Protocol Documentation

Constant function like `f(x_1, x_2) = 2`

Linear function like `f(x_1, x_2) = 2 x_1 + 3 x_2`

Quadratic function like `f(x_1, x_2) = 4 x_1 x_2 + 5 x_2`

Polynomial like `f(x_1, x_2) = 4 x_1^2 + 5 x_2^3 + 6 x_1 x_2^2 + 7 x_2^2 + 8 x_1 x_2 + 9 x_1 + 10 x_2 + 11`

Constraint ID - Constraint IDs are managed separately from decision variable IDs. We can use the same ID for both. For example, we have a decision variable `x` with decision variable ID `1`` and constraint `x == 0` with constraint ID `1`. - IDs are not required to be sequential. - IDs must be unique with other types of constraints.

Integer parameters of the constraint. Consider for example a problem constains a series of constraints `x[i, j] + y[i, j] <= 10` for `i = 1, 2, 3` and `j = 4, 5`, then 6 = 3x2 `Constraint` messages should be created corresponding to each pair of `i` and `j`. The `name` field of this message is intended to be a human-readable name of `x[i, j] + y[i, j] <= 10`, and the `subscripts` field is intended to be the value of `[i, j]` like `[1, 5]`.

Key-value parameters of the constraint.

Name of the constraint.

Detail human-readable description of the constraint.

The value of function for the state

IDs of decision variables used to evalute this constraint

Integer parameters of the constraint.

Key-value parameters of the constraint.

Name of the constraint.

Detail human-readable description of the constraint.

Value for the Lagrangian dual variable of this constraint. This is optional because not all solvers support to evaluate dual variables.

Short removed reason of the constraint. This field exists only if this message is evaluated from a removed constraint.

Detailed parameters why the constraint is removed. This field exists only if this message is evaluated from a removed constraint.

The removed constraint

Short reason why the constraint was removed. This should be the name of method, function or application which remove the constraint.

Arbitrary key-value parameters representing why the constraint was removed. This should be human-readable and can be used for debugging.

The ID of the constraint.

The list of ids of decision variables that are constrained to be one-hot.

One-hot constraint: e.g. `x_1 + ... + x_n = 1` for binary variables `x_1, ..., x_n`.

Lower bound of the decision variable.

Upper bound of the decision variable.

Decision variable ID. - IDs are not required to be sequential.

Kind of the decision variable

Bound of the decision variable If the bound is not specified, the decision variable is considered as unbounded.

Name of the decision variable. e.g. `x`

Subscripts of the decision variable. e.g. `[1, 3]` for an element of multidimensional deicion variable `x[1, 3]`

Additional parameters for decision variables

Detail human-readable description of the decision variable.

The value substituted by partial evaluation of the instance. Not determined by the solver.

Decision variables used in this instance - This must constain every decision variables used in the objective and constraints. - This can contains a decision variable that is not used in the objective or constraints.

Constraints of the optimization problem

The sense of this problem, i.e. minimize the objective or maximize it. Design decision note: - This is a required field. Most mathematical modeling tools allow for an empty sense and default to minimization. Alternatively, some tools do not create such a field and represent maximization problems by negating the objective function. This project prefers explicit descriptions over implicit ones to avoid such ambiguity and to make it unnecessary for developers to look up the reference for the treatment of omitted cases.

Parameters used when instantiating this instance

Constraint hints to be used by solver to gain performance. They are derived from one-or-more constraints in the instance and typically contains information of special types of constraints (e.g. one-hot, SOS, ...).

Constraints removed via preprocessing. These are restored when evaluated into `ommx.v1.Solution`.

When a decision variable is dependent on another decision variable as polynomial, this map contains the ID of the dependent decision variable as key and the polynomial as value.

The application or library name that created this message.

ID for the parameter - IDs are not required to be sequential. - The ID must be unique within the instance including the decision variables.

Name of the parameter. e.g. `x`

Subscripts of the parameter, same usage as DecisionVariable.subscripts

Additional metadata for the parameter, same usage as DecisionVariable.parameters

Human-readable description for the parameter

Decision variables used in this instance

Parameters of this instance - The ID must be unique within the instance including the decision variables.

Objective function of the optimization problem. This may contain parameters in addition to the decision variables.

Constraints of the optimization problem. This may contain parameters in addition to the decision variables.

The sense of this problem, i.e. minimize the objective or maximize it.

Constraint hints to be used by solver to gain performance. They are derived from one-or-more constraints in the instance and typically contains information of special types of constraints (e.g. one-hot, SOS, ...).

Constraints removed via preprocessing. These are restored when evaluated into `ommx.v1.Solution`.

When a decision variable is dependent on another decision variable as polynomial, this map contains the ID of the dependent decision variable as key and the polynomial as value.

Error information by the solver which cannot be expressed by other messages. This string should be human-readable.

Some feasible or infeasible solution for the problem is found. Most of heuristic solvers should use this value.

The solver proved that the problem is infeasible, i.e. all solutions of the problem are infeasible. If the solver cannot get the proof of infeasibility, and just cannot find any feasible solution due to the time limit or due to heuristic algorithm limitation, the solver should return its *best* `Solution` message with `feasible` field set to `false`.

The solver proved that the problem is unbounded.

The feasibility of the solution for all, remaining and removed constraints. The feasibility for the remaining constraints is represented by the `feasible_relaxed` field.

Feasibility of the solution for remaining constraints, ignoring removed constraints. This is optional due to the backward compatibility. If this field is NULL, the `feasible` field represents relaxed feasibility, and the deprecated `feasible_unrelaxed` field represents the feasibility including removed constraints.

Deprecated. [DEPRECATED] Feasibility of the solution for all constraints. This field has been introduced in Python SDK 1.6.0 and deprecated in 1.7.0. The feasibility in this sense is represented by the `feasible` field after 1.7.0.

The optimality of the solution.

Whether the solution is obtained by a relaxed linear programming solver.

The value of the solution for each variable ID.

Feasibility for *both* remaining and removed constraints of each sample. The meaning of `feasible` field in SDK changes between Python SDK 1.6.0 to 1.7.0. In Python SDK 1.6.0, `feasible` represents the feasibility of remaining constraints of each sample, i.e. removed constraints (introduced in 1.6.0) are not considered. After Python SDK 1.7.0, `feasible` represents the feasibility of all constraints of each sample. The feasibility of 1.6.0 is renamed to `feasible_relaxed` in 1.7.0.

Deprecated. [Deprecated] This field has been introduced in Python SDK 1.6.0 to represent the feasibility of all constraints of each sample. The `feasible` field is used in this sense after Python SDK 1.7.0.

Feasibility for remaining (non-removed) constraints of each sample.

Minimize or Maximize

Constraint ID

Name of the constraint.

Integer parameters of the constraint.

Key-value parameters of the constraint.

Detail human-readable description of the constraint.

Short removed reason of the constraint. This field exists only if this message is evaluated from a removed constraint.

Detailed parameters why the constraint is removed. This field exists only if this message is evaluated from a removed constraint.

Evaluated values of constraint for each sample

IDs of decision variables used to evaluate this constraint

Feasibility of each sample

Sampled values of decision variable. This becomes `None` if the decision variable is not sampled.

IDs of the sample

State of the sample

IDs of the sample