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-// Last edit: 04/03/10
-//
-// Name: CglRedSplit2.hpp
-// Author: Giacomo Nannicini
-// Singapore University of Technology and Design
-// Singapore
-// email: nannicini@sutd.edu.sg
-// based on CglRedSplit by Francois Margot
-// Date: 03/09/09
-//-----------------------------------------------------------------------------
-// Copyright (C) 2010, Giacomo Nannicini and others. All Rights Reserved.
-
-#ifndef CglRedSplit2_H
-#define CglRedSplit2_H
-
-#include "CglCutGenerator.hpp"
-#include "CglRedSplit2Param.hpp"
-#include "CoinWarmStartBasis.hpp"
-#include "CoinHelperFunctions.hpp"
-#include "CoinTime.hpp"
-
-/** Reduce-and-Split Cut Generator Class; See method generateCuts().
- Based on the papers "Practical strategies for generating rank-1
- split cuts in mixed-integer linear programming" by G. Cornuejols
- and G. Nannicini, published on Mathematical Programming
- Computation, and "Combining Lift-and-Project and Reduce-and-Split"
- by E. Balas, G. Cornuejols, T. Kis and G. Nannicini, published on
- INFORMS Journal on Computing. Part of this code is based on
- CglRedSplit by F. Margot. */
-
-class CglRedSplit2 : public CglCutGenerator {
-
- friend void CglRedSplit2UnitTest(const OsiSolverInterface * siP,
- const std::string mpdDir);
-public:
- /**@name generateCuts */
- //@{
- /** Generate Reduce-and-Split Mixed Integer Gomory cuts
- for the model of the solver interface si.
-
- Insert the generated cuts into OsiCuts cs.
-
- 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 a class of split cuts. We compute
- linear combinations of the rows of the simplex tableau, trying
- to reduce some of the coefficients on the nonbasic continuous
- columns. We have a large number of heuristics to choose which
- coefficients should be reduced, and by using which rows. The
- paper explains everything in detail.
-
- Note that this generator can potentially generate a huge number
- of cuts, depending on how it is parametered. Default parameters
- should be good for most situations; if you want to go heavy on
- split cuts, use more row selection strategies or a different
- number of rows in the linear combinations. Again, look at the
- paper for details. If you want to generate a small number of
- cuts, default parameters are not the best choice.
-
- A combination of Reduce-and-Split with Lift & Project is
- described in the paper "Combining Lift-and-Project and
- Reduce-and-Split". The Reduce-and-Split code for the
- implementation used in that paper is included here.
-
- This generator does not generate the same cuts as CglRedSplit,
- therefore both generators can be used in conjunction.
-
- */
-
- virtual void generateCuts(const OsiSolverInterface & si, OsiCuts & cs,
- const CglTreeInfo info = CglTreeInfo());
-
- /// Return true if needs optimal basis to do cuts (will return true)
- virtual bool needsOptimalBasis() const;
-
- // Generate the row multipliers computed by Reduce-and-Split from the
- // given OsiSolverInterface. The multipliers are written in lambda;
- // lambda should be of size nrow*maxNumMultipliers. We generate at most
- // maxNumMultipliers m-vectors of row multipliers, and return the number
- // of m-vectors that were generated.
- // If the caller wants to know which variables are basic in each row
- // (same order as lambda), basicVariables should be non-NULL (size nrow).
- // This method can also generate the cuts corresponding to the multipliers
- // returned; it suffices to pass non-NULL OsiCuts.
- // This method is not needed by the typical user; however, it is useful
- // in the context of generating Lift & Project cuts.
- int generateMultipliers(const OsiSolverInterface& si, int* lambda,
- int maxNumMultipliers, int* basicVariables = NULL,
- OsiCuts* cs = NULL);
-
- // Try to improve a Lift & Project cut, by employing the
- // Reduce-and-Split procedure. We start from a row of a L&P tableau,
- // and generate a cut trying to reduce the coefficients on the
- // nonbasic variables. Note that this L&P tableau will in general
- // have nonbasic variables which are nonzero in the point that we
- // want to cut off, so we should be careful. Arguments:
- // OsiSolverInterface which contains the simplex tableau, initial
- // row from which the cut is derived, row rhs, row number of the
- // source row (if it is in the simplex tableau; otherwise, a
- // negative number; needed to avoid using duplicate rows), point
- // that we want to cut off (note: this is NOT a basic solution for
- // the OsiSolverInterace!), list of variables which are basic in
- // xbar but are nonbasic in the OsiSolverInterface. The computed cut
- // is written in OsiRowCut* cs. Finally, if a starting disjunction
- // is provided in the vector lambda (of size ncols, i.e. a
- // disjunction on the structural variables), the disjunction is
- // modified according to the cut which is produced.
- int tiltLandPcut(const OsiSolverInterface* si, double* row,
- double rowRhs, int rownumber, const double* xbar,
- const int* newnonbasics, OsiRowCut* cs, int* lambda = NULL);
-
- //@}
-
-
- /**@name Public Methods */
- //@{
-
- // Set the parameters to the values of the given CglRedSplit2Param object.
- void setParam(const CglRedSplit2Param &source);
- // Return the CglRedSplit2Param object of the generator.
- inline CglRedSplit2Param& getParam() {return param;}
-
- /// Print some of the data members; used for debugging
- void print() const;
-
- /// Print the current simplex tableau
- void printOptTab(OsiSolverInterface *solver) const;
-
- //@}
-
- /**@name Constructors and destructors */
- //@{
- /// Default constructor
- CglRedSplit2();
-
- /// Constructor with specified parameters
- CglRedSplit2(const CglRedSplit2Param &RS_param);
-
- /// Copy constructor
- CglRedSplit2(const CglRedSplit2 &);
-
- /// Clone
- virtual CglCutGenerator * clone() const;
-
- /// Assignment operator
- CglRedSplit2 & operator=(const CglRedSplit2& rhs);
-
- /// Destructor
- virtual ~CglRedSplit2 ();
-
- //@}
-
-private:
-
- // Private member methods
-
-/**@name Private member methods */
-
- //@{
-
- // Method generating the cuts after all CglRedSplit2 members are
- // properly set. This does the actual work. Returns the number of
- // generated cuts (or multipliers).
- // Will generate cuts if cs != NULL, and will generate multipliers
- // if lambda != NULL.
- int generateCuts(OsiCuts* cs, int maxNumCuts, int* lambda = NULL);
-
- /// Compute the fractional part of value, allowing for small error.
- inline double rs_above_integer(const double value) const;
-
- /// Fill workNonBasicTab, depending on the column selection strategy.
- /// Accepts a list of variables indices that should be ignored; by
- /// default, this list is empty (it is only used by Lift & Project).
- /// The list ignore_list contains -1 as the last element.
- /// Note that the implementation of the ignore_list is not very efficient
- /// if the list is long, so it should be used only if its short.
- void fill_workNonBasicTab(CglRedSplit2Param::ColumnSelectionStrategy
- strategy, const int* ignore_list = NULL);
-
- /// Fill workNonBasicTab, alternate version for Lift & Project: also
- /// reduces columns which are now nonbasic but are basic in xbar.
- /// This function should be called only when CglRedSplit2 is used in
- /// conjunction with CglLandP to generate L&P+RS cuts.
- void fill_workNonBasicTab(const int* newnonbasics, const double* xbar,
- CglRedSplit2Param::ColumnScalingStrategy scaling);
-
- /// Reduce rows of workNonBasicTab, i.e. compute integral linear
- /// combinations of the rows in order to reduce row coefficients on
- /// workNonBasicTab
- void reduce_workNonBasicTab(int numRows,
- CglRedSplit2Param::RowSelectionStrategy
- rowSelectionStrategy,
- int maxIterations);
-
- /// Generate a linear combination of the rows of the current LP
- /// tableau, using the row multipliers stored in the matrix pi_mat
- /// on the row of index index_row
- void generate_row(int index_row, double *row);
-
- /// Generate a mixed integer Gomory cut, when all non basic
- /// variables are non negative and at their lower bound.
- int generate_cgcut(double *row, double *rhs);
-
- /// Use multiples of the initial inequalities to cancel out the coefficients
- /// of the slack variables.
- void eliminate_slacks(double *row,
- const double *elements,
- const int *start,
- const int *indices,
- const int *rowLength,
- const double *rhs, double *rowrhs);
-
- /// Change the sign of the coefficients of the continuous non basic
- /// variables at their upper bound.
- void flip(double *row);
-
- /// 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.
- void unflip(double *row, double *rowrhs);
-
- /// Returns 1 if the row has acceptable max/min coeff ratio.
- /// Compute max_coeff: maximum absolute value of the coefficients.
- /// Compute min_coeff: minimum absolute value of the coefficients
- /// larger than EPS_COEFF.
- /// Return 0 if max_coeff/min_coeff > MAXDYN.
- int check_dynamism(double *row);
-
- /// Generate the packed cut from the row representation.
- int generate_packed_row(const double *xlp, double *row,
- int *rowind, double *rowelem,
- int *card_row, double & rhs);
-
- // Compute entries of is_integer.
- void compute_is_integer();
-
- // Check that two vectors are different.
- bool rs_are_different_vectors(const int *vect1,
- const int *vect2,
- const int dim);
-
- // allocate matrix of integers
- void rs_allocmatINT(int ***v, int m, int n);
- // deallocate matrix of integers
- void rs_deallocmatINT(int ***v, int m);
- // allocate matrix of doubles
- void rs_allocmatDBL(double ***v, int m, int n);
- // deallocate matrix of doubles
- void rs_deallocmatDBL(double ***v, int m);
- // print a vector of integers
- void rs_printvecINT(const char *vecstr, const int *x, int n) const;
- // print a vector of doubles
- void rs_printvecDBL(const char *vecstr, const double *x, int n) const;
- // print a matrix of integers
- void rs_printmatINT(const char *vecstr, const int * const *x, int m, int n) const;
- // print a matrix of doubles
- void rs_printmatDBL(const char *vecstr, const double * const *x, int m, int n) const;
- // dot product
- double rs_dotProd(const double *u, const double *v, int dim) const;
- double rs_dotProd(const int *u, const double *v, int dim) const;
- // From Numerical Recipes in C: LU decomposition
- int ludcmp(double **a, int n, int *indx, double *d, double* vv) const;
- // from Numerical Recipes in C: backward substitution
- void lubksb(double **a, int n, int *indx, double *b) const;
-
- // Check if the linear combination given by listOfRows with given multipliers
- // improves the norm of row #rowindex; note: multipliers are rounded!
- // Returns the difference with respect to the old norm (if negative there is
- // an improvement, if positive norm increases)
- double compute_norm_change(double oldnorm, const int* listOfRows,
- int numElemList, const double* multipliers) const;
-
- // Compute the list of rows that should be used to reduce row #rowIndex
- int get_list_rows_reduction(int rowIndex, int numRowsReduction,
- int* list, const double* norm,
- CglRedSplit2Param::RowSelectionStrategy
- rowSelectionStrategy) const;
-
- // Sorts the rows by increasing number of nonzeroes with respect to a given
- // row (rowIndex), on the nonbasic variables (whichTab == 0 means only
- // integer, whichTab == 1 means only workTab, whichTab == 2 means both).
- // The array for sorting must be allocated (and deleted) by caller.
- // Corresponds to BRS1 in the paper.
- int sort_rows_by_nonzeroes(struct sortElement* array, int rowIndex,
- int maxRows, int whichTab) const;
-
- // Greedy variant of the previous function; slower but typically
- // more effective. Corresponds to BRS2 in the paper.
- int sort_rows_by_nonzeroes_greedy(struct sortElement* array, int rowIndex,
- int maxRows, int whichTab) const;
-
- // Sorts the rows by decreasing absolute value of the cosine of the
- // angle with respect to a given row (rowIndex), on the nonbasic
- // variables (whichTab == 0 means only integer, whichTab == 1 means
- // only workTab, whichTab == 2 means both). The array for sorting
- // must be allocated (and deleted) by caller. Very effective
- // strategy in practice. Corresponds to BRS3 in the paper.
- int sort_rows_by_cosine(struct sortElement* array, int rowIndex,
- int maxRows, int whichTab) const;
-
- // Did we hit the time limit?
- inline bool checkTime() const{
- if ((CoinCpuTime() - startTime) < param.getTimeLimit()){
- return true;
- }
- return false;
- }
-
- //@}
-
-
- // Private member data
-
- /**@name Private member data */
-
- //@{
-
- /// Object with CglRedSplit2Param members.
- CglRedSplit2Param param;
-
- /// Number of rows ( = number of slack variables) in the current LP.
- int nrow;
-
- /// Number of structural variables in the current LP.
- int ncol;
-
- /// Number of rows which have been reduced
- int numRedRows;
-
- /// Lower bounds for structural variables
- const double *colLower;
-
- /// Upper bounds for structural variables
- const double *colUpper;
-
- /// Lower bounds for constraints
- const double *rowLower;
-
- /// Upper bounds for constraints
- const double *rowUpper;
-
- /// Righ hand side for constraints (upper bound for ranged constraints).
- const double *rowRhs;
-
- /// Reduced costs for columns
- const double *reducedCost;
-
- /// Row price
- const double *rowPrice;
-
- /// Objective coefficients
- const double* objective;
-
- /// Number of integer basic structural variables
- int card_intBasicVar;
-
- /// Number of integer basic structural variables that are fractional in the
- /// current lp solution (at least param.away_ from being integer).
- int card_intBasicVar_frac;
-
- /// Number of integer non basic structural variables in the
- /// current lp solution.
- int card_intNonBasicVar;
-
- /// Number of continuous non basic variables (structural or slack) in the
- /// current lp solution.
- int card_contNonBasicVar;
-
- /// Number of continuous non basic variables (structural or slack) in the
- /// current working set for coefficient reduction
- int card_workNonBasicVar;
-
- /// Number of non basic variables (structural or slack) at their
- /// upper bound in the current lp solution.
- int card_nonBasicAtUpper;
-
- /// Number of non basic variables (structural or slack) at their
- /// lower bound in the current lp solution.
- int card_nonBasicAtLower;
-
- /// Characteristic vector for integer basic structural variables
- int *cv_intBasicVar;
-
- /// Characteristic vector for integer basic structural variables
- /// with non integer value in the current lp solution.
- int *cv_intBasicVar_frac;
-
- /// Characteristic vector for rows of the tableau selected for reduction
- /// with non integer value in the current lp solution
- int *cv_fracRowsTab;
-
- /// List of integer structural basic variables
- /// (in order of pivot in selected rows for cut generation).
- int *intBasicVar;
-
- /// List of integer structural basic variables with fractional value
- /// (in order of pivot in selected rows for cut generation).
- int *intBasicVar_frac;
-
- /// List of integer structural non basic variables.
- int *intNonBasicVar;
-
- /// List of continuous non basic variables (structural or slack).
- // slacks are considered continuous (no harm if this is not the case).
- int *contNonBasicVar;
-
- /// List of non basic variables (structural or slack) at their
- /// upper bound.
- int *nonBasicAtUpper;
-
- /// List of non basic variables (structural or slack) at their lower
- /// bound.
- int *nonBasicAtLower;
-
- /// Number of rows in the reduced tableau (= card_intBasicVar).
- int mTab;
-
- /// Number of columns in the reduced tableau (= card_contNonBasicVar)
- int nTab;
-
- /// Tableau of multipliers used to alter the rows used in generation.
- /// Dimensions: mTab by mTab. Initially, pi_mat is the identity matrix.
- int **pi_mat;
-
- /// Simplex tableau for continuous non basic variables (structural or slack).
- /// Only rows used for generation.
- /// Dimensions: mTab by card_contNonBasicVar.
- double **contNonBasicTab;
-
- /// Current tableau for continuous non basic variables (structural or slack).
- /// Only columns used for coefficient reduction.
- /// Dimensions: mTab by card_workNonBasicVar.
- double **workNonBasicTab;
-
- /// Simplex tableau for integer non basic structural variables.
- /// Only rows used for generation.
- // Dimensions: mTab by card_intNonBasicVar.
- double **intNonBasicTab;
-
- /// Right hand side of the tableau.
- /// Only rows used for generation.
- double *rhsTab;
-
- /// Norm of rows in workNonBasicTab; needed for faster computations
- double *norm;
-
- /// Characteristic vectors of structural integer variables or continuous
- /// variables currently fixed to integer values.
- int *is_integer;
-
- /// Pointer on solver. Reset by each call to generateCuts().
- OsiSolverInterface *solver;
-
- /// Pointer on point to separate. Reset by each call to generateCuts().
- const double *xlp;
-
- /// Pointer on row activity. Reset by each call to generateCuts().
- const double *rowActivity;
-
- /// Pointer on matrix of coefficient ordered by rows.
- /// Reset by each call to generateCuts().
- const CoinPackedMatrix *byRow;
-
- /// Time at which cut computations began.
- /// Reset by each call to generateCuts().
- double startTime;
-
- //@}
-};
-
-//#############################################################################
-/** A function that tests some of the methods in the CglRedSplit2
- class. The only reason for it not to be a member method is that
- this way it doesn't have to be compiled into the library. And
- that's a gain, because the library should be compiled with
- optimization on, but this method should be compiled with
- debugging. */
-void CglRedSplit2UnitTest(const OsiSolverInterface * siP,
- const std::string mpdDir );
-
-
-#endif