package ommx.v1

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Upper and lower bound of the decision variable.

Used in: DecisionVariable

• double lower = 1

  Lower bound of the decision variable.

• double upper = 2

  Upper bound of the decision variable.

Used in: Instance, ParametricInstance, RemovedConstraint

• uint64 id = 1

  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.

• Equality equality = 2

• optional Function function = 3

• repeated int64 subscripts = 8

  Integer parameters of the constraint. Consider for example a problem contains 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]`.

• map<string, string> parameters = 5

  Key-value parameters of the constraint.

• optional string name = 6

  Name of the constraint.

• optional string description = 7

  Detail human-readable description of the constraint.

A constraint hint is an additional inforomation 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, ...).

Used in: Instance, ParametricInstance

• repeated OneHot one_hot_constraints = 2

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

• repeated SOS1 sos1_constraints = 3

  SOS1 constraint: at most one of x_1, ..., x_n can be non-zero.

Decison variable which mathematical programming solver will optimize. It must have its kind, i.e. binary, integer, real or others and unique identifier of 64-bit integer. It may have its name and subscripts which are used to identify in modeling tools.

Used in: Instance, ParametricInstance, SampledDecisionVariable, Solution

• uint64 id = 1

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

• DecisionVariable.Kind kind = 2

  Kind of the decision variable

• optional Bound bound = 3

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

• optional string name = 4

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

• repeated int64 subscripts = 5

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

• map<string, string> parameters = 6

  Additional parameters for decision variables

• optional string description = 7

  Detail human-readable description of the decision variable.

• optional double substituted_value = 8

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

Kind of the decision variable

Used in: DecisionVariable

• KIND_UNSPECIFIED = 0

• KIND_BINARY = 1

• KIND_INTEGER = 2

• KIND_CONTINUOUS = 3

• KIND_SEMI_INTEGER = 4

  Semi-integer decision variable is a decision variable that can take only integer values in the given range or zero.

• KIND_SEMI_CONTINUOUS = 5

  Semi-continuous decision variable is a decision variable that can take only continuous values in the given range or zero.

Equality of a constraint.

Used in: Constraint, EvaluatedConstraint, SampledConstraint

• EQUALITY_UNSPECIFIED = 0

• EQUALITY_EQUAL_TO_ZERO = 1

• EQUALITY_LESS_THAN_OR_EQUAL_TO_ZERO = 2

A constraint evaluated with a state

Used in: Solution

• uint64 id = 1

• Equality equality = 2

• double evaluated_value = 3

  The value of function for the state

• repeated uint64 used_decision_variable_ids = 4

  IDs of decision variables used to evaluate this constraint

• repeated int64 subscripts = 9

  Integer parameters of the constraint.

• map<string, string> parameters = 5

  Key-value parameters of the constraint.

• optional string name = 6

  Name of the constraint.

• optional string description = 7

  Detail human-readable description of the constraint.

• optional double dual_variable = 8

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

• optional string removed_reason = 10

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

• map<string, string> removed_reason_parameters = 11

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

A named function evaluated with a state

Used in: Solution

• uint64 id = 1

• double evaluated_value = 2

• repeated uint64 used_decision_variable_ids = 3

  IDs of decision variables used to evaluate this named function

• repeated int64 subscripts = 4

  Integer parameters of the named function. Consider for example a problem contains a series of named functions `x[i, j] + y[i, j]` for `i = 1, 2, 3` and `j = 4, 5`, then 6 = 3x2 `NamedFunction` 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]`, and the `subscripts` field is intended to be the value of `[i, j]` like `[1, 5]`.

• map<string, string> parameters = 5

  Key-value parameters of the named function.

• optional string name = 6

  Name of the named function.

• optional string description = 7

  Detail human-readable description of the named function.

Real-valued multivariate function used for objective function and constraints.

Used in: Constraint, Instance, NamedFunction, ParametricInstance

• oneof function

  • double constant = 1

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

  • Linear linear = 2

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

  • Quadratic quadratic = 3

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

  • Polynomial polynomial = 4

    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`

The solver proved that the problem is infeasible.

TODO: Add more information about the infeasibility.

Used in: Result

(message has no fields)

• optional Instance.Description description = 1

• repeated DecisionVariable decision_variables = 2

  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.

• optional Function objective = 3

• repeated Constraint constraints = 4

  Constraints of the optimization problem

• Instance.Sense sense = 5

  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.

• optional Parameters parameters = 6

  Parameters used when instantiating this instance

• optional ConstraintHints constraint_hints = 7

  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, ...).

• repeated RemovedConstraint removed_constraints = 8

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

• map<uint64, Function> decision_variable_dependency = 9

  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.

• repeated NamedFunction named_functions = 10

• map<string, string> annotations = 11

  User-defined or third-party extension annotations. OMMX-reserved metadata must use explicit fields such as `description`. Keys in this map must be valid reverse-domain names and must not start with `org.ommx.v1.`.

• uint32 format_version = 100

  Format version of this message for forward compatibility checks. - 0 means the format as of OMMX Python SDK 2.5.1 and earlier. - This is only bumped by semantic-breaking format changes (major-only; no minor/patch). - Each SDK declares a current version; it writes that value and accepts any `<= current`. Data with a higher version fails with an "upgrade the SDK" error. - Non-semantic-breaking additions keep protobuf's standard forward compatibility (unknown fields ignored) and do not bump this.

Used in: Instance, ParametricInstance

• optional string name = 1

• optional string description = 2

• repeated string authors = 3

• optional string created_by = 4

  The application or library name that created this message.

• optional string created = 5

  When this instance was created, encoded as an RFC3339 string.

• optional string license = 6

  SPDX license identifier for this instance or dataset.

• optional string dataset = 7

  Name of the dataset this instance belongs to.

The sense of this instance

Used in: Instance, ParametricInstance, SampleSet, Solution

• SENSE_UNSPECIFIED = 0

• SENSE_MINIMIZE = 1

• SENSE_MAXIMIZE = 2

Used in: Function, Quadratic

• repeated Linear.Term terms = 1

• double constant = 2

Used in: Linear

• uint64 id = 1

• double coefficient = 2

A monomial in a multivariate polynomial.

Used in: Polynomial

• repeated uint64 ids = 1

• double coefficient = 2

Named Function

Used in: Instance, ParametricInstance

• uint64 id = 1

  Named Function ID - Named Function 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 named function `x * 2` with named function ID `1`. - IDs are not required to be sequential. - IDs must be unique with other types of constraints.

• optional Function function = 2

• repeated int64 subscripts = 3

  Integer parameters of the named function. Consider for example a problem contains a series of named functions `x[i, j] + y[i, j]` for `i = 1, 2, 3` and `j = 4, 5`, then 6 = 3x2 `NamedFunction` 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]`, and the `subscripts` field is intended to be the value of `[i, j]` like `[1, 5]`.

• map<string, string> parameters = 4

  Key-value parameters of the named function.

• optional string name = 5

  Name of the named function.

• optional string description = 6

  Detail human-readable description of the named function.

A message representing a one-hot constraint.

Used in: ConstraintHints

• uint64 constraint_id = 1

  The ID of the constraint.

• repeated uint64 decision_variables = 2

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

Used in: Solution

• OPTIMALITY_UNSPECIFIED = 0

  The solver cannot determine whether the solution is optimal. Most of heuristic solvers should use this value.

• OPTIMALITY_OPTIMAL = 1

  The solver has determined that the solution is optimal.

• OPTIMALITY_NOT_OPTIMAL = 2

  The solver has determined that the solution is not optimal.

Placeholder of a parameter in a parametrized optimization problem

Used in: ParametricInstance

• uint64 id = 1

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

• optional string name = 2

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

• repeated int64 subscripts = 3

  Subscripts of the parameter, same usage as DecisionVariable.subscripts

• map<string, string> parameters = 4

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

• optional string description = 5

  Human-readable description for the parameter

A set of parameters for instantiating an optimization problem from a parametric instance

Used in: Instance

• map<uint64, double> entries = 1

Optimization problem including parameter, variables varying while solving the problem like penalty weights or dual variables. These parameters are not decision variables.

• optional Instance.Description description = 1

• repeated DecisionVariable decision_variables = 2

  Decision variables used in this instance

• repeated Parameter parameters = 3

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

• optional Function objective = 4

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

• repeated Constraint constraints = 5

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

• Instance.Sense sense = 6

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

• optional ConstraintHints constraint_hints = 7

  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, ...).

• repeated RemovedConstraint removed_constraints = 8

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

• map<uint64, Function> decision_variable_dependency = 9

  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.

• repeated NamedFunction named_functions = 10

• map<string, string> annotations = 11

  User-defined or third-party extension annotations. OMMX-reserved metadata must use explicit fields such as `description`. Keys in this map must be valid reverse-domain names and must not start with `org.ommx.v1.`.

• uint32 format_version = 100

  Format version of this message for forward compatibility checks. See `Instance.format_version` for semantics.

Multi­variate polynomial

Used in: Function

• repeated Monomial terms = 1

Metadata for an optimization or sampling process that produced a Solution or SampleSet.

Used in: SampleSet, Solution

• optional string instance = 1

  Digest of the corresponding Instance, when this output is stored with one.

• optional string solver = 2

  Solver or sampler information encoded as JSON.

• optional string parameters = 3

  Solver or sampler parameters encoded as JSON.

• optional string start = 4

  Solver or sampler start time encoded as an RFC3339 string.

• optional string end = 5

  Solver or sampler end time encoded as an RFC3339 string.

Quadratic function as a COO-style sparse matrix and linear sparse vector. COOrdinate format, also known as triplet format, is a way to represent sparse matrices as a list of non-zero elements. It consists of three lists: the row indices, the column indices, and the values of the non-zero elements with following constraints: - Entries and coordinates sorted by row, then column. - There are no duplicate entries (i.e. duplicate (i,j) locations) - Data arrays MAY have explicit zeros. Note that this matrix is not assured to be symmetric nor upper triangular. For example, a quadratic function `x1^2 + x2^2 + 2x1*x2` can be represented as: - `{ rows: [0, 0, 1], columns: [0, 1, 1], values: [1, 2, 1] }`, i.e. an upper triangular matrix `[[1, 2], [0, 1]` - `{ rows: [0, 0, 1, 1], columns: [0, 1, 0, 1], values: [1, 1, 1, 1] }`, i.e. a symmetric matrix `[[1, 1], [1, 1]]` or even a non-symmetric, non-trianglar matrix as `x1^2 + 3x1*x2 - x2*x1 + x2^2`: - `{ rows: [0, 0, 1, 1], columns: [0, 1, 0, 1], values: [1, 3, -1, 1] }`, i.e. a non-symmetric matrix `[[1, 3], [-1, 1]]`

Used in: Function

• repeated uint64 rows = 1

• repeated uint64 columns = 2

• repeated double values = 3

• optional Linear linear = 4

Used in: Solution

• RELAXATION_UNSPECIFIED = 0

  No relaxation is used.

• RELAXATION_LP_RELAXED = 1

  The solution is obtained by a relaxed linear programming problem.

Used in: Instance, ParametricInstance

• optional Constraint constraint = 1

  The removed constraint

• string removed_reason = 2

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

• map<string, string> removed_reason_parameters = 3

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

• oneof result

  • string error = 1

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

  • Solution solution = 2

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

  • Infeasible infeasible = 3

    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`.

  • Unbounded unbounded = 4

    The solver proved that the problem is unbounded.

A message representing a [Spcial Ordered Set constraint of Type 1](https://en.wikipedia.org/wiki/Special_ordered_set#Types) (SOS1). SOS1 constraint on non-negative variables x_1, ..., x_n requires that at most one of x_i can be non-zero.

Used in: ConstraintHints

• uint64 binary_constraint_id = 1

  The ID of the SOS1 constraint on binary variables.

• repeated uint64 big_m_constraint_ids = 2

  The IDs of the big-M constraint on non-binary variables.

• repeated uint64 decision_variables = 3

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

Output of the sampling process.

• optional SampledValues objectives = 1

• repeated SampledDecisionVariable decision_variables = 2

• repeated SampledConstraint constraints = 3

• repeated SampledNamedFunction named_functions = 8

• map<uint64, bool> feasible = 4

  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.

• map<uint64, bool> feasible_unrelaxed = 6

  [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.

• map<uint64, bool> feasible_relaxed = 7

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

• Instance.Sense sense = 5

  Minimize or Maximize

• optional ProcessMetadata metadata = 9

  OMMX-defined provenance metadata for this SampleSet.

• map<string, string> annotations = 10

  User-defined or third-party extension annotations. OMMX-reserved metadata must use explicit fields such as `metadata`. Keys in this map must be valid reverse-domain names and must not start with `org.ommx.v1.`.

• uint32 format_version = 100

  Format version of this message for forward compatibility checks. See `Instance.format_version` for semantics.

Evaluated constraint for samples

Used in: SampleSet

• uint64 id = 1

  Constraint ID

• Equality equality = 2

• optional string name = 3

  Name of the constraint.

• repeated int64 subscripts = 4

  Integer parameters of the constraint.

• map<string, string> parameters = 5

  Key-value parameters of the constraint.

• optional string description = 6

  Detail human-readable description of the constraint.

• optional string removed_reason = 7

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

• map<string, string> removed_reason_parameters = 8

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

• optional SampledValues evaluated_values = 9

  Evaluated values of constraint for each sample

• repeated uint64 used_decision_variable_ids = 10

  IDs of decision variables used to evaluate this constraint

• map<uint64, bool> feasible = 11

  Feasibility of each sample

A pair of decision variable description and its sampled values

Used in: SampleSet

• optional DecisionVariable decision_variable = 1

• optional SampledValues samples = 2

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

Evaluated named function for samples

Used in: SampleSet

• uint64 id = 1

  Named Function ID

• optional string name = 2

  Name of the named function.

• repeated int64 subscripts = 3

  Integer parameters of the named function.

• map<string, string> parameters = 4

  Key-value parameters of the named function.

• optional string description = 5

  Detail human-readable description of the named function.

• optional SampledValues evaluated_values = 6

  Evaluated values of the named function for each sample

• repeated uint64 used_decision_variable_ids = 7

  IDs of decision variables used to evaluate this constraint

A map from sample IDs to sampled values

Used in: SampleSet, SampledConstraint, SampledDecisionVariable, SampledNamedFunction

• repeated SampledValues.SampledValuesEntry entries = 1

Compressed sampled values, but uncompressed state is also valid. The reader should not assume that every states are distinct.

Used in: SampledValues

• double value = 1

• repeated uint64 ids = 2

  IDs of the sample

A map from sample ID to state

• repeated Samples.SamplesEntry entries = 1

Sampling processes are likely to generate same samples multiple times. We compress the same samples into one entry. Note that uncompressed state is also valid. The reader should not assume that every states are distinct.

Used in: Samples

• optional State state = 1

  State of the sample

• repeated uint64 ids = 2

  IDs of the sample

Solution with evaluated objective and constraints

Used in: Result

• optional State state = 1

• double objective = 2

• repeated DecisionVariable decision_variables = 3

• repeated EvaluatedConstraint evaluated_constraints = 4

• repeated EvaluatedNamedFunction evaluated_named_functions = 11

• bool feasible = 5

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

• optional bool feasible_relaxed = 9

  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.

• bool feasible_unrelaxed = 8

  [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.

• Optimality optimality = 6

  The optimality of the solution.

• Relaxation relaxation = 7

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

• Instance.Sense sense = 10

  Whether the problem is a minimization or maximization problem.

• optional ProcessMetadata metadata = 12

  OMMX-defined provenance metadata for this Solution.

• map<string, string> annotations = 13

  User-defined or third-party extension annotations. OMMX-reserved metadata must use explicit fields such as `metadata`. Keys in this map must be valid reverse-domain names and must not start with `org.ommx.v1.`.

• uint32 format_version = 100

  Format version of this message for forward compatibility checks. See `Instance.format_version` for semantics.

A set of values of decision variables, without any evaluation, even the feasiblity of the solution.

Used in: Samples.SamplesEntry, Solution

• map<uint64, double> entries = 1

  The value of the solution for each variable ID.

The solver proved that the problem is unbounded.

TODO: Add more information about the unboundedness.

Used in: Result

(message has no fields)