Constraints

log_barrier(lhs, comparison, rhs, *, penalty_sign, sharpness=1.0, inf=None)

Return a penalty based on how close the constraint is to being violated.

If the left-hand-side is equal to the right-hand-side, or if the constraint is violated, the returned penalty will be infinite (+inf or -inf, depending on penalty_sign). Such inf values can result in numerical instabilities. To overcome such instabilities, you might want to set the keyword argument inf as a large-enough finite positive quantity M, so that very large (or infinite) penalties will be clipped down to M.

Parameters:

Name	Type	Description	Default
lhs	Union[float, Tensor]	The left-hand-side of the constraint. In the non-batched case, this is expected as a scalar. If it is given as an n-dimensional tensor where n is at least 1, this is considered as a batch of left-hand-side values.	required
comparison	str	The operator used for comparing the left-hand-side and the right-hand-side. Expected as a string. Acceptable values are: '<=', '>='.	required
rhs	Union[float, Tensor]	The right-hand-side of the constraint. In the non-batched case, this is expected as a scalar. If it is given as an n-dimensional tensor where n is at least 1, this is considered as a batch of right-hand-side values.	required
penalty_sign	str	Expected as string, either as '+' or '-', which determines the sign of the penalty (i.e. determines if the penalty will be positive or negative). One should consider the objective sense of the fitness function at hand for deciding penalty_sign. For example, if a fitness function is written from the perspective of maximization, the penalties should be negative, and therefore, penalty_sign must be given as '-'.	required
sharpness	Union[float, Tensor]	The logarithmic penalty will be divided by this number. By default, this value is 1. A sharper log-penalization allows the constraint to get closer to its boundary, and then makes a more sudden jump towards infinity.	1.0
inf	Optional[Union[float, Tensor]]	When concerned about the possible numerical instabilities caused by infinite penalties, one can specify a finite large-enough positive quantity M through this argument. As a result, infinite penalties will be clipped down to the finite M. One might also think of this as temporarily replacing inf with M while computing the log-penalties.	None

Source code in evotorch/tools/constraints.py

def log_barrier(
    lhs: Union[float, torch.Tensor],
    comparison: str,
    rhs: Union[float, torch.Tensor],
    *,
    penalty_sign: str,
    sharpness: Union[float, torch.Tensor] = 1.0,
    inf: Optional[Union[float, torch.Tensor]] = None,
) -> torch.Tensor:
    """
    Return a penalty based on how close the constraint is to being violated.

    If the left-hand-side is equal to the right-hand-side, or if the constraint
    is violated, the returned penalty will be infinite (`+inf` or `-inf`,
    depending on `penalty_sign`). Such `inf` values can result in numerical
    instabilities. To overcome such instabilities, you might want to set the
    keyword argument `inf` as a large-enough finite positive quantity `M`, so
    that very large (or infinite) penalties will be clipped down to `M`.

    Args:
        lhs: The left-hand-side of the constraint. In the non-batched case,
            this is expected as a scalar. If it is given as an n-dimensional
            tensor where n is at least 1, this is considered as a batch of
            left-hand-side values.
        comparison: The operator used for comparing the left-hand-side and the
            right-hand-side. Expected as a string. Acceptable values are:
            '<=', '>='.
        rhs: The right-hand-side of the constraint. In the non-batched case,
            this is expected as a scalar. If it is given as an n-dimensional
            tensor where n is at least 1, this is considered as a batch of
            right-hand-side values.
        penalty_sign: Expected as string, either as '+' or '-', which
            determines the sign of the penalty (i.e. determines if the penalty
            will be positive or negative). One should consider the objective
            sense of the fitness function at hand for deciding `penalty_sign`.
            For example, if a fitness function is written from the perspective
            of maximization, the penalties should be negative, and therefore,
            `penalty_sign` must be given as '-'.
        sharpness: The logarithmic penalty will be divided by this number.
            By default, this value is 1. A sharper log-penalization allows
            the constraint to get closer to its boundary, and then makes
            a more sudden jump towards infinity.
        inf: When concerned about the possible numerical instabilities caused
            by infinite penalties, one can specify a finite large-enough
            positive quantity `M` through this argument. As a result,
            infinite penalties will be clipped down to the finite `M`.
            One might also think of this as temporarily replacing `inf` with
            `M` while computing the log-penalties.
    Returns:
        Log-penalty amount(s), whose sign(s) is/are determined by
        `penalty_sign`.
    """
    from ..decorators import expects_ndim

    if inf is None:
        inf = float("inf")

    return expects_ndim(_log_barrier, (0, None, 0, 0, None, 0))(lhs, comparison, rhs, sharpness, penalty_sign, inf)

penalty(lhs, comparison, rhs, *, penalty_sign, linear=None, step=None, exp=None, exp_inf=None)

Return a penalty based on the amount of violation of the constraint.

Depending on the provided arguments, the penalty can be linear, or exponential, or based on step function, or a combination of these.

Parameters:

Name	Type	Description	Default
lhs	Union[float, Tensor]	The left-hand-side of the constraint. In the non-batched case, this is expected as a scalar. If it is given as an n-dimensional tensor where n is at least 1, this is considered as a batch of left-hand-side values.	required
comparison	str	The operator used for comparing the left-hand-side and the right-hand-side. Expected as a string. Acceptable values are: '<=', '==', '>='.	required
rhs	Union[float, Tensor]	The right-hand-side of the constraint. In the non-batched case, this is expected as a scalar. If it is given as an n-dimensional tensor where n is at least 1, this is considered as a batch of right-hand-side values.	required
penalty_sign	str	Expected as string, either as '+' or '-', which determines the sign of the penalty (i.e. determines if the penalty will be positive or negative). One should consider the objective sense of the fitness function at hand for deciding penalty_sign. For example, if a fitness function is written from the perspective of maximization, the penalties should be negative, and therefore, penalty_sign must be given as '-'.	required
linear	Optional[Union[float, Tensor]]	Multiplier for the linear component of the penalization. If omitted (i.e. left as None), the value of this multiplier will be 0 (meaning that there will not be any linear penalization). In the non-batched case, this argument is expected as a scalar. If this is provided as a tensor 1 or more dimensions, those dimensions will be considered as batch dimensions.	None
step	Optional[Union[float, Tensor]]	The constant amount that will be added onto the penalty if there is a violation. If omitted (i.e. left as None), this value is 0. In the non-batched case, this argument is expected as a scalar. If this is provided as a tensor 1 or more dimensions, those dimensions will be considered as batch dimensions.	None
exp	Optional[Union[float, Tensor]]	A constant p that will enable exponential penalization in the form amount_of_violation ** p. If this is left as None or is given as nan, there will be no exponential penalization. In the non-batched case, this argument is expected as a scalar. If this is provided as a tensor 1 or more dimensions, those dimensions will be considered as batch dimensions.	None
exp_inf	Optional[Union[float, Tensor]]	Upper bound for exponential penalty values. If exponential penalty is enabled but exp_inf is omitted (i.e. left as None), the exponential penalties can jump to very large values or to infinity, potentially causing numerical instabilities. To avoid such numerical instabilities, one might provide a large-enough positive constant M via the argument exp_inf. When such a value is given, exponential penalties will not be allowed to exceed M. One might also think of this as temporarily replacing inf with M while computing the exponential penalties.	None

Source code in evotorch/tools/constraints.py

def penalty(
    lhs: Union[float, torch.Tensor],
    comparison: str,
    rhs: Union[float, torch.Tensor],
    *,
    penalty_sign: str,
    linear: Optional[Union[float, torch.Tensor]] = None,
    step: Optional[Union[float, torch.Tensor]] = None,
    exp: Optional[Union[float, torch.Tensor]] = None,
    exp_inf: Optional[Union[float, torch.Tensor]] = None,
) -> torch.Tensor:
    """
    Return a penalty based on the amount of violation of the constraint.

    Depending on the provided arguments, the penalty can be linear,
    or exponential, or based on step function, or a combination of these.

    Args:
        lhs: The left-hand-side of the constraint. In the non-batched case,
            this is expected as a scalar. If it is given as an n-dimensional
            tensor where n is at least 1, this is considered as a batch of
            left-hand-side values.
        comparison: The operator used for comparing the left-hand-side and the
            right-hand-side. Expected as a string. Acceptable values are:
            '<=', '==', '>='.
        rhs: The right-hand-side of the constraint. In the non-batched case,
            this is expected as a scalar. If it is given as an n-dimensional
            tensor where n is at least 1, this is considered as a batch of
            right-hand-side values.
        penalty_sign: Expected as string, either as '+' or '-', which
            determines the sign of the penalty (i.e. determines if the penalty
            will be positive or negative). One should consider the objective
            sense of the fitness function at hand for deciding `penalty_sign`.
            For example, if a fitness function is written from the perspective
            of maximization, the penalties should be negative, and therefore,
            `penalty_sign` must be given as '-'.
        linear: Multiplier for the linear component of the penalization.
            If omitted (i.e. left as None), the value of this multiplier will
            be 0 (meaning that there will not be any linear penalization).
            In the non-batched case, this argument is expected as a scalar.
            If this is provided as a tensor 1 or more dimensions, those
            dimensions will be considered as batch dimensions.
        step: The constant amount that will be added onto the penalty if there
            is a violation. If omitted (i.e. left as None), this value is 0.
            In the non-batched case, this argument is expected as a scalar.
            If this is provided as a tensor 1 or more dimensions, those
            dimensions will be considered as batch dimensions.
        exp: A constant `p` that will enable exponential penalization in the
            form `amount_of_violation ** p`. If this is left as None or is
            given as `nan`, there will be no exponential penalization.
            In the non-batched case, this argument is expected as a scalar.
            If this is provided as a tensor 1 or more dimensions, those
            dimensions will be considered as batch dimensions.
        exp_inf: Upper bound for exponential penalty values. If exponential
            penalty is enabled but `exp_inf` is omitted (i.e. left as None),
            the exponential penalties can jump to very large values or to
            infinity, potentially causing numerical instabilities. To avoid
            such numerical instabilities, one might provide a large-enough
            positive constant `M` via the argument `exp_inf`. When such a value
            is given, exponential penalties will not be allowed to exceed `M`.
            One might also think of this as temporarily replacing `inf` with
            `M` while computing the exponential penalties.
    Returns:
        The penalty amount(s), whose sign(s) is/are determined by
        `sign_penalty`.
    """
    from ..decorators import expects_ndim

    if linear is None:
        linear = 0.0
    if step is None:
        step = 0.0
    if exp is None:
        exp = float("nan")
    if exp_inf is None:
        exp_inf = float("inf")

    return expects_ndim(_penalty, (0, None, 0, None, 0, 0, 0, 0))(
        lhs,
        comparison,
        rhs,
        penalty_sign,
        linear,
        step,
        exp,
        exp_inf,
    )

violation(lhs, comparison, rhs)

Get the amount of constraint violation.

Parameters:

Name	Type	Description	Default
lhs	Union[float, Tensor]	The left-hand-side of the constraint. In the non-batched case, this is expected as a scalar. If it is given as an n-dimensional tensor where n is at least 1, this is considered as a batch of left-hand-side values.	required
comparison	str	The operator used for comparing the left-hand-side and the right-hand-side. Expected as a string. Acceptable values are: '<=', '==', '>='.	required
rhs	Union[float, Tensor]	The right-hand-side of the constraint. In the non-batched case, this is expected as a scalar. If it is given as an n-dimensional tensor where n is at least 1, this is considered as a batch of right-hand-side values.	required

Source code in evotorch/tools/constraints.py

def violation(
    lhs: Union[float, torch.Tensor],
    comparison: str,
    rhs: Union[float, torch.Tensor],
) -> torch.Tensor:
    """
    Get the amount of constraint violation.

    Args:
        lhs: The left-hand-side of the constraint. In the non-batched case,
            this is expected as a scalar. If it is given as an n-dimensional
            tensor where n is at least 1, this is considered as a batch of
            left-hand-side values.
        comparison: The operator used for comparing the left-hand-side and the
            right-hand-side. Expected as a string. Acceptable values are:
            '<=', '==', '>='.
        rhs: The right-hand-side of the constraint. In the non-batched case,
            this is expected as a scalar. If it is given as an n-dimensional
            tensor where n is at least 1, this is considered as a batch of
            right-hand-side values.
    Returns:
        The amount of violation of the constraint. A value of 0 means that
        the constraint is not violated at all. The returned violation amount(s)
        are always non-negative.
    """
    from ..decorators import expects_ndim

    return expects_ndim(_violation, (0, None, 0))(lhs, comparison, rhs)