Cbranincurrin synthetic test function for cmoo

docs/refs.bib

@@ -512,6 +512,14 @@ @InProceedings{moss2023IPA
     year = {2023},
 }
 
+@article{belakaria2019max,
+  title={Max-value entropy search for multi-objective bayesian optimization},
+  author={Belakaria, Syrine and Deshwal, Aryan and Doppa, Janardhan Rao},
+  journal={Advances in Neural Information Processing Systems},
+  volume={32},
+  year={2019}
+}
+
 @inproceedings{wang2013bayesian,
   title={Bayesian Optimization in High Dimensions via Random Embeddings.},
   author={Wang, Ziyu and Zoghi, Masrour and Hutter, Frank and Matheson, David and de Freitas, Nando},

tests/unit/objectives/test_multi_objectives.py

@@ -11,14 +11,22 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Callable
+from typing import Callable, Union
 
 import numpy.testing as npt
 import pytest
 import tensorflow as tf
 
 from tests.util.misc import TF_DEBUGGING_ERROR_TYPES
-from trieste.objectives.multi_objectives import DTLZ1, DTLZ2, VLMOP2, MultiObjectiveTestProblem
+from trieste.objectives.multi_objectives import (
+    DTLZ1,
+    DTLZ2,
+    VLMOP2,
+    ConstrainedBraninCurrin,
+    ConstrainedMultiObjectiveTestProblem,
+    MultiObjectiveTestProblem,
+    NoAnalyticalParetoPointsError,
+)
 from trieste.types import TensorType
 
 
@@ -107,6 +115,47 @@ def test_dtlz2_has_expected_output(
     npt.assert_allclose(f(test_x), expected, rtol=1e-4)
 
 
+@pytest.mark.parametrize(
+    "test_x, expected_obj, expected_con, threshold",
+    [
+        (
+            tf.constant([[0.0, 0.0]]),
+            tf.constant([[308.12909601160663, 3.0]]),
+            tf.constant([[62.5]]),
+            0.0,
+        ),
+        (
+            tf.constant([[0.5, 1.0]]),
+            tf.constant([[150.45202034083485, 4.609388478538837]]),
+            tf.constant([[-3.75]]),
+            10.0,
+        ),
+        (
+            tf.constant([[[0.5, 1.0]], [[0.0, 0.0]]]),
+            tf.constant([[[150.45202034083485, 4.609388478538837]], [[308.12909601160663, 3.0]]]),
+            tf.constant([[[6.25]], [[62.5]]]),
+            0.0,
+        ),
+        (
+            tf.constant([[0.5, 1.0], [0.0, 0.0]]),
+            tf.constant([[150.45202034083485, 4.609388478538837], [308.12909601160663, 3.0]]),
+            tf.constant([[11.25], [67.5]]),
+            -5.0,
+        ),
+    ],
+)
+def test_constrainedbranincurrin_has_expected_output(
+    test_x: TensorType,
+    expected_obj: TensorType,
+    expected_con: TensorType,
+    threshold: Union[TensorType, float],
+) -> None:
+    f = ConstrainedBraninCurrin().objective
+    c = ConstrainedBraninCurrin().constraint
+    npt.assert_allclose(f(test_x), expected_obj, rtol=1e-5)
+    npt.assert_allclose(c(test_x, threshold), expected_con, rtol=1e-5)
+
+
 @pytest.mark.parametrize(
     "obj_type, input_dim, num_obj, gen_pf_num",
     [
@@ -137,45 +186,60 @@ def test_gen_pareto_front_is_equal_to_math_defined(
         (VLMOP2(2), tf.constant([[0.4, 0.2, 0.5]])),
         (DTLZ1(3, 2), tf.constant([[0.3, 0.1]])),
         (DTLZ2(5, 2), tf.constant([[0.3, 0.1]])),
+        (ConstrainedBraninCurrin(), tf.constant([[0.3, 0.2, 0.1]])),
     ],
 )
 def test_func_raises_specified_input_dim_not_align_with_actual_input_dim(
-    obj_inst: MultiObjectiveTestProblem, actual_x: TensorType
+    obj_inst: Union[MultiObjectiveTestProblem, ConstrainedMultiObjectiveTestProblem],
+    actual_x: TensorType,
 ) -> None:
     with pytest.raises(TF_DEBUGGING_ERROR_TYPES):
         obj_inst.objective(actual_x)
+    if isinstance(obj_inst, ConstrainedMultiObjectiveTestProblem):
+        with pytest.raises(TF_DEBUGGING_ERROR_TYPES):
+            obj_inst.constraint(actual_x)
 
 
 @pytest.mark.parametrize(
-    "problem, input_dim, num_obj",
+    "problem, input_dim, num_obj, num_con",
     [
-        (VLMOP2(2), 2, 2),
-        (VLMOP2(10), 10, 2),
-        (DTLZ1(3, 2), 3, 2),
-        (DTLZ1(10, 5), 10, 5),
-        (DTLZ2(3, 2), 3, 2),
-        (DTLZ2(10, 5), 10, 5),
+        (VLMOP2(2), 2, 2, 0),
+        (VLMOP2(10), 10, 2, 0),
+        (DTLZ1(3, 2), 3, 2, 0),
+        (DTLZ1(10, 5), 10, 5, 0),
+        (DTLZ2(3, 2), 3, 2, 0),
+        (DTLZ2(10, 5), 10, 5, 0),
+        (ConstrainedBraninCurrin(), 2, 2, 1),
     ],
 )
 @pytest.mark.parametrize("num_obs", [1, 5, 10])
 @pytest.mark.parametrize("dtype", [tf.float32, tf.float64])
-def test_objective_has_correct_shape_and_dtype(
+def test_objective_and_constraint_has_correct_shape_and_dtype(
     problem: MultiObjectiveTestProblem,
     input_dim: int,
     num_obj: int,
     num_obs: int,
+    num_con: int,
     dtype: tf.DType,
 ) -> None:
     x = problem.search_space.sample(num_obs)
     assert x.dtype == tf.float64  # default dtype
 
     x = tf.cast(x, dtype)
     y = problem.objective(x)
-    pf = problem.gen_pareto_optimal_points(num_obs * 2)
 
     assert y.dtype == x.dtype
     tf.debugging.assert_shapes([(x, [num_obs, input_dim])])
     tf.debugging.assert_shapes([(y, [num_obs, num_obj])])
 
-    assert pf.dtype == tf.float64  # default dtype
-    tf.debugging.assert_shapes([(pf, [num_obs * 2, num_obj])])
+    if isinstance(problem, ConstrainedMultiObjectiveTestProblem):
+        c = problem.constraint(x)
+        tf.debugging.assert_shapes([(c, [num_obs, num_con])])
+        assert x.dtype == c.dtype
+
+    try:  # check if the problem has a valid `gen_pareto_optimal_points` method
+        pf = problem.gen_pareto_optimal_points(num_obs * 2)
+        assert pf.dtype == tf.float64  # default dtype
+        tf.debugging.assert_shapes([(pf, [num_obs * 2, num_obj])])
+    except NoAnalyticalParetoPointsError:
+        pass

trieste/objectives/multi_objectives.py

@@ -19,13 +19,18 @@
 import math
 from dataclasses import dataclass
 from functools import partial
+from typing import Optional
 
 import tensorflow as tf
 from typing_extensions import Protocol
 
 from ..space import Box
 from ..types import TensorType
-from .single_objectives import ObjectiveTestProblem
+from .single_objectives import ObjectiveTestProblem, branin
+
+
+class NoAnalyticalParetoPointsError(Exception):
+    pass
 
 
 class GenParetoOptimalPoints(Protocol):
@@ -38,7 +43,21 @@ def __call__(self, n: int, seed: int | None = None) -> TensorType:
         :param n: The number of pareto optimal points to be generated.
         :param seed: An integer used to create a random seed for distributions that
          used to generate pareto optimal points.
-        :return: The Pareto optimal points
+        :return: The Pareto optimal points.
+        """
+
+
+class ConstraintTestProblem(Protocol):
+    """A Protocol representing function returning constraint values given specified inputs."""
+
+    def __call__(self, x: TensorType, threshold: Optional[float] = 0.0) -> TensorType:
+        """
+        return the constraint value given specified inputs `x` and `threshold`
+
+        :param x: The points at which to evaluate the function, with shape [..., d].
+        :param threshold: a feasibility threshold used to determine the constraint, by default 0 is
+            used as in the original problem.
+        :return: The constraint values.
         """
 
 
@@ -55,6 +74,17 @@ class MultiObjectiveTestProblem(ObjectiveTestProblem):
     random number seed."""
 
 
+@dataclass(frozen=True)
+class ConstrainedMultiObjectiveTestProblem(MultiObjectiveTestProblem):
+    """
+    Convenience container class for synthetic constrained multi-objective test functions, containing
+    additionally a constraint function.
+    """
+
+    constraint: ConstraintTestProblem
+    """The synthetic test function's constraints"""
+
+
 def vlmop2(x: TensorType, d: int) -> TensorType:
     """
     The VLMOP2 synthetic function.
@@ -236,3 +266,74 @@ def gen_pareto_optimal_points(n: int, seed: int | None = None) -> TensorType:
         search_space=Box([0.0], [1.0]) ** d,
         gen_pareto_optimal_points=gen_pareto_optimal_points,
     )
+
+
+def ConstrainedBraninCurrin() -> ConstrainedMultiObjectiveTestProblem:
+    """
+    The ConstrainedBraninCurrin problem, typically evaluated over :math:`[0, 1]^2`.
+    See :cite:`belakaria2019max` and :cite:`daulton2020differentiable`
+    (the latter for adding the constraint) for details.
+
+    :return: The problem specification.
+    """
+
+    def gen_pareto_optimal_points(n: int, seed: int | None = None) -> TensorType:
+        """
+        raise an `NoAnalyticalParetoPointsError` since there is no explicit way of defining
+        this problem's Pareto frontier.
+        """
+        raise NoAnalyticalParetoPointsError(
+            "No analytical approach to generate Pareto optimal points for this problem, "
+            "an optimization-based approach may be utilized to approximate the Pareto "
+            "optimal points"
+        )
+
+    def evaluate_constraint(x: TensorType, threshold: Optional[float] = 0.0) -> TensorType:
+        """
+        The constraint of branincurrin problem, < ``threshold`` is feasible.
+
+        :param x: The points at which to evaluate the function, with shape [..., d].
+        :param threshold: a feasibility threshold used to determine the constraint, by default 0 is
+            used as in the original problem.
+        :raise ValueError (or InvalidArgumentError): If ``x`` has an invalid shape.
+        """
+        x = x * (
+            tf.constant([10.0, 15.0], dtype=x.dtype) - tf.constant([-5.0, 0.0], dtype=x.dtype)
+        ) + tf.constant([-5.0, 0.0], dtype=x.dtype)
+        return (x[..., :1] - 2.5) ** 2 + (x[..., 1:] - 7.5) ** 2 - 50 - threshold
+
+    return ConstrainedMultiObjectiveTestProblem(
+        name="ConstrainedBraninCurrin",
+        objective=branin_currin,
+        constraint=evaluate_constraint,
+        search_space=Box([0.0], [1.0]) ** 2,
+        gen_pareto_optimal_points=gen_pareto_optimal_points,
+    )
+
+
+def branin_currin(x: TensorType) -> TensorType:
+    """
+    The branincurrin synthetic function.
+
+    :param x: The points at which to evaluate the function, with shape [..., d].
+    :raise ValueError (or InvalidArgumentError): If ``x`` has an invalid shape.
+    """
+    tf.debugging.assert_shapes([(x, (..., 2))])
+    return tf.concat([branin(x), currin(x)], axis=-1)
+
+
+def currin(x: TensorType) -> TensorType:
+    """
+    The currin synthetic function
+
+    :param x: The points at which to evaluate the function, with shape [..., d].
+    :raise ValueError (or InvalidArgumentError): If ``x`` has an invalid shape.
+    """
+    tf.debugging.assert_shapes([(x, (..., 2))])
+    return (
+        (1 - tf.math.exp(-0.5 * (1 / (x[..., 1] + 1e-100))))  # 1e-100 used for avoid zero division
+        * (
+            (2300 * x[..., 0] ** 3 + 1900 * x[..., 0] ** 2 + 2092 * x[..., 0] + 60)
+            / (100 * x[..., 0] ** 3 + 500 * x[..., 0] ** 2 + 4 * x[..., 0] + 20)
+        )
+    )[..., tf.newaxis]