

Iter: [000001] ; Step-Update-Norm: 1.03172338e-01
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Iter: [000459] ; Step-Update-Norm: 1.33721755e-12
Iter: [000460] ; Step-Update-Norm: 1.00781316e-12
Iter: [000461] ; Step-Update-Norm: 8.34038398e-13

[4]:

# Use optimizer plotter for visualization
_ = optimizer.plot_results(maximization_results, bruteforce=True, overwrite=True, keep_plots=True, )

Plots saved...
../_images/tutorials_binary_optimization_stochastic_5_1.png
../_images/tutorials_binary_optimization_stochastic_5_2.png
../_images/tutorials_binary_optimization_stochastic_5_3.png
../_images/tutorials_binary_optimization_stochastic_5_4.png
../_images/tutorials_binary_optimization_stochastic_5_5.png
../_images/tutorials_binary_optimization_stochastic_5_6.png

Minimization problem#

You can either recreate the optimizer with configuration maximize set to False, or simply update this configuration as follows

[5]:

# Set the optimization objective to minimization
optimizer.update_configurations(maximize=False)

# Solve
minimization_results = optimizer.solve()

Iter: [000001] ; Step-Update-Norm: 1.08913933e-01
Iter: [000002] ; Step-Update-Norm: 1.05078084e-01
Iter: [000003] ; Step-Update-Norm: 1.27931595e-01
Iter: [000004] ; Step-Update-Norm: 1.14399859e-01
Iter: [000005] ; Step-Update-Norm: 1.28601572e-01
Iter: [000006] ; Step-Update-Norm: 1.14012620e-01
Iter: [000007] ; Step-Update-Norm: 1.30406720e-01
Iter: [000008] ; Step-Update-Norm: 1.28884242e-01
Iter: [000009] ; Step-Update-Norm: 1.47773135e-01
Iter: [000010] ; Step-Update-Norm: 1.26499661e-01
Iter: [000011] ; Step-Update-Norm: 4.18627213e-02
Iter: [000012] ; Step-Update-Norm: 1.10129434e-01
Iter: [000013] ; Step-Update-Norm: 7.97901592e-02
Iter: [000014] ; Step-Update-Norm: 1.53177993e-02
Iter: [000015] ; Step-Update-Norm: 1.00618323e-01
Iter: [000016] ; Step-Update-Norm: 4.33638945e-02
Iter: [000017] ; Step-Update-Norm: 9.33403699e-03
Iter: [000018] ; Step-Update-Norm: 2.27476548e-02
Iter: [000019] ; Step-Update-Norm: 2.28075324e-03
Iter: [000020] ; Step-Update-Norm: 1.02120302e-01
Iter: [000021] ; Step-Update-Norm: 1.05731686e-02
Iter: [000022] ; Step-Update-Norm: 8.72084195e-03
Iter: [000023] ; Step-Update-Norm: 1.68006948e-02
Iter: [000024] ; Step-Update-Norm: 2.77842837e-03
Iter: [000025] ; Step-Update-Norm: 7.59176221e-03
Iter: [000026] ; Step-Update-Norm: 2.20911346e-03
Iter: [000027] ; Step-Update-Norm: 6.68111376e-02
Iter: [000028] ; Step-Update-Norm: 3.83142275e-02
Iter: [000029] ; Step-Update-Norm: 1.16624083e-02
Iter: [000030] ; Step-Update-Norm: 9.74207186e-02
Iter: [000031] ; Step-Update-Norm: 1.72002563e-03
Iter: [000032] ; Step-Update-Norm: 5.39758819e-02
Iter: [000033] ; Step-Update-Norm: 1.18421192e-02
Iter: [000034] ; Step-Update-Norm: 2.55186509e-02
Iter: [000035] ; Step-Update-Norm: 1.06237976e-02
Iter: [000036] ; Step-Update-Norm: 1.16861774e-02
Iter: [000037] ; Step-Update-Norm: 8.71452049e-02
Iter: [000038] ; Step-Update-Norm: 4.09324859e-02
Iter: [000039] ; Step-Update-Norm: 4.70260694e-04
Iter: [000040] ; Step-Update-Norm: 0.00000000e+00

[6]:

# Use optimizer plotter for visualization
_ = optimizer.plot_results(minimization_results, bruteforce=True, overwrite=True, keep_plots=True, )

Plots saved...
../_images/tutorials_binary_optimization_stochastic_8_1.png
../_images/tutorials_binary_optimization_stochastic_8_2.png
../_images/tutorials_binary_optimization_stochastic_8_3.png
../_images/tutorials_binary_optimization_stochastic_8_4.png
../_images/tutorials_binary_optimization_stochastic_8_5.png
../_images/tutorials_binary_optimization_stochastic_8_6.png 
[ ]: