linear_solver.h

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// 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.

// A C++ wrapper that provides a simple and unified interface to
// several linear programming and mixed integer programming solvers:
// GLOP, GLPK, CLP, CBC, and SCIP. The wrapper can also be used in Java, C#,
// and Python via SWIG.
//
//
// -----------------------------------
//
// What is Linear Programming?
//
//   In mathematics, linear programming (LP) is a technique for optimization of
//   a linear objective function, subject to linear equality and linear
//   inequality constraints. Informally, linear programming determines the way
//   to achieve the best outcome (such as maximum profit or lowest cost) in a
//   given mathematical model and given some list of requirements represented
//   as linear equations.
//
//   The most widely used technique for solving a linear program is the Simplex
//   algorithm, devised by George Dantzig in 1947. It performs very well on
//   most instances, for which its running time is polynomial. A lot of effort
//   has been put into improving the algorithm and its implementation. As a
//   byproduct, it has however been shown that one can always construct
//   problems that take exponential time for the Simplex algorithm to solve.
//   Research has thus focused on trying to find a polynomial algorithm for
//   linear programming, or to prove that linear programming is indeed
//   polynomial.
//
//   Leonid Khachiyan first exhibited in 1979 a weakly polynomial algorithm for
//   linear programming. "Weakly polynomial" means that the running time of the
//   algorithm is in O(P(n) * 2^p) where P(n) is a polynomial of the size of the
//   problem, and p is the precision of computations expressed in number of
//   bits. With a fixed-precision, floating-point-based implementation, a weakly
//   polynomial algorithm will  thus run in polynomial time. No implementation
//   of Khachiyan's algorithm has proved efficient, but a larger breakthrough in
//   the field came in 1984 when Narendra Karmarkar introduced a new interior
//   point method for solving linear programming problems. Interior point
//   algorithms have proved efficient on very large linear programs.
//
//   Check Wikipedia for more detail:
//     http://en.wikipedia.org/wiki/Linear_programming
//
// -----------------------------------
//
// Example of a Linear Program
//
//   maximize:
//     3x + y
//   subject to:
//     1.5 x + 2 y <= 12
//     0 <= x <= 3
//     0 <= y <= 5
//
//  A linear program has:
//    1) a linear objective function
//    2) linear constraints that can be equalities or inequalities
//    3) bounds on variables that can be positive, negative, finite or
//       infinite.
//
// -----------------------------------
//
// What is Mixed Integer Programming?
//
//   Here, the constraints and the objective are still linear but
//   there are additional integrality requirements for variables. If
//   all variables are required to take integer values, then the
//   problem is called an integer program (IP). In most cases, only
//   some variables are required to be integer and the rest of the
//   variables are continuous: this is called a mixed integer program
//   (MIP). IPs and MIPs are generally NP-hard.
//
//   Integer variables can be used to model discrete decisions (build a
//   datacenter in city A or city B), logical relationships (only
//   place machines in datacenter A if we have decided to build
//   datacenter A) and approximate non-linear functions with piecewise
//   linear functions (for example, the cost of machines as a function
//   of how many machines are bought, or the latency of a server as a
//   function of its load).
//
// -----------------------------------
//
// How to use the wrapper
//
//   The user builds the model and solves it through the MPSolver class,
//   then queries the solution through the MPSolver, MPVariable and
//   MPConstraint classes. To be able to query a solution, you need the
//   following:
//   - A solution exists: MPSolver::Solve has been called and a solution
//     has been found.
//   - The model has not been modified since the last time
//     MPSolver::Solve was called. Otherwise, the solution obtained
//     before the model modification may not longer be feasible or
//     optimal.
//
// @see ../examples/linear_programming.cc for a simple LP example.
//
// @see ../examples/integer_programming.cc for a simple MIP example.
//
//   All methods cannot be called successfully in all cases. For
//   example: you cannot query a solution when no solution exists, you
//   cannot query a reduced cost value (which makes sense only on
//   continuous problems) on a discrete problem. When a method is
//   called in an unsuitable context, it aborts with a
//   LOG(FATAL).
// TODO(user): handle failures gracefully.
//
// -----------------------------------
//
// For developers: How the wrapper works
//
//   MPSolver stores a representation of the model (variables,
//   constraints and objective) in its own data structures and a
//   pointer to a MPSolverInterface that wraps the underlying solver
//   (GLOP, CBC, CLP, GLPK, or SCIP) that does the actual work. The
//   underlying solver also keeps a representation of the model in its
//   own data structures. The model representations in MPSolver and in
//   the underlying solver are kept in sync by the 'extraction'
//   mechanism: synchronously for some changes and asynchronously
//   (when MPSolver::Solve is called) for others. Synchronicity
//   depends on the modification applied and on the underlying solver.

#ifndef OR_TOOLS_LINEAR_SOLVER_LINEAR_SOLVER_H_
#define OR_TOOLS_LINEAR_SOLVER_LINEAR_SOLVER_H_

#include <functional>
#include <limits>
#include <map>
#include <memory>
#include <string>
#include <utility>
#include <vector>

#include "absl/container/flat_hash_map.h"
#include "absl/strings/match.h"
#include "absl/strings/str_format.h"
#include "absl/types/optional.h"
#include "ortools/base/commandlineflags.h"
#include "ortools/base/integral_types.h"
#include "ortools/base/logging.h"
#include "ortools/base/macros.h"
#include "ortools/base/status.h"
#include "ortools/base/timer.h"
#include "ortools/glop/parameters.pb.h"
#include "ortools/linear_solver/linear_expr.h"
#include "ortools/linear_solver/linear_solver.pb.h"
#include "ortools/port/proto_utils.h"

namespace operations_research {

constexpr double kDefaultPrimalTolerance = 1e-07;

class MPConstraint;
class MPObjective;
class MPSolverInterface;
class MPSolverParameters;
class MPVariable;

class MPSolver {
 public:
   enum OptimizationProblemType {
#ifdef USE_CLP

     CLP_LINEAR_PROGRAMMING = 0,
#endif
#ifdef USE_GLPK

     GLPK_LINEAR_PROGRAMMING = 1,
#endif
#ifdef USE_GLOP

     GLOP_LINEAR_PROGRAMMING = 2,
#endif
#ifdef USE_GUROBI

     GUROBI_LINEAR_PROGRAMMING = 6,
#endif
#ifdef USE_CPLEX

     CPLEX_LINEAR_PROGRAMMING = 10,
#endif

// Integer programming problems.
#ifdef USE_SCIP

     SCIP_MIXED_INTEGER_PROGRAMMING = 3, // Recommended default value.
#endif
#ifdef USE_GLPK

     GLPK_MIXED_INTEGER_PROGRAMMING = 4,
#endif
#ifdef USE_CBC

     CBC_MIXED_INTEGER_PROGRAMMING = 5,
#endif
#if defined(USE_GUROBI)

     GUROBI_MIXED_INTEGER_PROGRAMMING = 7,
#endif
#if defined(USE_CPLEX)

     CPLEX_MIXED_INTEGER_PROGRAMMING = 11,
#endif
#if defined(USE_BOP)

     BOP_INTEGER_PROGRAMMING = 12,
#endif
   };

  MPSolver(const std::string& name, OptimizationProblemType problem_type);
  virtual ~MPSolver();

  static bool SupportsProblemType(OptimizationProblemType problem_type);

  static bool ParseSolverType(absl::string_view solver,
                              OptimizationProblemType* type);

  bool IsMIP() const;

  const std::string& Name() const {
    return name_;  // Set at construction.
  }

  virtual OptimizationProblemType ProblemType() const {
    return problem_type_;  // Set at construction.
  }

  void Clear();

  int NumVariables() const { return variables_.size(); }

  const std::vector<MPVariable*>& variables() const { return variables_; }

  MPVariable* LookupVariableOrNull(const std::string& var_name) const;

  MPVariable* MakeVar(double lb, double ub, bool integer,
                      const std::string& name);
  
  MPVariable* MakeNumVar(double lb, double ub, const std::string& name);

  MPVariable* MakeIntVar(double lb, double ub, const std::string& name);

  MPVariable* MakeBoolVar(const std::string& name);

  void MakeVarArray(int nb, double lb, double ub, bool integer,
                    const std::string& name_prefix,
                    std::vector<MPVariable*>* vars);
  
  void MakeNumVarArray(int nb, double lb, double ub, const std::string& name,
                       std::vector<MPVariable*>* vars);

  void MakeIntVarArray(int nb, double lb, double ub, const std::string& name,
                       std::vector<MPVariable*>* vars);

  void MakeBoolVarArray(int nb, const std::string& name,
                        std::vector<MPVariable*>* vars);

  int NumConstraints() const { return constraints_.size(); }

  const std::vector<MPConstraint*>& constraints() const { return constraints_; }

  MPConstraint* LookupConstraintOrNull(
      const std::string& constraint_name) const;

  MPConstraint* MakeRowConstraint(double lb, double ub);

  MPConstraint* MakeRowConstraint();

  MPConstraint* MakeRowConstraint(double lb, double ub,
                                  const std::string& name);
  MPConstraint* MakeRowConstraint(const std::string& name);

  MPConstraint* MakeRowConstraint(const LinearRange& range);

  MPConstraint* MakeRowConstraint(const LinearRange& range,
                                  const std::string& name);

  const MPObjective& Objective() const { return *objective_; }

  MPObjective* MutableObjective() { return objective_.get(); }

  enum ResultStatus {
    OPTIMAL,
    FEASIBLE,
    INFEASIBLE,
    UNBOUNDED,
    ABNORMAL,
    MODEL_INVALID,
    NOT_SOLVED = 6
  };

  ResultStatus Solve();

  ResultStatus Solve(const MPSolverParameters& param);

  void Write(const std::string& file_name);

  std::vector<double> ComputeConstraintActivities() const;

  bool VerifySolution(double tolerance, bool log_errors) const;

  void Reset();

  bool InterruptSolve();

  MPSolverResponseStatus LoadModelFromProto(const MPModelProto& input_model,
                                            std::string* error_message);
  MPSolverResponseStatus LoadModelFromProtoWithUniqueNamesOrDie(
      const MPModelProto& input_model, std::string* error_message);

  void FillSolutionResponseProto(MPSolutionResponse* response) const;

  static void SolveWithProto(const MPModelRequest& model_request,
                             MPSolutionResponse* response);

  void ExportModelToProto(MPModelProto* output_model) const;

  util::Status LoadSolutionFromProto(
      const MPSolutionResponse& response,
      double tolerance = kDefaultPrimalTolerance);

  util::Status ClampSolutionWithinBounds();

  bool ExportModelAsLpFormat(bool obfuscate, std::string* model_str) const;
  bool ExportModelAsMpsFormat(bool fixed_format, bool obfuscate,
                              std::string* model_str) const;

  util::Status SetNumThreads(int num_threads);
  int GetNumThreads() const { return num_threads_; }

  bool SetSolverSpecificParametersAsString(const std::string& parameters);
  std::string GetSolverSpecificParametersAsString() const {
    return solver_specific_parameter_string_;
  }

  void SetHint(std::vector<std::pair<const MPVariable*, double> > hint);

  enum BasisStatus {
    FREE = 0,
    AT_LOWER_BOUND,
    AT_UPPER_BOUND,
    FIXED_VALUE,
    BASIC
  };

  void SetStartingLpBasis(
      const std::vector<MPSolver::BasisStatus>& variable_statuses,
      const std::vector<MPSolver::BasisStatus>& constraint_statuses);

  static double infinity() { return std::numeric_limits<double>::infinity(); }

  bool OutputIsEnabled() const;
  void EnableOutput();
  void SuppressOutput();

  absl::Duration TimeLimit() const { return time_limit_; }
  void SetTimeLimit(absl::Duration time_limit) {
    DCHECK_GE(time_limit, absl::ZeroDuration());
    time_limit_ = time_limit;
  }

  absl::Duration DurationSinceConstruction() const {
    return absl::Now() - construction_time_;
  }

  int64 iterations() const;

  int64 nodes() const;

  std::string SolverVersion() const;

  void* underlying_solver();

  double ComputeExactConditionNumber() const;

  ABSL_MUST_USE_RESULT bool NextSolution();

  // DEPRECATED: Use TimeLimit() and SetTimeLimit(absl::Duration) instead.
  // NOTE: These deprecated functions used the convention time_limit = 0 to mean
  // "no limit", which now corresponds to time_limit_ = InfiniteDuration().
  int64 time_limit() const {
    return time_limit_ == absl::InfiniteDuration()
               ? 0
               : absl::ToInt64Milliseconds(time_limit_);
  }
  void set_time_limit(int64 time_limit_milliseconds) {
    SetTimeLimit(time_limit_milliseconds == 0
                     ? absl::InfiniteDuration()
                     : absl::Milliseconds(time_limit_milliseconds));
  }
  double time_limit_in_secs() const {
    return static_cast<double>(time_limit()) / 1000.0;
  }

  // DEPRECATED: Use DurationSinceConstruction() instead.
  int64 wall_time() const {
    return absl::ToInt64Milliseconds(DurationSinceConstruction());
  }

  friend class GLPKInterface;
  friend class CLPInterface;
  friend class CBCInterface;
  friend class SCIPInterface;
  friend class GurobiInterface;
  friend class CplexInterface;
  friend class SLMInterface;
  friend class MPSolverInterface;
  friend class GLOPInterface;
  friend class BopInterface;
  friend class SatInterface;
  friend class KnapsackInterface;

  // Debugging: verify that the given MPVariable* belongs to this solver.
  bool OwnsVariable(const MPVariable* var) const;

 private:
  // Computes the size of the constraint with the largest number of
  // coefficients with index in [min_constraint_index,
  // max_constraint_index)
  int ComputeMaxConstraintSize(int min_constraint_index,
                               int max_constraint_index) const;

  // Returns true if the model has constraints with lower bound > upper bound.
  bool HasInfeasibleConstraints() const;

  // Returns true if the model has at least 1 integer variable.
  bool HasIntegerVariables() const;

  // Generates the map from variable names to their indices.
  void GenerateVariableNameIndex() const;

  // Generates the map from constraint names to their indices.
  void GenerateConstraintNameIndex() const;

  // The name of the linear programming problem.
  const std::string name_;

  // The type of the linear programming problem.
  const OptimizationProblemType problem_type_;

  // The solver interface.
  std::unique_ptr<MPSolverInterface> interface_;

  // The vector of variables in the problem.
  std::vector<MPVariable*> variables_;
  // A map from a variable's name to its index in variables_.
  mutable absl::optional<absl::flat_hash_map<std::string, int> >
      variable_name_to_index_;
  // Whether variables have been extracted to the underlying interface.
  std::vector<bool> variable_is_extracted_;

  // The vector of constraints in the problem.
  std::vector<MPConstraint*> constraints_;
  // A map from a constraint's name to its index in constraints_.
  mutable absl::optional<absl::flat_hash_map<std::string, int> >
      constraint_name_to_index_;
  // Whether constraints have been extracted to the underlying interface.
  std::vector<bool> constraint_is_extracted_;

  // The linear objective function.
  std::unique_ptr<MPObjective> objective_;

  // Initial values for all or some of the problem variables that can be
  // exploited as a starting hint by a solver.
  //
  // Note(user): as of 05/05/2015, we can't use >> because of some SWIG errors.
  //
  // TODO(user): replace by two vectors, a std::vector<bool> to indicate if a
  // hint is provided and a std::vector<double> for the hint value.
  std::vector<std::pair<const MPVariable*, double> > solution_hint_;

  absl::Duration time_limit_ = absl::InfiniteDuration();  // Default = No limit.

  const absl::Time construction_time_;

  // Permanent storage for the number of threads.
  int num_threads_ = 1;

  // Permanent storage for SetSolverSpecificParametersAsString().
  std::string solver_specific_parameter_string_;

  MPSolverResponseStatus LoadModelFromProtoInternal(
      const MPModelProto& input_model, bool clear_names,
      std::string* error_message);

  DISALLOW_COPY_AND_ASSIGN(MPSolver);
};

const absl::string_view ToString(
    MPSolver::OptimizationProblemType optimization_problem_type);

inline std::ostream& operator<<(
    std::ostream& os,
    MPSolver::OptimizationProblemType optimization_problem_type) {
  return os << ToString(optimization_problem_type);
}

inline std::ostream& operator<<(std::ostream& os,
                                MPSolver::ResultStatus status) {
  return os << ProtoEnumToString<MPSolverResponseStatus>(
             static_cast<MPSolverResponseStatus>(status));
}

bool AbslParseFlag(absl::string_view text,
                   MPSolver::OptimizationProblemType* solver_type,
                   std::string* error);

inline std::string AbslUnparseFlag(
    MPSolver::OptimizationProblemType solver_type) {
  return std::string(ToString(solver_type));
}

class MPObjective {
 public:
   void Clear();

   void SetCoefficient(const MPVariable *const var, double coeff);

   double GetCoefficient(const MPVariable *const var) const;

   const absl::flat_hash_map<const MPVariable *, double> &terms() const {
     return coefficients_;
  }

  void SetOffset(double value);

  double offset() const { return offset_; }

  void OptimizeLinearExpr(const LinearExpr& linear_expr, bool is_maximization);

  void MaximizeLinearExpr(const LinearExpr& linear_expr) {
    OptimizeLinearExpr(linear_expr, true);
  }
  void MinimizeLinearExpr(const LinearExpr& linear_expr) {
    OptimizeLinearExpr(linear_expr, false);
  }

  void AddLinearExpr(const LinearExpr& linear_expr);

  void SetOptimizationDirection(bool maximize);

  void SetMinimization() { SetOptimizationDirection(false); }

  void SetMaximization() { SetOptimizationDirection(true); }

  bool maximization() const;
  bool minimization() const;

  double Value() const;

  double BestBound() const;

 private:
  friend class MPSolver;
  friend class MPSolverInterface;
  friend class CBCInterface;
  friend class CLPInterface;
  friend class GLPKInterface;
  friend class SCIPInterface;
  friend class SLMInterface;
  friend class GurobiInterface;
  friend class CplexInterface;
  friend class GLOPInterface;
  friend class BopInterface;
  friend class SatInterface;
  friend class KnapsackInterface;

  // Constructor. An objective points to a single MPSolverInterface
  // that is specified in the constructor. An objective cannot belong
  // to several models.
  // At construction, an MPObjective has no terms (which is equivalent
  // on having a coefficient of 0 for all variables), and an offset of 0.
  explicit MPObjective(MPSolverInterface* const interface_in)
      : interface_(interface_in), coefficients_(1), offset_(0.0) {}

  MPSolverInterface* const interface_;

  // Mapping var -> coefficient.
  absl::flat_hash_map<const MPVariable*, double> coefficients_;
  // Constant term.
  double offset_;

  DISALLOW_COPY_AND_ASSIGN(MPObjective);
};

class MPVariable {
 public:
  const std::string& name() const { return name_; }

  void SetInteger(bool integer);

  bool integer() const { return integer_; }

  double solution_value() const;

  int index() const { return index_; }

  double lb() const { return lb_; }

  double ub() const { return ub_; }

  void SetLB(double lb) { SetBounds(lb, ub_); }
  void SetUB(double ub) { SetBounds(lb_, ub); }
  
  void SetBounds(double lb, double ub);

  double unrounded_solution_value() const;

  double reduced_cost() const;

  MPSolver::BasisStatus basis_status() const;

  int branching_priority() const { return branching_priority_; }
  void SetBranchingPriority(int priority);

 protected:
  friend class MPSolver;
  friend class MPSolverInterface;
  friend class CBCInterface;
  friend class CLPInterface;
  friend class GLPKInterface;
  friend class SCIPInterface;
  friend class SLMInterface;
  friend class GurobiInterface;
  friend class CplexInterface;
  friend class GLOPInterface;
  friend class MPVariableSolutionValueTest;
  friend class BopInterface;
  friend class SatInterface;
  friend class KnapsackInterface;

  // Constructor. A variable points to a single MPSolverInterface that
  // is specified in the constructor. A variable cannot belong to
  // several models.
  MPVariable(int index, double lb, double ub, bool integer,
             const std::string& name, MPSolverInterface* const interface_in)
      : index_(index),
        lb_(lb),
        ub_(ub),
        integer_(integer),
        name_(name.empty() ? absl::StrFormat("auto_v_%09d", index) : name),
        solution_value_(0.0),
        reduced_cost_(0.0),
        interface_(interface_in) {}

  void set_solution_value(double value) { solution_value_ = value; }
  void set_reduced_cost(double reduced_cost) { reduced_cost_ = reduced_cost; }

 private:
  const int index_;
  double lb_;
  double ub_;
  bool integer_;
  const std::string name_;
  double solution_value_;
  double reduced_cost_;
  int branching_priority_ = 0;
  MPSolverInterface* const interface_;
  DISALLOW_COPY_AND_ASSIGN(MPVariable);
};

class MPConstraint {
 public:
  const std::string& name() const { return name_; }

  void Clear();

  void SetCoefficient(const MPVariable* const var, double coeff);

  double GetCoefficient(const MPVariable* const var) const;

  const absl::flat_hash_map<const MPVariable*, double>& terms() const {
    return coefficients_;
  }

  double lb() const { return lb_; }

  double ub() const { return ub_; }

  void SetLB(double lb) { SetBounds(lb, ub_); }

  void SetUB(double ub) { SetBounds(lb_, ub); }

  void SetBounds(double lb, double ub);

  bool is_lazy() const { return is_lazy_; }

  void set_is_lazy(bool laziness) { is_lazy_ = laziness; }

  const MPVariable* indicator_variable() const { return indicator_variable_; }
  bool indicator_value() const { return indicator_value_; }

  int index() const { return index_; }

  double dual_value() const;

  MPSolver::BasisStatus basis_status() const;

 protected:
  friend class MPSolver;
  friend class MPSolverInterface;
  friend class CBCInterface;
  friend class CLPInterface;
  friend class GLPKInterface;
  friend class SCIPInterface;
  friend class SLMInterface;
  friend class GurobiInterface;
  friend class CplexInterface;
  friend class GLOPInterface;
  friend class BopInterface;
  friend class SatInterface;
  friend class KnapsackInterface;

  // Constructor. A constraint points to a single MPSolverInterface
  // that is specified in the constructor. A constraint cannot belong
  // to several models.
  MPConstraint(int index, double lb, double ub, const std::string& name,
               MPSolverInterface* const interface_in)
      : coefficients_(1),
        index_(index),
        lb_(lb),
        ub_(ub),
        name_(name.empty() ? absl::StrFormat("auto_c_%09d", index) : name),
        is_lazy_(false),
        indicator_variable_(nullptr),
        dual_value_(0.0),
        interface_(interface_in) {}

  void set_dual_value(double dual_value) { dual_value_ = dual_value; }

 private:
  // Returns true if the constraint contains variables that have not
  // been extracted yet.
  bool ContainsNewVariables();

  // Mapping var -> coefficient.
  absl::flat_hash_map<const MPVariable*, double> coefficients_;

  const int index_;  // See index().

  // The lower bound for the linear constraint.
  double lb_;

  // The upper bound for the linear constraint.
  double ub_;

  // Name.
  const std::string name_;

  // True if the constraint is "lazy", i.e. the constraint is added to the
  // underlying Linear Programming solver only if it is violated.
  // By default this parameter is 'false'.
  bool is_lazy_;

  // If given, this constraint is only active if `indicator_variable_`'s value
  // is equal to `indicator_value_`.
  const MPVariable* indicator_variable_;
  bool indicator_value_;

  double dual_value_;
  MPSolverInterface* const interface_;
  DISALLOW_COPY_AND_ASSIGN(MPConstraint);
};

class MPSolverParameters {
 public:
   enum DoubleParam {
     RELATIVE_MIP_GAP = 0,

     PRIMAL_TOLERANCE = 1,
     DUAL_TOLERANCE = 2
   };

   enum IntegerParam {
     PRESOLVE = 1000,
     LP_ALGORITHM = 1001,
     INCREMENTALITY = 1002,
     SCALING = 1003
   };

   enum PresolveValues {
     PRESOLVE_OFF = 0, // Presolve is off.
     PRESOLVE_ON = 1   // Presolve is on.
   };

   enum LpAlgorithmValues {
     DUAL = 10,   // Dual simplex.
     PRIMAL = 11, // Primal simplex.
     BARRIER = 12 // Barrier algorithm.
   };

   enum IncrementalityValues {
     INCREMENTALITY_OFF = 0,

     INCREMENTALITY_ON = 1
   };

   enum ScalingValues {
     SCALING_OFF = 0, 
     SCALING_ON = 1   
   };

   // @{
   // Placeholder value to indicate that a parameter is set to
   // the default value defined in the wrapper.
   static const double kDefaultDoubleParamValue;
   static const int kDefaultIntegerParamValue;
   // @}

   // @{
   // Placeholder value to indicate that a parameter is unknown.
   static const double kUnknownDoubleParamValue;
   static const int kUnknownIntegerParamValue;
   // @}

   // @{
   // Default values for parameters. Only parameters that define the
   // properties of the solution returned need to have a default value
   // (that is the same for all solvers). You can also define a default
   // value for performance parameters when you are confident it is a
   // good choice (example: always turn presolve on).
   static const double kDefaultRelativeMipGap;
   static const double kDefaultPrimalTolerance;
   static const double kDefaultDualTolerance;
   static const PresolveValues kDefaultPresolve;
   static const IncrementalityValues kDefaultIncrementality;
   // @}

   MPSolverParameters();

   void SetDoubleParam(MPSolverParameters::DoubleParam param, double value);
   void SetIntegerParam(MPSolverParameters::IntegerParam param, int value);

   void ResetDoubleParam(MPSolverParameters::DoubleParam param);
   void ResetIntegerParam(MPSolverParameters::IntegerParam param);
   void Reset();

   double GetDoubleParam(MPSolverParameters::DoubleParam param) const;

   int GetIntegerParam(MPSolverParameters::IntegerParam param) const;

 private:
  // @{
  // Parameter value for each parameter.
  // @see DoubleParam
  // @see IntegerParam
  double relative_mip_gap_value_;
  double primal_tolerance_value_;
  double dual_tolerance_value_;
  int presolve_value_;
  int scaling_value_;
  int lp_algorithm_value_;
  int incrementality_value_;
  // @}

  // Boolean value indicating whether each parameter is set to the
  // solver's default value. Only parameters for which the wrapper
  // does not define a default value need such an indicator.
  bool lp_algorithm_is_default_;

  DISALLOW_COPY_AND_ASSIGN(MPSolverParameters);
};

// This class wraps the actual mathematical programming solvers. Each
// solver (GLOP, CLP, CBC, GLPK, SCIP) has its own interface class that
// derives from this abstract class. This class is never directly
// accessed by the user.
// @see glop_interface.cc
// @see cbc_interface.cc
// @see clp_interface.cc
// @see glpk_interface.cc
// @see scip_interface.cc
class MPSolverInterface {
 public:
  enum SynchronizationStatus {
    // The underlying solver (CLP, GLPK, ...) and MPSolver are not in
    // sync for the model nor for the solution.
    MUST_RELOAD,
    // The underlying solver and MPSolver are in sync for the model
    // but not for the solution: the model has changed since the
    // solution was computed last.
    MODEL_SYNCHRONIZED,
    // The underlying solver and MPSolver are in sync for the model and
    // the solution.
    SOLUTION_SYNCHRONIZED
  };

  // When the underlying solver does not provide the number of simplex
  // iterations.
  static const int64 kUnknownNumberOfIterations = -1;
  // When the underlying solver does not provide the number of
  // branch-and-bound nodes.
  static const int64 kUnknownNumberOfNodes = -1;

  // Constructor. The user will access the MPSolverInterface through the
  // MPSolver passed as argument.
  explicit MPSolverInterface(MPSolver* const solver);
  virtual ~MPSolverInterface();

  // ----- Solve -----
  // Solves problem with specified parameter values. Returns true if the
  // solution is optimal.
  virtual MPSolver::ResultStatus Solve(const MPSolverParameters& param) = 0;

  // Writes the model using the solver internal write function.  Currently only
  // available for GurobiInterface.
  virtual void Write(const std::string& filename);

  // ----- Model modifications and extraction -----
  // Resets extracted model.
  virtual void Reset() = 0;

  // Sets the optimization direction (min/max).
  virtual void SetOptimizationDirection(bool maximize) = 0;

  // Modifies bounds of an extracted variable.
  virtual void SetVariableBounds(int index, double lb, double ub) = 0;

  // Modifies integrality of an extracted variable.
  virtual void SetVariableInteger(int index, bool integer) = 0;

  // Modify bounds of an extracted variable.
  virtual void SetConstraintBounds(int index, double lb, double ub) = 0;

  // Adds a linear constraint.
  virtual void AddRowConstraint(MPConstraint* const ct) = 0;

  // Adds an indicator constraint. Returns true if the feature is supported by
  // the underlying solver.
  virtual bool AddIndicatorConstraint(MPConstraint* const ct) {
    LOG(ERROR) << "Solver doesn't support indicator constraints.";
    return false;
  }

  // Add a variable.
  virtual void AddVariable(MPVariable* const var) = 0;

  // Changes a coefficient in a constraint.
  virtual void SetCoefficient(MPConstraint* const constraint,
                              const MPVariable* const variable,
                              double new_value, double old_value) = 0;

  // Clears a constraint from all its terms.
  virtual void ClearConstraint(MPConstraint* const constraint) = 0;

  // Changes a coefficient in the linear objective.
  virtual void SetObjectiveCoefficient(const MPVariable* const variable,
                                       double coefficient) = 0;

  // Changes the constant term in the linear objective.
  virtual void SetObjectiveOffset(double value) = 0;

  // Clears the objective from all its terms.
  virtual void ClearObjective() = 0;

  virtual void BranchingPriorityChangedForVariable(int var_index) {}
  // ------ Query statistics on the solution and the solve ------
  // Returns the number of simplex iterations. The problem must be discrete,
  // otherwise it crashes, or returns kUnknownNumberOfIterations in NDEBUG mode.
  virtual int64 iterations() const = 0;
  // Returns the number of branch-and-bound nodes. The problem must be discrete,
  // otherwise it crashes, or returns kUnknownNumberOfNodes in NDEBUG mode.
  virtual int64 nodes() const = 0;
  // Returns the best objective bound. The problem must be discrete, otherwise
  // it crashes, or returns trivial_worst_objective_bound() in NDEBUG mode.
  virtual double best_objective_bound() const = 0;
  // A trivial objective bound: the worst possible value of the objective,
  // which will be +infinity if minimizing and -infinity if maximing.
  double trivial_worst_objective_bound() const;
  // Returns the objective value of the best solution found so far.
  double objective_value() const;

  // Returns the basis status of a row.
  virtual MPSolver::BasisStatus row_status(int constraint_index) const = 0;
  // Returns the basis status of a constraint.
  virtual MPSolver::BasisStatus column_status(int variable_index) const = 0;

  // Checks whether the solution is synchronized with the model, i.e. whether
  // the model has changed since the solution was computed last.
  // If it isn't, it crashes in NDEBUG, and returns false othwerwise.
  bool CheckSolutionIsSynchronized() const;
  // Checks whether a feasible solution exists. The behavior is similar to
  // CheckSolutionIsSynchronized() above.
  virtual bool CheckSolutionExists() const;
  // Handy shortcut to do both checks above (it is often used).
  bool CheckSolutionIsSynchronizedAndExists() const {
    return CheckSolutionIsSynchronized() && CheckSolutionExists();
  }
  // Checks whether information on the best objective bound exists. The behavior
  // is similar to CheckSolutionIsSynchronized() above.
  virtual bool CheckBestObjectiveBoundExists() const;

  // ----- Misc -----
  // Queries problem type. For simplicity, the distinction between
  // continuous and discrete is based on the declaration of the user
  // when the solver is created (example: GLPK_LINEAR_PROGRAMMING
  // vs. GLPK_MIXED_INTEGER_PROGRAMMING), not on the actual content of
  // the model.
  // Returns true if the problem is continuous.
  virtual bool IsContinuous() const = 0;
  // Returns true if the problem is continuous and linear.
  virtual bool IsLP() const = 0;
  // Returns true if the problem is discrete and linear.
  virtual bool IsMIP() const = 0;

  // Returns the index of the last variable extracted.
  int last_variable_index() const { return last_variable_index_; }

  bool variable_is_extracted(int var_index) const {
    return solver_->variable_is_extracted_[var_index];
  }
  void set_variable_as_extracted(int var_index, bool extracted) {
    solver_->variable_is_extracted_[var_index] = extracted;
  }
  bool constraint_is_extracted(int ct_index) const {
    return solver_->constraint_is_extracted_[ct_index];
  }
  void set_constraint_as_extracted(int ct_index, bool extracted) {
    solver_->constraint_is_extracted_[ct_index] = extracted;
  }

  // Returns the boolean indicating the verbosity of the solver output.
  bool quiet() const { return quiet_; }
  // Sets the boolean indicating the verbosity of the solver output.
  void set_quiet(bool quiet_value) { quiet_ = quiet_value; }

  // Returns the result status of the last solve.
  MPSolver::ResultStatus result_status() const {
    CheckSolutionIsSynchronized();
    return result_status_;
  }

  // Returns a std::string describing the underlying solver and its version.
  virtual std::string SolverVersion() const = 0;

  // Returns the underlying solver.
  virtual void* underlying_solver() = 0;

  // Computes exact condition number. Only available for continuous
  // problems and only implemented in GLPK.
  virtual double ComputeExactConditionNumber() const;

  // See MPSolver::SetStartingLpBasis().
  virtual void SetStartingLpBasis(
      const std::vector<MPSolver::BasisStatus>& variable_statuses,
      const std::vector<MPSolver::BasisStatus>& constraint_statuses) {
    LOG(FATAL) << "Not supported by this solver.";
  }

  virtual bool InterruptSolve() { return false; }

  // See MPSolver::NextSolution() for contract.
  virtual bool NextSolution() { return false; }

  friend class MPSolver;

  // To access the maximize_ bool and the MPSolver.
  friend class MPConstraint;
  friend class MPObjective;

 protected:
  MPSolver* const solver_;
  // Indicates whether the model and the solution are synchronized.
  SynchronizationStatus sync_status_;
  // Indicates whether the solve has reached optimality,
  // infeasibility, a limit, etc.
  MPSolver::ResultStatus result_status_;
  // Optimization direction.
  bool maximize_;

  // Index in MPSolver::variables_ of last constraint extracted.
  int last_constraint_index_;
  // Index in MPSolver::constraints_ of last variable extracted.
  int last_variable_index_;

  // The value of the objective function.
  double objective_value_;

  // Boolean indicator for the verbosity of the solver output.
  bool quiet_;

  // Index of dummy variable created for empty constraints or the
  // objective offset.
  static const int kDummyVariableIndex;

  // Extracts model stored in MPSolver.
  void ExtractModel();
  // Extracts the variables that have not been extracted yet.
  virtual void ExtractNewVariables() = 0;
  // Extracts the constraints that have not been extracted yet.
  virtual void ExtractNewConstraints() = 0;
  // Extracts the objective.
  virtual void ExtractObjective() = 0;
  // Resets the extraction information.
  void ResetExtractionInformation();
  // Change synchronization status from SOLUTION_SYNCHRONIZED to
  // MODEL_SYNCHRONIZED. To be used for model changes.
  void InvalidateSolutionSynchronization();

  // Sets parameters common to LP and MIP in the underlying solver.
  void SetCommonParameters(const MPSolverParameters& param);
  // Sets MIP specific parameters in the underlying solver.
  void SetMIPParameters(const MPSolverParameters& param);
  // Sets all parameters in the underlying solver.
  virtual void SetParameters(const MPSolverParameters& param) = 0;
  // Sets an unsupported double parameter.
  void SetUnsupportedDoubleParam(MPSolverParameters::DoubleParam param);
  // Sets an unsupported integer parameter.
  virtual void SetUnsupportedIntegerParam(
      MPSolverParameters::IntegerParam param);
  // Sets a supported double parameter to an unsupported value.
  void SetDoubleParamToUnsupportedValue(MPSolverParameters::DoubleParam param,
                                        double value);
  // Sets a supported integer parameter to an unsupported value.
  virtual void SetIntegerParamToUnsupportedValue(
      MPSolverParameters::IntegerParam param, int value);
  // Sets each parameter in the underlying solver.
  virtual void SetRelativeMipGap(double value) = 0;
  virtual void SetPrimalTolerance(double value) = 0;
  virtual void SetDualTolerance(double value) = 0;
  virtual void SetPresolveMode(int value) = 0;

  // Sets the number of threads to be used by the solver.
  virtual util::Status SetNumThreads(int num_threads);

  // Pass solver specific parameters in text format. The format is
  // solver-specific and is the same as the corresponding solver configuration
  // file format. Returns true if the operation was successful.
  //
  // The default implementation of this method stores the parameters in a
  // temporary file and calls ReadParameterFile to import the parameter file
  // into the solver. Solvers that support passing the parameters directly can
  // override this method to skip the temporary file logic.
  virtual bool SetSolverSpecificParametersAsString(
      const std::string& parameters);

  // Reads a solver-specific file of parameters and set them.
  // Returns true if there was no errors.
  virtual bool ReadParameterFile(const std::string& filename);

  // Returns a file extension like ".tmp", this is needed because some solvers
  // require a given extension for the ReadParameterFile() filename and we need
  // to know it to generate a temporary parameter file.
  virtual std::string ValidFileExtensionForParameterFile() const;

  // Sets the scaling mode.
  virtual void SetScalingMode(int value) = 0;
  virtual void SetLpAlgorithm(int value) = 0;
};

}  // namespace operations_research

#endif  // OR_TOOLS_LINEAR_SOLVER_LINEAR_SOLVER_H_