ortools-clone/ortools/service/v1/mathopt/model.proto

// Copyright 2010-2025 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.

// An encoding format for mathematical optimization problems.

syntax = "proto3";

package operations_research.service.v1.mathopt;

import "ortools/service/v1/mathopt/sparse_containers.proto";

option java_multiple_files = true;
option java_package = "com.google.ortools.service.v1.mathopt";

option csharp_namespace = "Google.OrTools.Service";

// As used below, we define "#variables" = size(VariablesProto.ids).
message VariablesProto {
  // Must be nonnegative and strictly increasing. The max(int64) value can't be
  // used.
  repeated int64 ids = 1;

  // Should have length equal to #variables, values in [-inf, inf).
  repeated double lower_bounds = 2;

  // Should have length equal to #variables, values in (-inf, inf].
  repeated double upper_bounds = 3;

  // Should have length equal to #variables. Value is false for continuous
  // variables and true for integer variables.
  repeated bool integers = 4;

  // If not set, assumed to be all empty strings. Otherwise, should have length
  // equal to #variables.
  //
  // All nonempty names must be distinct. TODO(b/169575522): we may relax this.
  repeated string names = 5;
}

message ObjectiveProto {
  // false is minimize, true is maximize
  bool maximize = 1;

  // Must be finite and not NaN.
  double offset = 2;

  // ObjectiveProto terms that are linear in the decision variables.
  //
  // Requirements:
  //  * linear_coefficients.ids are elements of VariablesProto.ids.
  //  * VariablesProto not specified correspond to zero.
  //  * linear_coefficients.values must all be finite.
  //  * linear_coefficients.values can be zero, but this just wastes space.
  SparseDoubleVectorProto linear_coefficients = 3;

  // Objective terms that are quadratic in the decision variables.
  //
  // Requirements in addition to those on SparseDoubleMatrixProto messages:
  //  * Each element of quadratic_coefficients.row_ids and each element of
  //    quadratic_coefficients.column_ids must be an element of
  //    VariablesProto.ids.
  //  * The matrix must be upper triangular: for each i,
  //    quadratic_coefficients.row_ids[i] <=
  //    quadratic_coefficients.column_ids[i].
  //
  // Notes:
  //  * Terms not explicitly stored have zero coefficient.
  //  * Elements of quadratic_coefficients.coefficients can be zero, but this
  //    just wastes space.
  SparseDoubleMatrixProto quadratic_coefficients = 4;

  // Parent messages may have uniqueness requirements on this field; e.g., see
  // ModelProto.objectives and AuxiliaryObjectivesUpdatesProto.new_objectives.
  string name = 5;

  // For multi-objective problems, the priority of this objective relative to
  // the others (lower is more important). This value must be nonnegative.
  // Furthermore, each objective priority in the model must be distinct at solve
  // time. This condition is not validated at the proto level, so models may
  // temporarily have objectives with the same priority.
  int64 priority = 6;
}

// As used below, we define "#linear constraints" =
// size(LinearConstraintsProto.ids).
message LinearConstraintsProto {
  // Must be nonnegative and strictly increasing. The max(int64) value can't be
  // used.
  repeated int64 ids = 1;

  // Should have length equal to #linear constraints, values in [-inf, inf).
  repeated double lower_bounds = 2;

  // Should have length equal to #linear constraints, values in (-inf, inf].
  repeated double upper_bounds = 3;

  // If not set, assumed to be all empty strings. Otherwise, should have length
  // equal to #linear constraints.
  //
  // All nonempty names must be distinct. TODO(b/169575522): we may relax this.
  repeated string names = 4;
}

// A single quadratic constraint of the form:
//    lb <= sum{linear_terms} + sum{quadratic_terms} <= ub.
//
// If a variable involved in this constraint is deleted, it is treated as if it
// were set to zero.
message QuadraticConstraintProto {
  // Terms that are linear in the decision variables.
  //
  // In addition to requirements on SparseDoubleVectorProto messages we require
  // that:
  //  * linear_terms.ids are elements of VariablesProto.ids.
  //  * linear_terms.values must all be finite and not-NaN.
  //
  // Notes:
  //  * Variable ids omitted have a corresponding coefficient of zero.
  //  * linear_terms.values can be zero, but this just wastes space.
  SparseDoubleVectorProto linear_terms = 1;

  // Terms that are quadratic in the decision variables.
  //
  // In addition to requirements on SparseDoubleMatrixProto messages we require
  // that:
  //  * Each element of quadratic_terms.row_ids and each element of
  //    quadratic_terms.column_ids must be an element of VariablesProto.ids.
  //  * The matrix must be upper triangular: for each i,
  //    quadratic_terms.row_ids[i] <= quadratic_terms.column_ids[i].
  //
  // Notes:
  //  * Terms not explicitly stored have zero coefficient.
  //  * Elements of quadratic_terms.coefficients can be zero, but this just
  //    wastes space.
  SparseDoubleMatrixProto quadratic_terms = 2;

  // Must have value in [-inf, inf), and be less than or equal to `upper_bound`.
  double lower_bound = 3;

  // Must have value in (-inf, inf], and be greater than or equal to
  // `lower_bound`.
  double upper_bound = 4;

  // Parent messages may have uniqueness requirements on this field; e.g., see
  // ModelProto.quadratic_constraints and
  // QuadraticConstraintUpdatesProto.new_constraints.
  string name = 5;
}

// A single second-order cone constraint of the form:
//
//    ||`arguments_to_norm`||_2 <= `upper_bound`,
//
// where `upper_bound` and each element of `arguments_to_norm` are linear
// expressions.
//
// If a variable involved in this constraint is deleted, it is treated as if it
// were set to zero.
message SecondOrderConeConstraintProto {
  LinearExpressionProto upper_bound = 1;
  repeated LinearExpressionProto arguments_to_norm = 2;

  // Parent messages may have uniqueness requirements on this field; e.g., see
  // `ModelProto.second_order_cone_constraints` and
  // `SecondOrderConeConstraintUpdatesProto.new_constraints`.
  string name = 3;
}

// Data for representing a single SOS1 or SOS2 constraint.
//
// If a variable involved in this constraint is deleted, it is treated as if it
// were set to zero.
message SosConstraintProto {
  // The expressions over which to apply the SOS constraint:
  //   * SOS1: At most one element takes a nonzero value.
  //   * SOS2: At most two elements take nonzero values, and they must be
  //           adjacent in the repeated ordering.
  repeated LinearExpressionProto expressions = 1;

  // Either empty or of equal length to expressions. If empty, default weights
  // are 1, 2, ...
  // If present, the entries must be unique.
  repeated double weights = 2;

  // Parent messages may have uniqueness requirements on this field; e.g., see
  // ModelProto.sos1_constraints and SosConstraintUpdatesProto.new_constraints.
  string name = 3;
}

// Data for representing a single indicator constraint of the form:
//    Variable(indicator_id) = (activate_on_zero ? 0 : 1) ⇒
//    lower_bound <= expression <= upper_bound.
//
// If a variable involved in this constraint (either the indicator, or appearing
// in `expression`) is deleted, it is treated as if it were set to zero. In
// particular, deleting the indicator variable means that the indicator
// constraint is vacuous if `activate_on_zero` is false, and that it is
// equivalent to a linear constraint if `activate_on_zero` is true.
message IndicatorConstraintProto {
  // An ID corresponding to a binary variable, or unset. If unset, the indicator
  // constraint is ignored. If set, we require that:
  //   * VariablesProto.integers[indicator_id] = true,
  //   * VariablesProto.lower_bounds[indicator_id] >= 0,
  //   * VariablesProto.upper_bounds[indicator_id] <= 1.
  // These conditions are not validated by MathOpt, but if not satisfied will
  // lead to the solver returning an error upon solving.
  optional int64 indicator_id = 1;

  // If true, then if the indicator variable takes value 0, the implied
  // constraint must hold. Otherwise, if the indicator variable takes value 1,
  // then the implied constraint must hold.
  bool activate_on_zero = 6;

  // Must be a valid linear expression with respect to the containing model:
  //   * All stated conditions on `SparseDoubleVectorProto`,
  //   * All elements of `expression.values` must be finite,
  //   * `expression.ids` are a subset of `VariablesProto.ids`.
  SparseDoubleVectorProto expression = 2;

  // Must have value in [-inf, inf); cannot be NaN.
  double lower_bound = 3;

  // Must have value in (-inf, inf]; cannot be NaN.
  double upper_bound = 4;

  // Parent messages may have uniqueness requirements on this field; e.g., see
  // `ModelProto.indicator_constraints` and
  // `IndicatorConstraintUpdatesProto.new_constraints`.
  string name = 5;
}

// An optimization problem.
// MathOpt supports:
//   - Continuous and integer decision variables with optional finite bounds.
//   - Linear and quadratic objectives (single or multiple objectives), either
//   minimized or maximized.
//   - A number of constraints types, including:
//     * Linear constraints
//     * Quadratic constraints
//     * Second-order cone constraints
//     * Logical constraints
//       > SOS1 and SOS2 constraints
//       > Indicator constraints
//
// By default, constraints are represented in "id-to-data" maps. However, we
// represent linear constraints in a more efficient "struct-of-arrays" format.
message ModelProto {
  string name = 1;
  VariablesProto variables = 2;

  // The primary objective in the model.
  ObjectiveProto objective = 3;

  // Auxiliary objectives for use in multi-objective models.
  //
  // Map key IDs must be in [0, max(int64)). Each priority, and each nonempty
  // name, must be unique and also distinct from the primary `objective`.
  map<int64, ObjectiveProto> auxiliary_objectives = 10;
  LinearConstraintsProto linear_constraints = 4;

  // The variable coefficients for the linear constraints.
  //
  // If a variable involved in this constraint is deleted, it is treated as if
  // it were set to zero.
  //
  // Requirements:
  //  * linear_constraint_matrix.row_ids are elements of linear_constraints.ids.
  //  * linear_constraint_matrix.column_ids are elements of variables.ids.
  //  * Matrix entries not specified are zero.
  //  * linear_constraint_matrix.values must all be finite.
  SparseDoubleMatrixProto linear_constraint_matrix = 5;

  // Mapped constraints (i.e., stored in "constraint ID"-to-"constraint data"
  // map). For each subsequent submessage, we require that:
  //   * Each key is in [0, max(int64)).
  //   * Each key is unique in its respective map (but not necessarily across
  //     constraint types)
  //   * Each value contains a name field (called `name`), and each nonempty
  //     name must be distinct across all map entries (but not necessarily
  //     across constraint types).

  // Quadratic constraints in the model.
  map<int64, QuadraticConstraintProto> quadratic_constraints = 6;

  // Second-order cone constraints in the model.
  map<int64, SecondOrderConeConstraintProto> second_order_cone_constraints = 11;

  // SOS1 constraints in the model, which constrain that at most one
  // `expression` can be nonzero. The optional `weights` entries are an
  // implementation detail used by the solver to (hopefully) converge more
  // quickly. In more detail, solvers may (or may not) use these weights to
  // select branching decisions that produce "balanced" children nodes.
  map<int64, SosConstraintProto> sos1_constraints = 7;

  // SOS2 constraints in the model, which constrain that at most two entries of
  // `expression` can be nonzero, and they must be adjacent in their ordering.
  // If no `weights` are provided, this ordering is their linear ordering in the
  // `expressions` list; if `weights` are presented, the ordering is taken with
  // respect to these values in increasing order.
  map<int64, SosConstraintProto> sos2_constraints = 8;

  // Indicator constraints in the model, which enforce that, if a binary
  // "indicator variable" is set to one, then an "implied constraint" must hold.
  map<int64, IndicatorConstraintProto> indicator_constraints = 9;
}