ortools-clone/ortools/linear_solver/linear_solver.proto

// Copyright 2010-2018 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// 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.

// Linear Programming Protocol Buffers.
//
// The protocol buffers below make it possible to store and transfer the
// representation of Linear and Mixed-Integer Programs.
//
// A Linear Program (LP) is a mathematical optimization model with a linear
// objective function, and linear equality and inequality constraints.
// The goal is to achieve the best outcome (such as maximum profit or lowest
// cost) by modeling the real-world problem at hand using linear functions.
// In a Mixed Integer Program (MIP), some variables may also be constrained to
// take integer values.
//
// Check ./linear_solver.h and Wikipedia for more detail:
//   http://en.wikipedia.org/wiki/Linear_programming
//

syntax = "proto2";

option java_package = "com.google.ortools.linearsolver";
option java_multiple_files = true;

// import "google/protobuf/wrappers.proto";
import "ortools/util/optional_boolean.proto";

package operations_research;

// A variable is always constrained in the form:
//    lower_bound <= x <= upper_bound
// where lower_bound and upper_bound:
// - Can form a singleton: x = constant = lower_bound = upper_bound.
// - Can form a finite interval: lower_bound <= x <= upper_bound. (x is boxed.)
// - Can form a semi-infinite interval.
//     - lower_bound = -infinity: x <= upper_bound.
//     - upper_bound = +infinity: x >= lower_bound.
// - Can form the infinite interval: lower_bound = -infinity and
//   upper_bound = +infinity, x is free.
// MPVariableProto furthermore stores:
//  - The coefficient of the variable in the objective.
//  - Whether the variable is integer.
message MPVariableProto {
  // lower_bound must be <= upper_bound.
  optional double lower_bound = 1 [default = -inf];
  optional double upper_bound = 2 [default = inf];

  // The coefficient of the variable in the objective. Must be finite.
  optional double objective_coefficient = 3 [default = 0.0];

  // True if the variable is constrained to be integer.
  // Ignored if MPModelProto::solver_type is *LINEAR_PROGRAMMING*.
  optional bool is_integer = 4 [default = false];

  // The name of the variable.
  optional string name = 5 [default = ""];

  optional int32 branching_priority = 6 [default = 0];
}

// A linear constraint is always of the form:
// lower_bound <= sum of linear term elements <= upper_bound,
// where lower_bound and upper_bound:
// - Can form a singleton: lower_bound == upper_bound. The constraint is an
//   equation.
// - Can form a finite interval [lower_bound, upper_bound]. The constraint is
//   both lower- and upper-bounded, i.e. "boxed".
// - Can form a semi-infinite interval. lower_bound = -infinity: the constraint
//   is upper-bounded. upper_bound = +infinity: the constraint is lower-bounded.
// - Can form the infinite interval: lower_bound = -infinity and
//   upper_bound = +infinity. The constraint is free.
message MPConstraintProto {
  // var_index[i] is the variable index (w.r.t. to "variable" field of
  // MPModelProto) of the i-th linear term involved in this constraint, and
  // coefficient[i] is its coefficient. Only the terms with non-zero
  // coefficients need to appear. var_index may not contain duplicates.
  repeated int32 var_index = 6 [packed = true];
  repeated double coefficient = 7 [packed = true];  // Must be finite.

  // lower_bound must be <= upper_bound.
  optional double lower_bound = 2 [default = -inf];
  optional double upper_bound = 3 [default = inf];

  // The name of the constraint.
  optional string name = 4 [default = ""];

  // [Advanced usage: do not use this if you don't know what you're doing.]
  // A lazy constraint is handled differently by the core solving engine, but
  // it does not change the result. It may or may not impact the performance.
  // For more info see: http://tinyurl.com/lazy-constraints.
  optional bool is_lazy = 5 [default = false];
}

// General constraints. See each individual proto type for more information.
message MPGeneralConstraintProto {
  // The name of the constraint.
  optional string name = 1 [default = ""];

  oneof general_constraint {
    MPIndicatorConstraint indicator_constraint = 2;
    MPSosConstraint sos_constraint = 3;
    MPQuadraticConstraint quadratic_constraint = 4;
    MPAbsConstraint abs_constraint = 5;
    // All variables in "and" constraints must be Boolean.
    // resultant_var = and(var_1, var_2... var_n)
    MPArrayConstraint and_constraint = 6;
    // All variables in "or" constraints must be Boolean.
    // resultant_var = or(var_1, var_2... var_n)
    MPArrayConstraint or_constraint = 7;
    // resultant_var = min(var_1, var_2, ..., constant)
    MPArrayWithConstantConstraint min_constraint = 8;
    // resultant_var = max(var_1, var_2, ..., constant)
    MPArrayWithConstantConstraint max_constraint = 9;
  }
}

// Indicator constraints encode the activation or deactivation of linear
// constraints given the value of one Boolean variable in the model. For
// example:
//     y = 0 => 2 * x1 + 3 * x2 >= 42
// The 2 * x1 + 3 * x2 >= 42 constraint is only active if the variable y is
// equal to 0.
// As of 2019/04, only SCIP, CP-SAT and Gurobi support this constraint type.
message MPIndicatorConstraint {
  // Variable index (w.r.t. the "variable" field of MPModelProto) of the Boolean
  // variable used as indicator.
  optional int32 var_index = 1;

  // Value the above variable should take. Must be 0 or 1.
  optional int32 var_value = 2;

  // The constraint activated by the indicator variable.
  optional MPConstraintProto constraint = 3;
}

// Special Ordered Set (SOS) constraints of type 1 or 2.
// See https://en.wikipedia.org/wiki/Special_ordered_set
// As of 2019/04, only SCIP and Gurobi support this constraint type.
message MPSosConstraint {
  enum Type {
    // At most one variable in `var_index` must be non-zero.
    SOS1_DEFAULT = 0;
    // At most two consecutive variables from `var_index` can be non-zero (i.e.
    // for some i, var_index[i] and var_index[i+1]). See
    // http://www.eudoxus.com/lp-training/5/5-6-special-ordered-sets-of-type-2
    SOS2 = 1;
  }
  optional Type type = 1 [default = SOS1_DEFAULT];

  // Variable index (w.r.t. the "variable" field of MPModelProto) of the
  // variables in the SOS.
  repeated int32 var_index = 2;

  // Optional: SOS weights. If non-empty, must be of the same size as
  // "var_index", and strictly increasing. If empty and required by the
  // underlying solver, the 1..n sequence will be given as weights.
  // SUBTLE: The weights can help the solver make branch-and-bound decisions
  // that fit the underlying optimization model: after each LP relaxation, it
  // will compute the "average weight" of the SOS variables, weighted by value
  // (this is confusing: here we're using the values as weights), and the binary
  // branch decision will be: is the non-zero variable above or below that?
  // (weights are strictly monotonous, so the "cutoff" average weight
  // corresponds to a "cutoff" index in the var_index sequence).
  repeated double weight = 3;
}

// Quadratic constraints of the form lb <= sum a_i x_i + sum b_ij x_i x_j <= ub,
// where a, b, lb and ub are constants, and x are the model's variables.
// Quadratic matrices that are Positive Semi-Definite, Second-Order Cones or
// rotated Second-Order Cones are always accepted. Other forms may or may not be
// accepted depending on the underlying solver used.
// See https://scip.zib.de/doc/html/cons__quadratic_8h.php and
// https://www.gurobi.com/documentation/8.1/refman/constraints.html#subsubsection:QuadraticConstraints
message MPQuadraticConstraint {
  // Sparse representation of linear terms in the quadratic constraint, where
  // term i is var_index[i] * coefficient[i].
  // `var_index` are variable indices w.r.t the "variable" field in
  // MPModelProto.
  repeated int32 var_index = 1;
  repeated double coefficient = 2;  // Must be finite.

  // Sparse representation of quadratic terms in the quadratic constraint, where
  // term i is qvar1_index[i] * qvar2_index[i] * qcoefficient[i].
  // `qvar1_index` and `qvar2_index` are variable indices w.r.t the "variable"
  // field in MPModelProto.
  // `qvar1_index`, `qvar2_index` and `coefficients` must have the same size.
  // If the same unordered pair (qvar1_index, qvar2_index) appears several
  // times, the sum of all of the associated coefficients will be applied.
  repeated int32 qvar1_index = 3;
  repeated int32 qvar2_index = 4;
  repeated double qcoefficient = 5;  // Must be finite.

  // lower_bound must be <= upper_bound.
  optional double lower_bound = 6 [default = -inf];
  optional double upper_bound = 7 [default = inf];
}

// Sets a variable's value to the absolute value of another variable.
message MPAbsConstraint {
  // Variable indices are relative to the "variable" field in MPModelProto.
  // resultant_var = abs(var)
  optional int32 var_index = 1;
  optional int32 resultant_var_index = 2;
}

// Sets a variable's value equal to a function on a set of variables.
message MPArrayConstraint {
  // Variable indices are relative to the "variable" field in MPModelProto.
  repeated int32 var_index = 1;
  optional int32 resultant_var_index = 2;
}

// Sets a variable's value equal to a function on a set of variables and,
// optionally, a constant.
message MPArrayWithConstantConstraint {
  // Variable indices are relative to the "variable" field in MPModelProto.
  // resultant_var = f(var_1, var_2, ..., constant)
  repeated int32 var_index = 1;
  optional double constant = 2;
  optional int32 resultant_var_index = 3;
}

// Quadratic part of a model's objective. Added with other objectives (such as
// linear), this creates the model's objective function to be optimized.
// Note: the linear part of the objective currently needs to be specified in the
// MPVariableProto.objective_coefficient fields. If you'd rather have a
// dedicated linear array here, talk to or-core-team@
message MPQuadraticObjective {
  // Sparse representation of quadratic terms in the objective function, where
  // term i is qvar1_index[i] * qvar2_index[i] * coefficient[i].
  // `qvar1_index` and `qvar2_index` are variable indices w.r.t the "variable"
  // field in MPModelProto.
  // `qvar1_index`, `qvar2_index` and `coefficients` must have the same size.
  // If the same unordered pair (qvar1_index, qvar2_index) appears several
  // times, the sum of all of the associated coefficients will be applied.
  repeated int32 qvar1_index = 1;
  repeated int32 qvar2_index = 2;
  repeated double coefficient = 3;  // Must be finite.
}

// This message encodes a partial (or full) assignment of the variables of a
// MPModelProto problem. The indices in var_index should be unique and valid
// variable indices of the associated problem.
message PartialVariableAssignment {
  repeated int32 var_index = 1 [packed = true];
  repeated double var_value = 2 [packed = true];
}

// MPModelProto contains all the information for a Linear Programming model.
message MPModelProto {
  // All the variables appearing in the model.
  repeated MPVariableProto variable = 3;

  // All the constraints appearing in the model.
  repeated MPConstraintProto constraint = 4;

  // All the general constraints appearing in the model. Note that not all
  // solvers support all types of general constraints.
  repeated MPGeneralConstraintProto general_constraint = 7;

  // True if the problem is a maximization problem. Minimize by default.
  optional bool maximize = 1 [default = false];

  // Offset for the objective function. Must be finite.
  optional double objective_offset = 2 [default = 0.0];

  // Optionally, a quadratic objective.
  // As of 2019/06, only SCIP and Gurobi support quadratic objectives.
  optional MPQuadraticObjective quadratic_objective = 8;

  // Name of the model.
  optional string name = 5 [default = ""];

  // Solution hint.
  //
  // If a feasible or almost-feasible solution to the problem is already known,
  // it may be helpful to pass it to the solver so that it can be used. A solver
  // that supports this feature will try to use this information to create its
  // initial feasible solution.
  //
  // Note that it may not always be faster to give a hint like this to the
  // solver. There is also no guarantee that the solver will use this hint or
  // try to return a solution "close" to this assignment in case of multiple
  // optimal solutions.
  optional PartialVariableAssignment solution_hint = 6;
}

// To support 'unspecified' double value in proto3, the simplest is to wrap
// any double value in a nested message (has_XXX works for message fields).
// We don't use google/protobuf/wrappers.proto because depending on it makes
// the following android integration test fail:
// http://sponge/c4bce1fd-41bd-4d0b-b4ca-fc04d4d64621
message OptionalDouble {
  optional double value = 1;
}

// MPSolverCommonParameters holds advanced usage parameters that apply to any of
// the solvers we support.
// All of the fields in this proto can have a value of unspecified. In this
// case each inner solver will use their own safe defaults.
// Some values won't be supported by some solvers. The behavior in that case is
// not defined yet.
message MPSolverCommonParameters {
  // The solver stops if the relative MIP gap reaches this value or below.
  // The relative MIP gap is an upper bound of the relative distance to the
  // optimum, and it is defined as:
  //
  //   abs(best_bound - incumbent) / abs(incumbent) [Gurobi]
  //   abs(best_bound - incumbent) / min(abs(best_bound), abs(incumbent)) [SCIP]
  //
  // where "incumbent" is the objective value of the best solution found so far
  // (i.e., lowest when minimizing, highest when maximizing), and "best_bound"
  // is the tightest bound of the objective determined so far (i.e., highest
  // when minimizing, and lowest when maximizing). The MIP Gap is sensitive to
  // objective offset. If the denominator is 0 the MIP Gap is INFINITY for SCIP
  // and Gurobi. Of note, "incumbent" and "best bound" are called "primal bound"
  // and "dual bound" in SCIP, respectively.
  // Ask or-core-team@ for other solvers.
  optional OptionalDouble relative_mip_gap = 1;

  // Tolerance for primal feasibility of basic solutions: this is the maximum
  // allowed error in constraint satisfiability.
  // For SCIP this includes integrality constraints. For Gurobi it does not, you
  // need to set the custom parameter IntFeasTol.
  optional OptionalDouble primal_tolerance = 2;

  // Tolerance for dual feasibility.
  // For SCIP and Gurobi this is the feasibility tolerance for reduced costs in
  // LP solution: reduced costs must all be smaller than this value in the
  // improving direction in order for a model to be declared optimal.
  // Not supported for other solvers.
  optional OptionalDouble dual_tolerance = 3;

  enum LPAlgorithmValues {
    LP_ALGO_UNSPECIFIED = 0;
    LP_ALGO_DUAL = 1;     // Dual simplex.
    LP_ALGO_PRIMAL = 2;   // Primal simplex.
    LP_ALGO_BARRIER = 3;  // Barrier algorithm.
  }

  // Algorithm to solve linear programs.
  // Ask or-core-team@ if you want to know what this does exactly.
  optional LPAlgorithmValues lp_algorithm = 4 [default = LP_ALGO_UNSPECIFIED];

  // Gurobi and SCIP enable presolve by default.
  // Ask or-core-team@ for other solvers.
  optional OptionalBoolean presolve = 5 [default = BOOL_UNSPECIFIED];

  // Enable automatic scaling of matrix coefficients and objective. Available
  // for Gurobi and GLOP.
  // Ask or-core-team@ if you want more details.
  optional OptionalBoolean scaling = 7 [default = BOOL_UNSPECIFIED];
}

// Encodes a full MPModelProto by way of referencing to a "baseline"
// MPModelProto stored in a file, and a "delta" to apply to this model.
message MPModelDeltaProto {
  optional /*required*/ string baseline_model_file_path = 1;

  // The variable protos listed here will override (via MergeFrom()) the ones
  // in the baseline model: you only need to specify the fields that change.
  // To add a new variable, add it with a new variable index (variable indices
  // still need to span a dense integer interval).
  // You can't "delete" a variable but you can "neutralize" it by fixing its
  // value, setting its objective coefficient to zero, and by nullifying all
  // the terms involving it in the constraints.
  map<int32, MPVariableProto> variable_overrides = 2;

  // Constraints can be changed (or added) in the same way as variables, see
  // above. It's mostly like applying MergeFrom(), except that:
  // - the "var_index" and "coefficient" fields will be overridden like a map:
  //   if a key pre-exists, we overwrite its value, otherwise we add it.
  // - if you set the lower bound to -inf and the upper bound to +inf, thus
  //   effectively neutralizing the constraint, the solver will implicitly
  //   remove all of the constraint's terms.
  map<int32, MPConstraintProto> constraint_overrides = 3;

  // NOTE(user): We may also add more deltas, eg. objective offset.
}

// Next id: 9.
message MPModelRequest {
  // The model to be optimized by the server.
  optional MPModelProto model = 1;

  // The solver type, which will select a specific implementation, and will also
  // impact the interpretation of the model (i.e. are we solving the problem
  // as a mixed integer program or are we relaxing it as a continuous linear
  // program?).
  // This must remain consistent with MPSolver::OptimizationProblemType.
  enum SolverType {
    GLOP_LINEAR_PROGRAMMING = 2;  // Recommended default for LP models.
    CLP_LINEAR_PROGRAMMING = 0;
    GLPK_LINEAR_PROGRAMMING = 1;
    GUROBI_LINEAR_PROGRAMMING = 6;    // Commercial, needs a valid license.
    XPRESS_LINEAR_PROGRAMMING = 101;  // Commercial, needs a valid license.
    CPLEX_LINEAR_PROGRAMMING = 10;  // Commercial, needs a valid
    // license.

    SCIP_MIXED_INTEGER_PROGRAMMING = 3;  // Recommended default for MIP models.
    GLPK_MIXED_INTEGER_PROGRAMMING = 4;
    CBC_MIXED_INTEGER_PROGRAMMING = 5;
    GUROBI_MIXED_INTEGER_PROGRAMMING = 7;  // Commercial, needs a valid license.
    XPRESS_MIXED_INTEGER_PROGRAMMING =
        102;  // Commercial, needs a valid license.
    CPLEX_MIXED_INTEGER_PROGRAMMING = 11;  // Commercial, needs a
    // valid license.
    BOP_INTEGER_PROGRAMMING = 12;

    // WARNING: This solver will currently interpret all variables as integer,
    // so any solution you get will be valid, but the optimal might be far away
    // for the real one (when you authorise non-integer value for continuous
    // variables).
    SAT_INTEGER_PROGRAMMING = 14;

    KNAPSACK_MIXED_INTEGER_PROGRAMMING = 13;
  }
  optional SolverType solver_type = 2;

  // Maximum time to be spent by the solver to solve 'model'. If the server is
  // busy and the RPC's deadline_left is less than this, it will immediately
  // give up and return an error, without even trying to solve.
  //
  // The client can use this to have a guarantee on how much time the
  // solver will spend on the problem (unless it finds and proves
  // an optimal solution more quickly).
  //
  // If not specified, the time limit on the solver is the RPC's deadline_left.
  optional double solver_time_limit_seconds = 3;

  // If this is set, then EnableOutput() will be set on the internal MPSolver
  // that solves the model.
  // WARNING: if you set this on a request to prod servers, it will be rejected
  // and yield the RPC Application Error code MPSOLVER_SOLVER_TYPE_UNAVAILABLE.
  optional bool enable_internal_solver_output = 4 [default = false];

  // Advanced usage. Solver-specific parameters in the solver's own format,
  // different for each solver. For example, if you use SCIP and you want to
  // stop the solve earlier than the time limit if it reached a solution that is
  // at most 1% away from the optimal, you can set this to "limits/gap=0.01".
  //
  // Note however that there is no "security" mechanism in place so it is up to
  // the client to make sure that the given options don't make the solve
  // non thread safe or use up too much memory for instance.
  //
  // If the option format is not understood by the solver, the request will be
  // rejected and yield an RPC Application error with code
  // MPSOLVER_MODEL_INVALID_SOLVER_PARAMETERS.
  optional string solver_specific_parameters = 5;


  // Advanced usage: model "delta". If used, "model" must be unset. See the
  // definition of MPModelDeltaProto.
  optional MPModelDeltaProto model_delta = 8;

}

// Status returned by the solver. They follow a hierarchical nomenclature, to
// allow us to add more enum values in the future. Clients should use
// InCategory() to match these enums, with the following C++ pseudo-code:
//
// bool InCategory(MPSolverResponseStatus status, MPSolverResponseStatus cat) {
//   if (cat == MPSOLVER_OPTIMAL) return status == MPSOLVER_OPTIMAL;
//   while (status > cat) status >>= 4;
//   return status == cat;
// }
enum MPSolverResponseStatus {
  // Normal responses -- the model was valid, and the solver ran.
  // These statuses should be "somewhat" repeatable, modulo the fact that the
  // solver's time limit makes it undeterministic, and could change a FEASIBLE
  // model to an OPTIMAL and vice-versa (the others, except NOT_SOLVED, should
  // normally be deterministic). Also, the solver libraries can be buggy.

  // The solver found the proven optimal solution. This is what should be
  // returned in most cases.
  //
  // WARNING: for historical reason, the value is zero, which means that this
  // value can't have any subcategories.
  MPSOLVER_OPTIMAL = 0x0;

  // The solver had enough time to find some solution that satisfies all
  // constraints, but it did not prove optimality (which means it may or may
  // not have reached the optimal).
  //
  // This can happen for large LP models (Linear Programming), and is a frequent
  // response for time-limited MIPs (Mixed Integer Programming). In the MIP
  // case, the difference between the solution 'objective_value' and
  // 'best_objective_bound' fields of the MPSolutionResponse will give an
  // indication of how far this solution is from the optimal one.
  MPSOLVER_FEASIBLE = 0x1;

  // The model does not have any solution, according to the solver (which
  // "proved" it, with the caveat that numerical proofs aren't actual proofs),
  // or based on trivial considerations (eg. a variable whose lower bound is
  // strictly greater than its upper bound).
  MPSOLVER_INFEASIBLE = 0x2;

  // There exist solutions that make the magnitude of the objective value
  // as large as wanted (i.e. -infinity (resp. +infinity) for a minimization
  // (resp. maximization) problem.
  MPSOLVER_UNBOUNDED = 0x3;

  // An error (most probably numerical) occurred.
  // One likely cause for such errors is a large numerical range among variable
  // coefficients (eg. 1e-16, 1e20), in which case one should try to shrink it.
  MPSOLVER_ABNORMAL = 0x4;

  // The solver did not have a chance to diagnose the model in one of the
  // categories above.
  MPSOLVER_NOT_SOLVED = 0x6;
  // Like "NOT_SOLVED", but typically used by model validation functions
  // returning a "model status", to enhance readability of the client code.
  MPSOLVER_MODEL_IS_VALID = 0x61;
  // Special value: the solver status could not be properly translated and is
  // unknown.
  MPSOLVER_UNKNOWN_STATUS = 0x63;

  // Model errors. These are always deterministic and repeatable.
  // They should be accompanied with a string description of the error.
  MPSOLVER_MODEL_INVALID = 0x5;
  // Something is wrong with the fields "solution_hint_var_index" and/or
  // "solution_hint_var_value".
  MPSOLVER_MODEL_INVALID_SOLUTION_HINT = 0x54;
  // Something is wrong with the solver_specific_parameters request field.
  MPSOLVER_MODEL_INVALID_SOLVER_PARAMETERS = 0x55;

  // Implementation error: the requested solver implementation is not
  // available (see MPModelRequest.solver_type).
  // The linear solver binary was probably not linked with the required library,
  // eg //ortools/linear_solver:linear_solver_scip for SCIP.
  MPSOLVER_SOLVER_TYPE_UNAVAILABLE = 0x7;

}

message MPSolutionResponse {
  // Result of the optimization.
  optional /*required*/ MPSolverResponseStatus status = 1
      [default = MPSOLVER_UNKNOWN_STATUS];

  // Human-readable string giving more details about the status. For example,
  // when the status is MPSOLVER_INVALID_MODE, this can hold a description of
  // why the model is invalid.
  // This isn't always filled: don't depend on its value or even its presence.
  optional string status_str = 7;

  // Objective value corresponding to the "variable_value" below, taking into
  // account the source "objective_offset" and "objective_coefficient".
  // This is set iff 'status' is OPTIMAL or FEASIBLE.
  optional double objective_value = 2;

  // This field is only filled for MIP problems. For a minimization problem,
  // this is a lower bound on the optimal objective value. For a maximization
  // problem, it is an upper bound. It is only filled if the status is OPTIMAL
  // or FEASIBLE. In the former case, best_objective_bound should be equal to
  // objective_value (modulo numerical errors).
  optional double best_objective_bound = 5;

  // Variable values in the same order as the MPModelProto::variable field.
  // This is a dense representation. These are set iff 'status' is OPTIMAL or
  // FEASIBLE.
  repeated double variable_value = 3 [packed = true];

  // [Advanced usage.]
  // Values of the dual variables values in the same order as the
  // MPModelProto::constraint field. This is a dense representation.
  // These are not set if the problem was solved with a MIP solver (even if
  // it is actually a linear program).
  // These are set iff 'status' is OPTIMAL or FEASIBLE.
  repeated double dual_value = 4 [packed = true];

  // [Advanced usage.]
  // Values of the reduced cost of the variables in the same order as the
  // MPModelProto::variable. This is a dense representation.
  // These are not set if the problem was solved with a MIP solver (even if it
  // is actually a linear program).
  // These are set iff 'status' is OPTIMAL or FEASIBLE.
  repeated double reduced_cost = 6 [packed = true];
}