Binary Optimization with Budget Constraints#

References:#

  1. Attia, Ahmed. “Probabilistic approach to black-box binary optimization with budget constraints: Application to sensor placement.” arXiv preprint arXiv:2406.05830 (2024).

[1]:

from pyoed.optimization.binary_optimization import ConstrainedBinaryReinforceOptimizer
from pyoed.optimization.test_functions.binary_test_functions import WeightedAlternatingSignOptimizationFunction

Maximization problem#

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

[2]:

## Settings
# Objective function (Define your own)
fun = WeightedAlternatingSignOptimizationFunction(10)

# Dimension of the optimization variable
size = 10

# The budget constraint(s)
budgets = range(5)  # the constraint on binary x is: sum(x) < 5

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

[3]:

# Solve the optimization problem
maximization_results = optimizer.solve()

Iter: [000001] ; Step-Update-Norm: 8.22463722e-02
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Iter: [000500] ; Step-Update-Norm: 9.16379446e-04

[4]:

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

Plots saved...
../_images/tutorials_binary_optimization_constrained_stochastic_5_1.png
../_images/tutorials_binary_optimization_constrained_stochastic_5_2.png
../_images/tutorials_binary_optimization_constrained_stochastic_5_3.png
../_images/tutorials_binary_optimization_constrained_stochastic_5_4.png
../_images/tutorials_binary_optimization_constrained_stochastic_5_5.png
../_images/tutorials_binary_optimization_constrained_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 & Plot
minimization_results = optimizer.solve()

Iter: [000001] ; Step-Update-Norm: 1.08512367e-01
Iter: [000002] ; Step-Update-Norm: 8.77801690e-02
Iter: [000003] ; Step-Update-Norm: 9.82377876e-02
Iter: [000004] ; Step-Update-Norm: 1.20100050e-01
Iter: [000005] ; Step-Update-Norm: 1.31333092e-01
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Iter: [000035] ; Step-Update-Norm: 3.58200162e-02
Iter: [000036] ; Step-Update-Norm: 1.61709626e-02
Iter: [000037] ; Step-Update-Norm: 3.02167838e-02
Iter: [000038] ; Step-Update-Norm: 1.79165984e-02
Iter: [000039] ; Step-Update-Norm: 2.06585611e-02
Iter: [000040] ; Step-Update-Norm: 5.07553778e-02
Iter: [000041] ; Step-Update-Norm: 1.66665478e-02
Iter: [000042] ; Step-Update-Norm: 1.42498456e-02
Iter: [000043] ; Step-Update-Norm: 1.39430084e-02
Iter: [000044] ; Step-Update-Norm: 3.80621377e-02
Iter: [000045] ; Step-Update-Norm: 1.29161944e-02
Iter: [000046] ; Step-Update-Norm: 1.33909753e-02
Iter: [000047] ; Step-Update-Norm: 1.79144140e-02
Iter: [000048] ; Step-Update-Norm: 2.75763173e-02
Iter: [000049] ; Step-Update-Norm: 4.93724937e-02
Iter: [000050] ; Step-Update-Norm: 3.13437535e-03
Iter: [000051] ; Step-Update-Norm: 3.35407965e-02
Iter: [000052] ; 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_constrained_stochastic_8_1.png
../_images/tutorials_binary_optimization_constrained_stochastic_8_2.png
../_images/tutorials_binary_optimization_constrained_stochastic_8_3.png
../_images/tutorials_binary_optimization_constrained_stochastic_8_4.png
../_images/tutorials_binary_optimization_constrained_stochastic_8_5.png
../_images/tutorials_binary_optimization_constrained_stochastic_8_6.png 
[ ]: