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 and wrapped via the botorch_function_wrapper. 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
from botorch.test_functions import Rastrigin

from baybe import Campaign
from baybe.constraints import (
    ContinuousLinearEqualityConstraint,
    ContinuousLinearInequalityConstraint,
)
from baybe.objectives import SingleTargetObjective
from baybe.parameters import NumericalContinuousParameter
from baybe.searchspace import SearchSpace
from baybe.targets import NumericalTarget
from baybe.utils.botorch_wrapper import botorch_function_wrapper

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
WRAPPED_FUNCTION = botorch_function_wrapper(test_function=TestFunction)

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 = [
    ContinuousLinearEqualityConstraint(
        parameters=["x_1", "x_2"], coefficients=[1.0, 1.0], rhs=1.0
    ),
    ContinuousLinearEqualityConstraint(
        parameters=["x_3", "x_4"], coefficients=[1.0, -1.0], rhs=2.0
    ),
    ContinuousLinearInequalityConstraint(
        parameters=["x_1", "x_3"], coefficients=[1.0, 1.0], rhs=1.0
    ),
    ContinuousLinearInequalityConstraint(
        parameters=["x_2", "x_4"], coefficients=[-2.0, -3.0], rhs=-1.0
    ),
]

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

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)

    # target value are looked up via the botorch wrapper
    target_values = []
    for index, row in recommendation.iterrows():
        target_values.append(WRAPPED_FUNCTION(*row.to_list()))

    recommendation["Target"] = target_values

    campaign.add_measurements(recommendation)

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