Files
ortools-clone/linear_solver/linear_solver.h
2011-08-11 18:44:23 +00:00

799 lines
27 KiB
C++

// Copyright 2010-2011 Google
// 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.
//
// (Laurent Perron).
//
// A C++, Python and Java wrapper for linear programming and mixed
// integer programming solvers: GLPK, CLP and CBC.
//
//
// -----------------------------------
// 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 linear programming problem was first shown to be
// solvable in polynomial time by Leonid Khachiyan in 1979, but a larger
// theoretical and practical breakthrough in the field came in 1984 when
// Narendra Karmarkar introduced a new interior point method for solving
// linear programming problems.
//
// -----------------------------------
// What is Mixed Integer Programming ?
//
// If only some of the unknown variables are required to be integers, then
// the problem is called a mixed integer programming (MIP) problem. These are
// generally also NP-hard.
//
// -----------------------------------
// Check Wikipedia for more detail:
//
// http://en.wikipedia.org/wiki/Linear_programming
//
// -----------------------------------
// Example of a Linear Programming:
//
// mimimize:
// f1*x1+f2*x2+...fn*xn
// subject to:
// a1*x1+a2*x2+...an*xn >= k1
// b1*x1+b2*x2+...bn*xn <= k2
// c1*x1+c2*x2+...cn*xn = k3
// ......
// u1 <= x1 <= v1
// u2 <= x2 <= v2
// .....
//
// As can be seen, Linear Programming has:
// 1) linear objective function
// 2) linear constraint
//
// Note:
// The objective function is linear and convex.
// The constraints form a convex space if feasible.
//
// -----------------------------------
#ifndef OR_TOOLS_LINEAR_SOLVER_LINEAR_SOLVER_H_
#define OR_TOOLS_LINEAR_SOLVER_LINEAR_SOLVER_H_
#include "base/hash.h"
#include "base/hash.h"
#include <limits>
#include <string>
#include <vector>
#include "base/commandlineflags.h"
#include "base/integral_types.h"
#include "base/logging.h"
#include "base/macros.h"
#include "base/scoped_ptr.h"
#include "base/timer.h"
#include "base/strutil.h"
#include "base/sparsetable.h"
#include "base/hash.h"
using std::string;
namespace operations_research {
class MPModelProto;
class MPModelRequest;
class MPSolutionResponse;
class MPSolverInterface;
class MPSolverParameters;
// A class to express a variable that will appear in a constraint.
class MPVariable {
public:
const string& name() const { return name_; }
void SetInteger(bool integer);
bool integer() const { return integer_; }
double solution_value() const;
// Only available for continuous problems.
double reduced_cost() 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);
protected:
friend class MPSolver;
friend class MPSolverInterface;
friend class CBCInterface;
friend class CLPInterface;
friend class GLPKInterface;
friend class SCIPInterface;
MPVariable(double lb, double ub, bool integer, const string& name,
MPSolverInterface* const interface)
: lb_(lb), ub_(ub), integer_(integer), name_(name), index_(-1),
solution_value_(0.0), reduced_cost_(0.0), interface_(interface) {}
void set_index(int index) { index_ = index; }
void set_solution_value(double value) { solution_value_ = value; }
void set_reduced_cost(double reduced_cost) { reduced_cost_ = reduced_cost; }
private:
double lb_;
double ub_;
bool integer_;
const string name_;
int index_;
double solution_value_;
double reduced_cost_;
MPSolverInterface* const interface_;
DISALLOW_COPY_AND_ASSIGN(MPVariable);
};
// A class to express constraints for a linear programming problem. A
// constraint is represented as a linear equation/inequality.
class MPConstraint {
public:
const string& name() const { return name_; }
// Clears all variables and coefficients.
void Clear();
// Add (var * coeff) to the current constraint.
void AddTerm(MPVariable* const var, double coeff);
// Add var to the current constraint.
void AddTerm(MPVariable* const var);
// Set the coefficient of the variable on the constraint.
void SetCoefficient(MPVariable* const var, double coeff);
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);
// Returns the constraint's activity in the current solution:
// sum over all terms of (coefficient * variable value)
double activity() const;
// Only available for continuous problems.
double dual_value() const;
int index() const { return index_; }
protected:
friend class MPSolver;
friend class MPSolverInterface;
friend class CBCInterface;
friend class CLPInterface;
friend class GLPKInterface;
friend class SCIPInterface;
// Creates a constraint and updates the pointer to its MPSolverInterface.
MPConstraint(double lb,
double ub,
const string& name,
MPSolverInterface* const interface)
: lb_(lb), ub_(ub), name_(name), index_(-1), dual_value_(0.0),
activity_(0.0), interface_(interface) {}
void set_index(int index) { index_ = index; }
void set_dual_value(double dual_value) { dual_value_ = dual_value; }
void set_activity(double activity) { activity_ = activity; }
private:
// Returns true if the constraint contains variables that have not
// been extracted yet.
bool ContainsNewVariables();
// Mapping var -> coefficient.
hash_map<MPVariable*, double> coefficients_;
// The lower bound for the linear constraint.
double lb_;
// The upper bound for the linear constraint.
double ub_;
// Name.
const string name_;
int index_;
double dual_value_;
double activity_;
MPSolverInterface* const interface_;
DISALLOW_COPY_AND_ASSIGN(MPConstraint);
};
// A class to express a linear objective function
class MPObjective {
public:
// Clears all variables and coefficients.
void Clear();
// Add (var * coeff) to the objective
void AddTerm(MPVariable* const var, double coeff);
// Add var to the objective
void AddTerm(MPVariable* const var);
// Set the coefficient of the variable in the objective
void SetCoefficient(MPVariable* const var, double coeff);
// Add constant term to the objective.
void AddOffset(double value);
// Set constant term in the objective.
void SetOffset(double value);
private:
friend class MPSolver;
friend class MPSolverInterface;
friend class CBCInterface;
friend class CLPInterface;
friend class GLPKInterface;
friend class SCIPInterface;
// Creates an objective and updates the pointer to its parent 'MPSolver'.
explicit MPObjective(MPSolverInterface* const interface)
: offset_(0.0), interface_(interface) {}
// Mapping var -> coefficient.
hash_map<MPVariable*, double> coefficients_;
// Constant term.
double offset_;
MPSolverInterface* const interface_;
DISALLOW_COPY_AND_ASSIGN(MPObjective);
};
class MPSolver {
public:
// The LP/MIP problem type.
enum OptimizationProblemType {
#if defined(USE_GLPK)
GLPK_LINEAR_PROGRAMMING,
GLPK_MIXED_INTEGER_PROGRAMMING,
#endif
#if defined(USE_CLP)
CLP_LINEAR_PROGRAMMING,
#endif
#if defined(USE_CBC)
CBC_MIXED_INTEGER_PROGRAMMING,
#endif
#if defined(USE_SCIP)
SCIP_MIXED_INTEGER_PROGRAMMING,
#endif
};
enum ResultStatus {
OPTIMAL, // optimal
FEASIBLE, // feasible, or stopped by limit.
INFEASIBLE, // proven infeasible
UNBOUNDED, // unbounded
ABNORMAL, // abnormal, i.e., error of some kind.
NOT_SOLVED // not been solved yet.
};
enum LoadStatus {
NO_ERROR,
DUPLICATE_VARIABLE_ID,
UNKNOWN_VARIABLE_ID
};
// Constructor that takes a name for the underlying solver.
MPSolver(const string& name, OptimizationProblemType problem_type);
virtual ~MPSolver();
// ----- Methods using protocol buffers -----
// Loads model from protocol buffer.
LoadStatus LoadModel(const MPModelProto& model);
// Exports model to protocol buffer.
void ExportModel(MPModelProto* model) const;
// Encode current solution in a solution response protocol buffer.
void FillSolutionResponse(MPSolutionResponse* response) const;
// Solves the model encoded by a MPModelRequest protocol buffer and
// fills the solution encoded as a MPSolutionResponse.
// The model is solved by the interface specified in the constructor
// of MPSolver, MPModelRequest.OptimizationProblemType is ignored.
void SolveWithProtocolBuffers(const MPModelRequest& model_request,
MPSolutionResponse* response);
// ----- Init and Clear -----
void Init() {} // To remove.
void Clear();
// ----- Variables ------
// Returns the number of variables.
int NumVariables() const { return variables_.size(); }
// Create a variable with the given bounds.
MPVariable* MakeVar(double lb, double ub, bool integer, const string& name);
MPVariable* MakeNumVar(double lb, double ub, const string& name);
MPVariable* MakeIntVar(double lb, double ub, const string& name);
MPVariable* MakeBoolVar(const string& name);
void MakeVarArray(int nb,
double lb,
double ub,
bool integer,
const string& name,
std::vector<MPVariable*>* vars);
void MakeNumVarArray(int nb,
double lb,
double ub,
const string& name,
std::vector<MPVariable*>* vars);
void MakeIntVarArray(int nb,
double lb,
double ub,
const string& name,
std::vector<MPVariable*>* vars);
void MakeBoolVarArray(int nb,
const string& name,
std::vector<MPVariable*>* vars);
// ----- Constraints -----
// Returns the number of constraints.
int NumConstraints() const { return constraints_.size(); }
// Returns a pointer to a newly created constraint for the linear programming
// problem. The MPSolver class assumes ownership of the constraint.
MPConstraint* MakeRowConstraint(double lb, double ub);
MPConstraint* MakeRowConstraint();
MPConstraint* MakeRowConstraint(double lb, double ub, const string& name);
MPConstraint* MakeRowConstraint(const string& name);
// ----- Objective -----
// Return the objective value of the best solution found so far. It
// is the optimal objective value if the problem has been solved to
// optimality.
double objective_value() const;
// Returns the best objective bound. In case of minimization, it is
// a lower bound on the objective value of the optimal integer
// solution. Only available for discrete problems.
double best_objective_bound() const;
// Clear objective.
void ClearObjective();
// Add var * coeff to the objective function.
void AddObjectiveTerm(MPVariable* const var, double coeff);
// Add var to the objective function.
void AddObjectiveTerm(MPVariable* const var);
// Set the objective coefficient of a variable in the objective.
void SetObjectiveCoefficient(MPVariable* const var, double coeff);
// Add constant term to the objective.
void AddObjectiveOffset(double value);
// Set constant term in the objective.
void SetObjectiveOffset(double value);
// Sets the optimization direction (min/max).
void SetOptimizationDirection(bool maximize);
// Minimizing or maximizing?
bool Maximization() const;
// Minimizing or maximizing?
bool Minimization() const;
// Set minimization mode.
void SetMinimization() { SetOptimizationDirection(false); }
// Set maximization mode.
void SetMaximization() { SetOptimizationDirection(true); }
// ----- Solve -----
// Solve the problem using default parameter values.
ResultStatus Solve();
// Solve the problem using the parameter values specified.
ResultStatus Solve(const MPSolverParameters& param);
// Reset extracted model to solve from scratch
void Reset();
// Misc.
static double infinity() {
return std::numeric_limits<double>::infinity();
}
// Suppress all output from solver.
void SuppressOutput();
// Enable a reasonably verbose output from solver.
void EnableOutput();
// Set the name of the file where the solver writes out the model
void set_write_model_filename(const string &filename) {
write_model_filename_ = filename;
}
string write_model_filename() const {
return write_model_filename_;
}
// Return true if filename ends in ".lp"
bool IsLPFormat(const string &filename) {
return HasSuffixString (filename, ".lp");
}
// Set Time limit in ms. (0 = no limit).
void set_time_limit(int64 time_limit) {
DCHECK_GE(time_limit, 0);
time_limit_ = time_limit;
}
int64 time_limit() const {
return time_limit_;
}
// wall_time() in ms since the creation of the solver.
int64 wall_time() const {
return timer_.GetInMs();
}
// Number of simplex iterations
int64 iterations() const;
// Number of branch-and-bound nodes. Only available for discrete problems.
int64 nodes() const;
// Check validity of a name.
bool CheckNameValidity(const string& name);
// Check validity of all variables and constraints names.
bool CheckAllNamesValidity();
// return a string describing the engine used.
string SolverVersion() const;
// Returns the underlying solver so that the user can use
// solver-specific features or features that are not exposed in the
// simple API of MPSolver. This method is for advanced users, use at
// your own risk! In particular, if you modify the model or the
// solution by accessing the underlying solver directly, then the
// underlying solver will be out of sync with the information kept
// in the wrapper (MPSolver, MPVariable, MPConstraint,
// MPObjective). You need to cast the void* returned back to its
// original type that depends on the interface (CBC:
// OsiClpSolverInterface*, CLP: ClpSimplex*, GLPK: glp_prob*, SCIP:
// SCIP*).
void* underlying_solver();
friend class GLPKInterface;
friend class CLPInterface;
friend class CBCInterface;
friend class SCIPInterface;
friend class MPSolverInterface;
private:
// Compute 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;
// Return true if the model has constraints with lb > ub.
bool HasInfeasibleConstraints() const;
// The name of the linear programming problem.
const string name_;
// The solver interface.
scoped_ptr<MPSolverInterface> interface_;
// vector of problem variables.
std::vector<MPVariable*> variables_;
hash_set<string> variables_names_;
// The list of constraints for the problem.
std::vector<MPConstraint*> constraints_;
hash_set<string> constraints_names_;
// The linear objective function
MPObjective linear_objective_;
// Time limit in ms.
int64 time_limit_;
// Name of the file where the solver writes out the model when Solve
// is called. If empty, no file is written.
string write_model_filename_;
WallTimer timer_;
DISALLOW_COPY_AND_ASSIGN(MPSolver);
};
// This class stores parameter settings for LP and MIP solvers.
// How to add a new parameter:
// - Add the new Foo parameter in the DoubleParam or IntegerParam enum.
// - If it is a categorical param, add a FooValues enum.
// - Decide if the wrapper should define a default value for it: yes
// if it controls the properties of the solution (example:
// tolerances) or if it consistently improves performance, no
// otherwise. If yes, define kDefaultFoo.
// - Add a foo_value_ member and, if no default value is defined, a
// foo_is_default_ member.
// - Add code to handle Foo in Set...Param, Reset...Param,
// Get...Param, Reset and the constructor.
// - In class MPSolverInterface, add a virtual method SetFoo and
// implement it for each solver.
// - Add a test in linear_solver_test.cc.
class MPSolverParameters {
public:
// Enumeration of parameters that take continuous values.
enum DoubleParam {
RELATIVE_MIP_GAP = 0, // Limit for relative MIP gap.
};
// Enumeration of parameters that take integer or categorical values.
enum IntegerParam {
PRESOLVE = 1000, // Presolve mode.
LP_ALGORITHM = 1001 // Algorithm to solve linear programs.
};
// For each categorical parameter, enumeration of possible values.
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.
};
// Values to indicate that a parameter is set to the solver's
// default value.
static const double kDefaultDoubleParamValue;
static const int kDefaultIntegerParamValue;
// Values 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 PresolveValues kDefaultPresolve;
// The constructor sets all parameters to their default value.
MPSolverParameters();
// Set parameter to a specific value.
void SetDoubleParam(MPSolverParameters::DoubleParam param, double value);
void SetIntegerParam(MPSolverParameters::IntegerParam param, int value);
// Reset parameter to the default value.
void ResetDoubleParam(MPSolverParameters::DoubleParam param);
void ResetIntegerParam(MPSolverParameters::IntegerParam param);
// Set all parameters to their default value.
void Reset();
// Get parameter's value.
double GetDoubleParam(MPSolverParameters::DoubleParam param) const;
int GetIntegerParam(MPSolverParameters::IntegerParam param) const;
private:
// Parameter value for each parameter.
double relative_mip_gap_value_;
int presolve_value_;
int lp_algorithm_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 serves as a proxy to open sources linear solver.
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;
// When the underlying solver does not provide the number of simplex
// nodes.
static const int64 kUnknownNumberOfNodes;
// When the index of a variable or constraint has not been assigned yet.
static const int kNoIndex;
// Constructor that takes a name for the underlying glpk solver.
explicit MPSolverInterface(MPSolver* const solver);
virtual ~MPSolverInterface();
// ----- Solve -----
// Solves problem with specified parameter values. Returns true if the
// solution is optimal. Calls WriteModelToPredefinedFiles as a
// temporary solution to allow the user to write the model to a
// file.
virtual MPSolver::ResultStatus Solve(const MPSolverParameters& param) = 0;
// ----- Model modifications and extraction -----
// Resets extracted model
virtual void Reset() = 0;
// Sets the optimization direction (min/max).
virtual void SetOptimizationDirection(bool minimize) = 0;
// Modify bounds of an extracted variable.
virtual void SetVariableBounds(int index, double lb, double ub) = 0;
// Modify 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;
// Add a constraint.
virtual void AddRowConstraint(MPConstraint* const ct) = 0;
// Add a variable.
virtual void AddVariable(MPVariable* const var) = 0;
// Change a coefficient in a constraint.
virtual void SetCoefficient(MPConstraint* const constraint,
MPVariable* const variable,
double new_value,
double old_value) = 0;
// Clear a constraint from all its terms.
virtual void ClearConstraint(MPConstraint* const constraint) = 0;
// Change a coefficient in the linear objective.
virtual void SetObjectiveCoefficient(MPVariable* const variable,
double coefficient) = 0;
// Change the constant term in the linear objective.
virtual void SetObjectiveOffset(double value) = 0;
// Clear the objective from all its terms.
virtual void ClearObjective() = 0;
// ------ Query statistics on the solution and the solve ------
// Number of simplex iterations
virtual int64 iterations() const = 0;
// Number of branch-and-bound nodes
virtual int64 nodes() const = 0;
// Best objective bound. Only available for discrete problems.
virtual double best_objective_bound() const = 0;
// Objective value of the best solution found so far.
double objective_value() const;
// Checks whether the solution is synchronized with the model,
// i.e. whether the model has changed since the solution was
// computed last.
void CheckSolutionIsSynchronized() const;
// Checks whether a feasible solution exists.
virtual void CheckSolutionExists() const;
// Checks whether information on the best objective bound exists.
virtual void CheckBestObjectiveBoundExists() const;
// ----- Misc -----
// Write model to file.
virtual void WriteModel(const string& filename) = 0;
// Query 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;
int last_variable_index() const {
return last_variable_index_;
}
bool quiet() const {
return quiet_;
}
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 string describing the solver.
virtual string SolverVersion() const = 0;
// Returns the underlying solver.
virtual void* underlying_solver() = 0;
friend class MPSolver;
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_;
bool maximize_;
// Index of last constraint extracted
int last_constraint_index_;
// Index 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;
// Writes out the model to a file specified by the
// --solver_write_model command line argument or
// MPSolver::set_write_model_filename.
// The file is written by each solver interface (CBC, CLP, GLPK) and
// each behaves a little differently.
// If filename ends in ".lp", then the file is written in the
// LP format (except for the CLP solver that does not support the LP
// format). In all other cases it is written in the MPS format.
void WriteModelToPredefinedFiles();
// Extracts model stored in MPSolver
void ExtractModel();
virtual void ExtractNewVariables() = 0;
virtual void ExtractNewConstraints() = 0;
virtual void ExtractObjective() = 0;
void ResetExtractionInformation();
// Change synchronization status from SOLUTION_SYNCHRONIZED to
// MODEL_SYNCHRONIZED. To be used for model changes.
void InvalidateSolutionSynchronization();
// Set parameters common to LP and MIP in the underlying solver.
void SetCommonParameters(const MPSolverParameters& param);
// Set MIP specific parameters in the underlying solver.
void SetMIPParameters(const MPSolverParameters& param);
// Set all parameters in the underlying solver.
virtual void SetParameters(const MPSolverParameters& param) = 0;
// Set an unsupported parameter.
void SetUnsupportedDoubleParam(MPSolverParameters::DoubleParam param) const;
void SetUnsupportedIntegerParam(MPSolverParameters::IntegerParam param) const;
// Set a supported parameter to an unsupported value.
void SetDoubleParamToUnsupportedValue(MPSolverParameters::DoubleParam param,
int value) const;
void SetIntegerParamToUnsupportedValue(MPSolverParameters::IntegerParam param,
double value) const;
// Set each parameter in the underlying solver.
virtual void SetRelativeMipGap(double value) = 0;
virtual void SetPresolveMode(int value) = 0;
virtual void SetLpAlgorithm(int value) = 0;
};
} // namespace operations_research
#endif // OR_TOOLS_LINEAR_SOLVER_LINEAR_SOLVER_H_