pubo_builder

class BinaryModel

BinaryModel(coeff: 'dict[tuple[int, ...], float]', constant: 'float')

normalize (self, factor) -> -

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class Constraint

Constraint(name: 'str', condition: 'subs_expr.ConstraintCondition', forall: 'list[tuple[subs_expr.Element, subs_expr.SubstitutableCondition]]')

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class PuboBuilder

A class to build a PUBO from a problem and an instance.

Attributes

• objective(BinaryModel) : a binary model of the objective function
• linear_penalty(dict[str, dict[tuple[int, ...], BinaryModel]]) : a binary model of linear penalties
• penalty(dict[str, dict[tuple[int, ...], BinaryModel]]) : a binary model of penalties
• custom_penalty(dict[str, dict[tuple[int, ...], BinaryModel]]) : a binary model of custom penalties
• binary_encoder(dict[str, IntegerEncoder]) : a binary encoder for each variable
• constraint_expr(dict[str, jm.Constraint]) : a constraint expression
• obj_norm(float) : a normalization factor of the objective function
• const_norm(dict[str, dict[tuple[int, ...], float]]) : a normalization factor of constraints
• pena_norm(dict[str, dict[tuple[int, ...], float]]) : a normalization factor of penalties

get_hubo_dict (self, multipliers, detail_parameters) -> tuple[dict[tuple[int, ...], float], float]

Get a HUBO from the built PUBO.

A constraint with label=const

$$g_k(x) = C_k, \forall k$$

is converted to a penalty term by the following equation:

$$A_{\text{const}} \left[\sum_{k} \lambda_k \left( g_k(x) - C_k \right)^2 + \sum_k \mu_k (g_k(x) - C_k) \right]$$

where $\lambda_k$ and $\mu_k$ are detail parameters for each constraint and $A_{\text{const}}$ is uniformal weight for each penalties.

$A$ is parameters provided to set the weights for each penalty, independently of the index of the constraint and penalty. You can set $A$ using multipliers. By default $A=1$.

The weight of parameters $\lambda_k$ and $\mu_k$ are set by detail_parameters. By default, $\lambda_k=1$ and $\mu_k=0$ for the penalty is converted from equality constraint, and $\lambda_k=1$ and $\mu_k=1$ for the penalty is converted from inequality constraint.

For example, the following constraint

$$\sum_{i=1}^N x_{ij} = 1, \forall j \in \{0, 1\}~\text{label=onehot}$$

is converted to the following penalty term with multipliers={"onehot": 1} and detail_parameters={"onehot": {(1,): (1/2, 1)}} that means $A_{\text{onehot}}=1$ and $\lambda_{1}=1/2, \mu_{1}=1$:

$$\begin{align} &A_{\text{onehot}}\sum_j \left(\lambda_j \left(\sum_{i=1}^N x_{ij} - 1\right)^2 + \mu_j \left(\sum_{i=1}^N x_{ij} - 1\right)\right)\\ &= \left(\sum_{i=1}^N x_{i0} - 1\right)^2 + \frac{1}{2}\left(\sum_{i=1}^N x_{i1} - 1\right)^2 + \left(\sum_{i=1}^N x_{i1} - 1\right) \end{align}$$

Parameters

• multipliers(dict[str, float]) : a multiplier for each penalty. Defaults to None.
• detail_parameters(dict[str, dict[tuple[int, ...], tuple[float, float]]]) : detail parameters for each penalty. Defaults to None.

Returns

• tuple[dict[tuple[int, ...], float], float] : a HUBO dictionary and a constant term

get_qubo_dict (self, multipliers, detail_parameters) -> dict[tuple[int, int], float]

Get a QUBO COO format dictionary.

Please see the document of get_hubo_dict for the detail.

Parameters

• multipliers(dict[str, float]) : a multiplier for each penalty. Defaults to None.
• detail_parameters(dict[str, dict[tuple[int, ...], tuple[float, float]]]) : detail parameters for each penalty. Defaults to None.

Returns

• dict[tuple[int, int], float] : a QUBO dictionary