Example for linear constraints in a continuous searchspace

Example for optimizing a synthetic test functions in a continuous space with linear constraints. All test functions that are available in BoTorch are also available here. This example assumes some basic familiarity with using BayBE. We thus refer to campaign for a basic example. Also, there is a large overlap with other examples with regards to using the test function. We thus refer to discrete_space for details on this aspect.

Necessary imports for this example

import os

import numpy as np
import pandas as pd
from botorch.test_functions import Rastrigin

from baybe import Campaign
from baybe.constraints import ContinuousLinearConstraint
from baybe.parameters import NumericalContinuousParameter
from baybe.searchspace import SearchSpace
from baybe.targets import NumericalTarget
from baybe.utils.dataframe import arrays_to_dataframes

Defining the test function

See discrete_space for details.

DIMENSION = 4
TestFunctionClass = Rastrigin

if not hasattr(TestFunctionClass, "dim"):
    TestFunction = TestFunctionClass(dim=DIMENSION)
else:
    TestFunction = TestFunctionClass()
    DIMENSION = TestFunctionClass().dim

BOUNDS = TestFunction.bounds

Creating the searchspace and the objective

Since the searchspace is continuous test, we construct NumericalContinuousParameters We use that data of the test function to deduce bounds and number of parameters.

parameters = [
    NumericalContinuousParameter(
        name=f"x_{k+1}",
        bounds=(BOUNDS[0, k], BOUNDS[1, k]),
    )
    for k in range(DIMENSION)
]

We model the following constraints:

• \(1.0*x_1 + 1.0*x_2 = 1.0\)

• \(1.0*x_3 - 1.0*x_4 = 2.0\)

• \(1.0*x_1 + 1.0*x_3 >= 1.0\)

• \(2.0*x_2 + 3.0*x_4 <= 1.0\) which is equivalent to \(-2.0*x_2 - 3.0*x_4 >= -1.0\)

constraints = [
    ContinuousLinearConstraint(
        parameters=["x_1", "x_2"], operator="=", coefficients=[1.0, 1.0], rhs=1.0
    ),
    ContinuousLinearConstraint(
        parameters=["x_3", "x_4"], operator="=", coefficients=[1.0, -1.0], rhs=2.0
    ),
    ContinuousLinearConstraint(
        parameters=["x_1", "x_3"], operator=">=", coefficients=[1.0, 1.0], rhs=1.0
    ),
    ContinuousLinearConstraint(
        parameters=["x_2", "x_4"], operator="<=", coefficients=[2.0, 3.0], rhs=-1.0
    ),
]

searchspace = SearchSpace.from_product(parameters=parameters, constraints=constraints)
target = NumericalTarget(name="Target", mode="MIN")
objective = target.to_objective()

Wrap the test function as a dataframe-based lookup callable

lookup = arrays_to_dataframes(
    [p.name for p in parameters], [target.name], use_torch=True
)(TestFunction)

Construct the campaign and run some iterations

campaign = Campaign(
    searchspace=searchspace,
    objective=objective,
)

Improve running time for CI via SMOKE_TEST

SMOKE_TEST = "SMOKE_TEST" in os.environ

BATCH_SIZE = 2 if SMOKE_TEST else 3
N_ITERATIONS = 2 if SMOKE_TEST else 3

for k in range(N_ITERATIONS):
    recommendation = campaign.recommend(batch_size=BATCH_SIZE)
    lookup_values = lookup(recommendation)
    measurements = pd.concat([recommendation, lookup_values], axis=1)
    campaign.add_measurements(measurements)

Verify the constraints

measurements = campaign.measurements
TOLERANCE = 0.01

\(1.0*x_1 + 1.0*x_2 = 1.0\)

print(
    "1.0*x_1 + 1.0*x_2 = 1.0 satisfied in all recommendations? ",
    np.allclose(
        1.0 * measurements["x_1"] + 1.0 * measurements["x_2"], 1.0, atol=TOLERANCE
    ),
)

1.0*x_1 + 1.0*x_2 = 1.0 satisfied in all recommendations?  True

\(1.0*x_3 - 1.0*x_4 = 2.0\)

print(
    "1.0*x_3 - 1.0*x_4 = 2.0 satisfied in all recommendations? ",
    np.allclose(
        1.0 * measurements["x_3"] - 1.0 * measurements["x_4"], 2.0, atol=TOLERANCE
    ),
)

1.0*x_3 - 1.0*x_4 = 2.0 satisfied in all recommendations?  True

\(1.0*x_1 + 1.0*x_3 >= 1.0\)

print(
    "1.0*x_1 + 1.0*x_3 >= 1.0 satisfied in all recommendations? ",
    (1.0 * measurements["x_1"] + 1.0 * measurements["x_3"]).ge(1.0 - TOLERANCE).all(),
)

1.0*x_1 + 1.0*x_3 >= 1.0 satisfied in all recommendations?  True

\(2.0*x_2 + 3.0*x_4 <= 1.0\)

print(
    "2.0*x_2 + 3.0*x_4 <= 1.0 satisfied in all recommendations? ",
    (2.0 * measurements["x_2"] + 3.0 * measurements["x_4"]).le(1.0 + TOLERANCE).all(),
)

2.0*x_2 + 3.0*x_4 <= 1.0 satisfied in all recommendations?  True