CglRedSplit Class Reference

Gomory Reduce-and-Split Cut Generator Class; See method generateCuts(). More...

#include <CglRedSplit.hpp>

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List of all members.

Public Member Functions

Generate Cuts
virtual void generateCuts (const OsiSolverInterface &si, OsiCuts &cs, const CglTreeInfo info=CglTreeInfo())
 Generate Reduce-and-Split Mixed Integer Gomory cuts for the model of the solver interface si.
virtual void generateCuts (const OsiSolverInterface &si, OsiCuts &cs, const CglTreeInfo info=CglTreeInfo()) const
 For compatibility with CglCutGenerator (const method).
virtual bool needsOptimalBasis () const
 Return true if needs optimal basis to do cuts (will return true).
Parameters
void setLimit (int limit)
 Set limit, the maximum number of non zero coefficients in generated cut; Default: 50.
int getLimit () const
 Get value of limit.
void setAway (double value)
 Set away, the minimum distance from being integer used for selecting rows for cut generation; all rows whose pivot variable should be integer but is more than away from integrality will be selected; Default: 0.05.
double getAway () const
 Get value of away.
void setLUB (double value)
 Set the value of LUB, value considered large for the absolute value of a lower or upper bound on a variable; Default: 1000.
double getLUB () const
 Get the value of LUB.
void setEPS (double value)
 Set the value of EPS, epsilon for double computations; Default: 1e-7.
double getEPS () const
 Get the value of EPS.
void setEPS_COEFF (double value)
 Set the value of EPS_COEFF, epsilon for values of coefficients; Default: 1e-8.
double getEPS_COEFF () const
 Get the value of EPS_COEFF.
void setEPS_COEFF_LUB (double value)
 Set the value of EPS_COEFF_LUB, epsilon for values of coefficients for variables with absolute value of lower or upper bound larger than LUB; Default: 1e-13.
double getEPS_COEFF_LUB () const
 Get the value of EPS_COEFF_LUB.
void setEPS_RELAX (double value)
 Set the value of EPS_RELAX, value used for relaxing the right hand side of each generated cut; Default: 1e-8.
double getEPS_RELAX () const
 Get the value of EPS_RELAX.
void setNormIsZero (double value)
 Set the value of normIsZero, the threshold for considering a norm to be 0; Default: 1e-5.
double getNormIsZero () const
 Get the value of normIsZero.
void setMinReduc (double value)
 Set the value of minReduc, threshold for relative norm improvement for performing a reduction; Default: 0.05.
double getMinReduc () const
 Get the value of minReduc.
void setMaxTab (double value)
 Set the maximum allowed value for (mTab * mTab * max(mTab, nTab)) where mTab is the number of rows used in the combinations and nTab is the number of continuous non basic variables.
double getMaxTab () const
 Get the value of maxTab.
void set_given_optsol (const double *given_sol, const int card_sol)
 Set given_optsol to the given optimal solution given_sol.
void print () const
 Print some of the data members.
void printOptTab (OsiSolverInterface *solver) const
 Print the current simplex tableau.
Constructors and destructors
 CglRedSplit ()
 Default constructor.
 CglRedSplit (const CglRedSplit &)
 Copy constructor.
virtual CglCutGeneratorclone () const
 Clone.
CglRedSplitoperator= (const CglRedSplit &rhs)
 Assignment operator.
virtual ~CglRedSplit ()
 Destructor.
virtual std::string generateCpp (FILE *fp)
 Create C++ lines to get to current state.

Private Member Functions

Private member methods
double rs_above_integer (double value)
 Compute the fractional part of value, allowing for small error.
void update_pi_mat (int r1, int r2, int step)
 Perform row r1 of pi := row r1 of pi - step * row r2 of pi.
void update_redTab (int r1, int r2, int step)
 Perform row r1 of tab := row r1 of tab - step * row r2 of tab.
void find_step (int r1, int r2, int *step, double *reduc, double *norm)
 Find optimal integer step for changing row r1 by adding to it a multiple of another row r2.
int test_pair (int r1, int r2, double *norm)
 Test if an ordered pair of rows yields a reduction.
void reduce_contNonBasicTab ()
 Reduce rows of contNonBasicTab.
void generate_row (int index_row, double *row)
 Generate a row of the current LP tableau.
int generate_cgcut (double *row, double *rhs)
 Generate a mixed integer Chvatal-Gomory cut, when all non basic variables are non negative and at their lower bound.
void eliminate_slacks (double *row, const double *elements, const int *start, const int *indices, const int *rowLength, const double *rhs, double *rowrhs)
 Use multiples of the initial inequalities to cancel out the coefficients of the slack variables.
void flip (double *row)
 Change the sign of the coefficients of the continuous non basic variables at their upper bound.
void unflip (double *row, double *rowrhs, const double *colLower, const double *colUpper, double *slack_val)
 Change the sign of the coefficients of the continuous non basic variables at their upper bound and do the translations restoring the original bounds.
int generate_packed_row (const OsiSolverInterface *solver, double *row, int *rowind, double *rowelem, int *card_row, double &rhs)
 Generate the packed cut from the row representation.
void check_optsol (const OsiSolverInterface *solver, const int calling_place, const double *xlp, const double *slack_val, const int do_flip)
 Check that the generated cuts do not cut a given optimal solution.
void check_optsol (const OsiSolverInterface *solver, const int calling_place, const double *ck_row, const double ck_rhs, const int cut_number, const int do_flip)
 Check that the generated cuts do not cut a given optimal solution.

Private Attributes

Private member data
int nrow
 Number of rows ( = number of slack variables) in the current LP.
int ncol
 Number of structural variables in the current LP.
double LUB
 Value considered large for the absolute value of lower or upper bound on a variable.
double EPS
 Epsilon for precision. Default: 1e-7.
double EPS_COEFF
 Epsilon for value of coefficients. Default: 1e-8.
double EPS_COEFF_LUB
 Epsilon for value of coefficients for variables with absolute value of lower or upper bound larger than LUB.
double EPS_RELAX
 Epsilon for relaxing the right hand side of each generated constraint.
double normIsZero
 Norm of a vector is considered zero if smaller than normIsZero; Default: 1e-5.
double minReduc
 Minimum reduction in percent that must be achieved by a potential reduction step in order to be performed; Between 0 and 1, default: 0.05.
int card_intBasicVar_frac
 Number of integer basic structural variables that are fractional in the current lp solution (at least away_ from being integer).
int card_intNonBasicVar
 Number of integer non basic structural variables in the current lp solution.
int card_contNonBasicVar
 Number of continuous non basic variables (structural or slack) in the current lp solution.
int card_nonBasicAtUpper
 Number of non basic variables (structural or slack) at their upper bound in the current lp solution.
int card_nonBasicAtLower
 Number of non basic variables (structural or slack) at their lower bound in the current lp solution.
int * cv_intBasicVar_frac
 Characteristic vector for integer basic structural variables with non integer value in the current lp solution.
int * intBasicVar_frac
 List of integer structural basic variables (in order of pivot in selected rows for cut generation).
int * intNonBasicVar
 List of integer structural non basic variables.
int * contNonBasicVar
 List of continuous non basic variables (structural or slack).
int * nonBasicAtUpper
 List of non basic variables (structural or slack) at their upper bound.
int * nonBasicAtLower
 List of non basic variables (structural or slack) at their lower bound.
int mTab
 Number of rows in the reduced tableau (= card_intBasicVar_frac).
int nTab
 Number of columns in the reduced tableau (= card_contNonBasicVar).
int ** pi_mat
 Tableau of multipliers used to alter the rows used in generation.
double ** contNonBasicTab
 Current tableau for continuous non basic variables (structural or slack).
double ** intNonBasicTab
 Current tableau for integer non basic structural variables.
double * rhsTab
 Right hand side of the tableau.
double away_
 Use row only if pivot variable should be integer but is more than away_ from being integer.
int limit_
 Generate cut only if at most limit_ non zero coefficients in cut.
double maxTab_
 Maximum value for (mTab * mTab * max(mTab, nTab)).
double * given_optsol
 Given optimal solution that should not be cut; only for debug.
int card_given_optsol
 Number of entries in given_optsol.

Detailed Description

Gomory Reduce-and-Split Cut Generator Class; See method generateCuts().

Based on the paper by K. Anderson, G. Cornuejols, Yanjun Li, "Reduce-and-Split Cuts: Improving the Performance of Mixed Integer Gomory Cuts", (2005), to appear in Management Science

Definition at line 22 of file CglRedSplit.hpp.


Constructor & Destructor Documentation

CglRedSplit::CglRedSplit (  ) 

Default constructor.

CglRedSplit::CglRedSplit ( const CglRedSplit  ) 

Copy constructor.

virtual CglRedSplit::~CglRedSplit (  )  [virtual]

Destructor.


Member Function Documentation

virtual void CglRedSplit::generateCuts ( const OsiSolverInterface si,
OsiCuts cs,
const CglTreeInfo  info = CglTreeInfo() 
) [virtual]

Generate Reduce-and-Split Mixed Integer Gomory cuts for the model of the solver interface si.

Insert the generated cuts into OsiCuts cs.

Warning: This generator currently works only with the Lp solvers Clp or Cplex9.0 or higher. It requires access to the optimal tableau and optimal basis inverse and makes assumptions on the way slack variables are added by the solver. The Osi implementations for Clp and Cplex verify these assumptions.

When calling the generator, the solver interface si must contain an optimized problem and information related to the optimal basis must be available through the OsiSolverInterface methods (si->optimalBasisIsAvailable() must return 'true'). It is also essential that the integrality of structural variable i can be obtained using si->isInteger(i).

Reduce-and-Split cuts are variants of Gomory cuts: Starting from the current optimal tableau, linear combinations of the rows of the current optimal simplex tableau are used for generating Gomory cuts. The choice of the linear combinations is driven by the objective of reducing the coefficients of the non basic continuous variables in the resulting row. Note that this generator might not be able to generate cuts for some solutions violating integrality constraints.

Parameters of the generator are listed below. Modifying the default values for parameters other than the last five might result in invalid cuts.

virtual void CglRedSplit::generateCuts ( const OsiSolverInterface si,
OsiCuts cs,
const CglTreeInfo  info = CglTreeInfo() 
) const [virtual]

For compatibility with CglCutGenerator (const method).

Implements CglCutGenerator.

virtual bool CglRedSplit::needsOptimalBasis (  )  const [virtual]

Return true if needs optimal basis to do cuts (will return true).

Reimplemented from CglCutGenerator.

void CglRedSplit::setLimit ( int  limit  ) 

Set limit, the maximum number of non zero coefficients in generated cut; Default: 50.

int CglRedSplit::getLimit (  )  const

Get value of limit.

void CglRedSplit::setAway ( double  value  ) 

Set away, the minimum distance from being integer used for selecting rows for cut generation; all rows whose pivot variable should be integer but is more than away from integrality will be selected; Default: 0.05.

double CglRedSplit::getAway (  )  const

Get value of away.

void CglRedSplit::setLUB ( double  value  ) 

Set the value of LUB, value considered large for the absolute value of a lower or upper bound on a variable; Default: 1000.

double CglRedSplit::getLUB (  )  const

Get the value of LUB.

void CglRedSplit::setEPS ( double  value  ) 

Set the value of EPS, epsilon for double computations; Default: 1e-7.

double CglRedSplit::getEPS (  )  const

Get the value of EPS.

void CglRedSplit::setEPS_COEFF ( double  value  ) 

Set the value of EPS_COEFF, epsilon for values of coefficients; Default: 1e-8.

double CglRedSplit::getEPS_COEFF (  )  const

Get the value of EPS_COEFF.

void CglRedSplit::setEPS_COEFF_LUB ( double  value  ) 

Set the value of EPS_COEFF_LUB, epsilon for values of coefficients for variables with absolute value of lower or upper bound larger than LUB; Default: 1e-13.

double CglRedSplit::getEPS_COEFF_LUB (  )  const

Get the value of EPS_COEFF_LUB.

void CglRedSplit::setEPS_RELAX ( double  value  ) 

Set the value of EPS_RELAX, value used for relaxing the right hand side of each generated cut; Default: 1e-8.

double CglRedSplit::getEPS_RELAX (  )  const

Get the value of EPS_RELAX.

void CglRedSplit::setNormIsZero ( double  value  ) 

Set the value of normIsZero, the threshold for considering a norm to be 0; Default: 1e-5.

double CglRedSplit::getNormIsZero (  )  const

Get the value of normIsZero.

void CglRedSplit::setMinReduc ( double  value  ) 

Set the value of minReduc, threshold for relative norm improvement for performing a reduction; Default: 0.05.

double CglRedSplit::getMinReduc (  )  const

Get the value of minReduc.

void CglRedSplit::setMaxTab ( double  value  ) 

Set the maximum allowed value for (mTab * mTab * max(mTab, nTab)) where mTab is the number of rows used in the combinations and nTab is the number of continuous non basic variables.

The work of the generator is proportional to (mTab * mTab * max(mTab, nTab)). Reducing the value of maxTab makes the generator faster, but weaker. Default: 1e7.

double CglRedSplit::getMaxTab (  )  const

Get the value of maxTab.

void CglRedSplit::set_given_optsol ( const double *  given_sol,
const int  card_sol 
)

Set given_optsol to the given optimal solution given_sol.

If given_optsol is set using this method, the code will stop as soon as a generated cut is violated by the given solution; exclusively for debugging purposes.

void CglRedSplit::print (  )  const

Print some of the data members.

void CglRedSplit::printOptTab ( OsiSolverInterface solver  )  const

Print the current simplex tableau.

virtual CglCutGenerator* CglRedSplit::clone (  )  const [virtual]

Clone.

Implements CglCutGenerator.

CglRedSplit& CglRedSplit::operator= ( const CglRedSplit rhs  ) 

Assignment operator.

virtual std::string CglRedSplit::generateCpp ( FILE *  fp  )  [virtual]

Create C++ lines to get to current state.

Reimplemented from CglCutGenerator.

double CglRedSplit::rs_above_integer ( double  value  )  [inline, private]

Compute the fractional part of value, allowing for small error.

void CglRedSplit::update_pi_mat ( int  r1,
int  r2,
int  step 
) [private]

Perform row r1 of pi := row r1 of pi - step * row r2 of pi.

void CglRedSplit::update_redTab ( int  r1,
int  r2,
int  step 
) [private]

Perform row r1 of tab := row r1 of tab - step * row r2 of tab.

void CglRedSplit::find_step ( int  r1,
int  r2,
int *  step,
double *  reduc,
double *  norm 
) [private]

Find optimal integer step for changing row r1 by adding to it a multiple of another row r2.

int CglRedSplit::test_pair ( int  r1,
int  r2,
double *  norm 
) [private]

Test if an ordered pair of rows yields a reduction.

Perform the reduction if it is acceptable.

void CglRedSplit::reduce_contNonBasicTab (  )  [private]

Reduce rows of contNonBasicTab.

void CglRedSplit::generate_row ( int  index_row,
double *  row 
) [private]

Generate a row of the current LP tableau.

int CglRedSplit::generate_cgcut ( double *  row,
double *  rhs 
) [private]

Generate a mixed integer Chvatal-Gomory cut, when all non basic variables are non negative and at their lower bound.

void CglRedSplit::eliminate_slacks ( double *  row,
const double *  elements,
const int *  start,
const int *  indices,
const int *  rowLength,
const double *  rhs,
double *  rowrhs 
) [private]

Use multiples of the initial inequalities to cancel out the coefficients of the slack variables.

void CglRedSplit::flip ( double *  row  )  [private]

Change the sign of the coefficients of the continuous non basic variables at their upper bound.

void CglRedSplit::unflip ( double *  row,
double *  rowrhs,
const double *  colLower,
const double *  colUpper,
double *  slack_val 
) [private]

Change the sign of the coefficients of the continuous non basic variables at their upper bound and do the translations restoring the original bounds.

Modify the right hand side accordingly.

int CglRedSplit::generate_packed_row ( const OsiSolverInterface solver,
double *  row,
int *  rowind,
double *  rowelem,
int *  card_row,
double &  rhs 
) [private]

Generate the packed cut from the row representation.

void CglRedSplit::check_optsol ( const OsiSolverInterface solver,
const int  calling_place,
const double *  xlp,
const double *  slack_val,
const int  do_flip 
) [private]

Check that the generated cuts do not cut a given optimal solution.

void CglRedSplit::check_optsol ( const OsiSolverInterface solver,
const int  calling_place,
const double *  ck_row,
const double  ck_rhs,
const int  cut_number,
const int  do_flip 
) [private]

Check that the generated cuts do not cut a given optimal solution.


Member Data Documentation

int CglRedSplit::nrow [private]

Number of rows ( = number of slack variables) in the current LP.

Definition at line 282 of file CglRedSplit.hpp.

int CglRedSplit::ncol [private]

Number of structural variables in the current LP.

Definition at line 285 of file CglRedSplit.hpp.

double CglRedSplit::LUB [private]

Value considered large for the absolute value of lower or upper bound on a variable.

Default: 1000.

Definition at line 289 of file CglRedSplit.hpp.

double CglRedSplit::EPS [private]

Epsilon for precision. Default: 1e-7.

Definition at line 292 of file CglRedSplit.hpp.

double CglRedSplit::EPS_COEFF [private]

Epsilon for value of coefficients. Default: 1e-8.

Definition at line 295 of file CglRedSplit.hpp.

double CglRedSplit::EPS_COEFF_LUB [private]

Epsilon for value of coefficients for variables with absolute value of lower or upper bound larger than LUB.

Default: 1e-13.

Definition at line 299 of file CglRedSplit.hpp.

double CglRedSplit::EPS_RELAX [private]

Epsilon for relaxing the right hand side of each generated constraint.

Default: 1e-8.

Definition at line 303 of file CglRedSplit.hpp.

double CglRedSplit::normIsZero [private]

Norm of a vector is considered zero if smaller than normIsZero; Default: 1e-5.

Definition at line 307 of file CglRedSplit.hpp.

double CglRedSplit::minReduc [private]

Minimum reduction in percent that must be achieved by a potential reduction step in order to be performed; Between 0 and 1, default: 0.05.

Definition at line 311 of file CglRedSplit.hpp.

int CglRedSplit::card_intBasicVar_frac [private]

Number of integer basic structural variables that are fractional in the current lp solution (at least away_ from being integer).

Definition at line 315 of file CglRedSplit.hpp.

int CglRedSplit::card_intNonBasicVar [private]

Number of integer non basic structural variables in the current lp solution.

Definition at line 319 of file CglRedSplit.hpp.

int CglRedSplit::card_contNonBasicVar [private]

Number of continuous non basic variables (structural or slack) in the current lp solution.

Definition at line 323 of file CglRedSplit.hpp.

int CglRedSplit::card_nonBasicAtUpper [private]

Number of non basic variables (structural or slack) at their upper bound in the current lp solution.

Definition at line 327 of file CglRedSplit.hpp.

int CglRedSplit::card_nonBasicAtLower [private]

Number of non basic variables (structural or slack) at their lower bound in the current lp solution.

Definition at line 331 of file CglRedSplit.hpp.

int* CglRedSplit::cv_intBasicVar_frac [private]

Characteristic vector for integer basic structural variables with non integer value in the current lp solution.

Definition at line 335 of file CglRedSplit.hpp.

int* CglRedSplit::intBasicVar_frac [private]

List of integer structural basic variables (in order of pivot in selected rows for cut generation).

Definition at line 339 of file CglRedSplit.hpp.

int* CglRedSplit::intNonBasicVar [private]

List of integer structural non basic variables.

Definition at line 342 of file CglRedSplit.hpp.

int* CglRedSplit::contNonBasicVar [private]

List of continuous non basic variables (structural or slack).

Definition at line 346 of file CglRedSplit.hpp.

int* CglRedSplit::nonBasicAtUpper [private]

List of non basic variables (structural or slack) at their upper bound.

Definition at line 350 of file CglRedSplit.hpp.

int* CglRedSplit::nonBasicAtLower [private]

List of non basic variables (structural or slack) at their lower bound.

Definition at line 354 of file CglRedSplit.hpp.

int CglRedSplit::mTab [private]

Number of rows in the reduced tableau (= card_intBasicVar_frac).

Definition at line 357 of file CglRedSplit.hpp.

int CglRedSplit::nTab [private]

Number of columns in the reduced tableau (= card_contNonBasicVar).

Definition at line 360 of file CglRedSplit.hpp.

int** CglRedSplit::pi_mat [private]

Tableau of multipliers used to alter the rows used in generation.

Dimensions: mTab by mTab. Initially, pi_mat is the identity matrix.

Definition at line 364 of file CglRedSplit.hpp.

double** CglRedSplit::contNonBasicTab [private]

Current tableau for continuous non basic variables (structural or slack).

Only rows used for generation. Dimensions: mTab by nTab.

Definition at line 369 of file CglRedSplit.hpp.

double** CglRedSplit::intNonBasicTab [private]

Current tableau for integer non basic structural variables.

Only rows used for generation.

Definition at line 374 of file CglRedSplit.hpp.

double* CglRedSplit::rhsTab [private]

Right hand side of the tableau.

Only rows used for generation.

Definition at line 378 of file CglRedSplit.hpp.

double CglRedSplit::away_ [private]

Use row only if pivot variable should be integer but is more than away_ from being integer.

Definition at line 382 of file CglRedSplit.hpp.

int CglRedSplit::limit_ [private]

Generate cut only if at most limit_ non zero coefficients in cut.

Definition at line 384 of file CglRedSplit.hpp.

double CglRedSplit::maxTab_ [private]

Maximum value for (mTab * mTab * max(mTab, nTab)).

See method setMaxTab().

Definition at line 388 of file CglRedSplit.hpp.

double* CglRedSplit::given_optsol [private]

Given optimal solution that should not be cut; only for debug.

Definition at line 391 of file CglRedSplit.hpp.

int CglRedSplit::card_given_optsol [private]

Number of entries in given_optsol.

Definition at line 394 of file CglRedSplit.hpp.


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