/*
It may be the case that the bounds on the variables in a constraint are
such that no matter what feasible value the variables take, the constraint
cannot be violated. In this case we can drop the constraint as useless.
On the other hand, it may be that the only way to satisfy a constraint
is to jam all the variables in the constraint to one of their bounds, fixing
the variables. This is a forcing constraint, the primary target of this
transform.
Detection of both useless and forcing constraints requires calculation of
bounds on the row activity (often referred to as lhs bounds, from the common
form ax <= b). This routine will remember useless constraints as it finds
them and invoke useless_constraint_action to deal with them.
The transform applied here simply tightens the bounds on the variables.
Other transforms will remove the fixed variables, leaving an empty row which
is ultimately dropped.
A reasonable question to ask is ``If a variable is already fixed, why do
we need a record in the postsolve object?'' The answer is that in postsolve
we'll be dealing with a column-major representation and we may need to scan
the row (see postsolve comments). So it's useful to record all variables in
the constraint.
On the other hand, it's definitely harmful to ask remove_fixed_action
to process a variable more than once (causes problems in
remove_fixed_action::postsolve).
Original comments:
It looks like these checks could be performed in parallel, that is,
the tests could be carried out for all rows in parallel, and then the
rows deleted and columns tightened afterward. Obviously, this is true
for useless rows. By doing it in parallel rather than sequentially,
we may miss transformations due to variables that were fixed by forcing
constraints, though.
Note that both of these operations will cause problems if the variables
in question really need to exceed their bounds in order to make the
problem feasible.
*/
const CoinPresolveAction*
forcing_constraint_action::presolve (CoinPresolveMatrix *prob,
const CoinPresolveAction *next)
{
# if PRESOLVE_DEBUG > 0 || COIN_PRESOLVE_TUNING
int startEmptyRows = 0 ;
int startEmptyColumns = 0 ;
startEmptyRows = prob->countEmptyRows() ;
startEmptyColumns = prob->countEmptyCols() ;
# endif
# if PRESOLVE_DEBUG > 0 || PRESOLVE_CONSISTENCY > 0
# if PRESOLVE_DEBUG > 0
std::cout
<< "Entering forcing_constraint_action::presolve, considering "
<< prob->numberRowsToDo_ << " rows." << std::endl ;
# endif
presolve_check_sol(prob) ;
presolve_check_nbasic(prob) ;
# endif
# if COIN_PRESOLVE_TUNING
double startTime = 0.0 ;
if (prob->tuning_) {
startTime = CoinCpuTime() ;
}
# endif
// Column solution and bounds
double *clo = prob->clo_ ;
double *cup = prob->cup_ ;
double *csol = prob->sol_ ;
// Row-major representation
const CoinBigIndex *mrstrt = prob->mrstrt_ ;
const double *rowels = prob->rowels_ ;
const int *hcol = prob->hcol_ ;
const int *hinrow = prob->hinrow_ ;
const int nrows = prob->nrows_ ;
const double *rlo = prob->rlo_ ;
const double *rup = prob->rup_ ;
const double tol = ZTOLDP ;
const double inftol = prob->feasibilityTolerance_ ;
// for redundant rows be safe
const double inftol2 = 0.01*prob->feasibilityTolerance_ ;
const int ncols = prob->ncols_ ;
int *fixed_cols = new int[ncols] ;
int nfixed_cols = 0 ;
action *actions = new action [nrows] ;
int nactions = 0 ;
int *useless_rows = new int[nrows] ;
int nuseless_rows = 0 ;
const int numberLook = prob->numberRowsToDo_ ;
int *look = prob->rowsToDo_ ;
bool fixInfeasibility = ((prob->presolveOptions_&0x4000) != 0) ;
/*
Open a loop to scan the constraints of interest. There must be variables
left in the row.
*/
for (int iLook = 0 ; iLook < numberLook ; iLook++) {
int irow = look[iLook] ;
if (hinrow[irow] <= 0) continue ;
const CoinBigIndex krs = mrstrt[irow] ;
const CoinBigIndex kre = krs+hinrow[irow] ;
/*
Calculate upper and lower bounds on the row activity based on upper and lower
bounds on the variables. If these are finite and incompatible with the given
row bounds, we have infeasibility.
*/
double maxup, maxdown ;
implied_row_bounds(rowels,clo,cup,hcol,krs,kre,maxup,maxdown) ;
# if PRESOLVE_DEBUG > 2
std::cout
<< " considering row " << irow << ", rlo " << rlo[irow]
<< " LB " << maxdown << " UB " << maxup << " rup " << rup[irow] ;
# endif
/*
If the maximum lhs value is less than L(i) or the minimum lhs value is
greater than U(i), we're infeasible.
*/
if (maxup < PRESOLVE_INF &&
maxup+inftol < rlo[irow] && !fixInfeasibility) {
CoinMessageHandler *hdlr = prob->messageHandler() ;
prob->status_|= 1 ;
hdlr->message(COIN_PRESOLVE_ROWINFEAS,prob->messages())
<< irow << rlo[irow] << rup[irow] << CoinMessageEol ;
# if PRESOLVE_DEBUG > 2
std::cout << "; infeasible." << std::endl ;
# endif
break ;
}
if (-PRESOLVE_INF < maxdown &&
rup[irow] < maxdown-inftol && !fixInfeasibility) {
CoinMessageHandler *hdlr = prob->messageHandler() ;
prob->status_|= 1 ;
hdlr->message(COIN_PRESOLVE_ROWINFEAS,prob->messages())
<< irow << rlo[irow] << rup[irow] << CoinMessageEol ;
# if PRESOLVE_DEBUG > 2
std::cout << "; infeasible." << std::endl ;
# endif
break ;
}
/*
We've dealt with prima facie infeasibility. Now check if the constraint
is trivially satisfied. If so, add it to the list of useless rows and move
on.
The reason we require maxdown and maxup to be finite if the row bound is
finite is to guard against some subsequent transform changing a column
bound from infinite to finite. Once finite, bounds continue to tighten,
so we're safe.
*/
/* Test changed to use +small tolerance rather than -tolerance
as test fails often */
if (((rlo[irow] <= -PRESOLVE_INF) ||
(-PRESOLVE_INF < maxdown && rlo[irow] <= maxdown+inftol2)) &&
((rup[irow] >= PRESOLVE_INF) ||
(maxup < PRESOLVE_INF && rup[irow] >= maxup-inftol2))) {
// check none prohibited
if (prob->anyProhibited_) {
bool anyProhibited=false;
for (int k=krs; k<kre; k++) {
int jcol = hcol[k];
if (prob->colProhibited(jcol)) {
anyProhibited=true;
break;
}
}
if (anyProhibited)
continue; // skip row
}
useless_rows[nuseless_rows++] = irow ;
# if PRESOLVE_DEBUG > 2
std::cout << "; useless." << std::endl ;
# endif
continue ;
}
/*
Is it the case that we can just barely attain L(i) or U(i)? If so, we have a
forcing constraint. As explained above, we need maxup and maxdown to be
finite in order for the test to be valid.
*/
const bool tightAtLower = ((maxup < PRESOLVE_INF) &&
(fabs(rlo[irow]-maxup) < tol)) ;
const bool tightAtUpper = ((-PRESOLVE_INF < maxdown) &&
(fabs(rup[irow]-maxdown) < tol)) ;
# if PRESOLVE_DEBUG > 2
if (tightAtLower || tightAtUpper) std::cout << "; forcing." ;
std::cout << std::endl ;
# endif
if (!(tightAtLower || tightAtUpper)) continue ;
// check none prohibited
if (prob->anyProhibited_) {
bool anyProhibited=false;
for (int k=krs; k<kre; k++) {
int jcol = hcol[k];
if (prob->colProhibited(jcol)) {
anyProhibited=true;
break;
}
}
if (anyProhibited)
continue; // skip row
}
/*
We have a forcing constraint.
Get down to the business of fixing the variables at the appropriate bound.
We need to remember the original value of the bound we're tightening.
Allocate a pair of arrays the size of the row. Load variables fixed at l<j>
from the start, variables fixed at u<j> from the end. Add the column to
the list of columns to be processed further.
*/
double *bounds = new double[hinrow[irow]] ;
int *rowcols = new int[hinrow[irow]] ;
CoinBigIndex lk = krs ;
CoinBigIndex uk = kre ;
for (CoinBigIndex k = krs ; k < kre ; k++) {
const int j = hcol[k] ;
const double lj = clo[j] ;
const double uj = cup[j] ;
const double coeff = rowels[k] ;
PRESOLVEASSERT(fabs(coeff) > ZTOLDP) ;
/*
If maxup is tight at L(i), then we want to force variables x<j> to the bound
that produced maxup: u<j> if a<ij> > 0, l<j> if a<ij> < 0. If maxdown is
tight at U(i), it'll be just the opposite.
*/
if (tightAtLower == (coeff > 0.0)) {
--uk ;
bounds[uk-krs] = lj ;
rowcols[uk-krs] = j ;
if (csol != 0) {
csol[j] = uj ;
}
clo[j] = uj ;
} else {
bounds[lk-krs] = uj ;
rowcols[lk-krs] = j ;
++lk ;
if (csol != 0) {
csol[j] = lj ;
}
cup[j] = lj ;
}
/*
Only add a column to the list of fixed columns the first time it's fixed.
*/
if (lj != uj) {
fixed_cols[nfixed_cols++] = j ;
prob->addCol(j) ;
}
}
PRESOLVEASSERT(uk == lk) ;
PRESOLVE_DETAIL_PRINT(printf("pre_forcing %dR E\n",irow)) ;
# if PRESOLVE_DEBUG > 1
std::cout
<< "FORCING: row(" << irow << "), " << (kre-krs) << " variables."
<< std::endl ;
# endif
/*
Done with this row. Remember the changes in a postsolve action.
*/
action *f = &actions[nactions] ;
nactions++ ;
f->row = irow ;
f->nlo = lk-krs ;
f->nup = kre-uk ;
f->rowcols = rowcols ;
f->bounds = bounds ;
}
/*
Done processing the rows of interest. No sense doing any additional work
unless we're feasible.
*/
if (prob->status_ == 0) {
# if PRESOLVE_DEBUG > 0
std::cout
<< "FORCING: " << nactions << " forcing, " << nuseless_rows << " useless."
<< std::endl ;
# endif
/*
Trim the actions array to size and create a postsolve object.
*/
if (nactions) {
next = new forcing_constraint_action(nactions,
CoinCopyOfArray(actions,nactions),next) ;
}
/*
Hand off the job of dealing with the useless rows to a specialist.
*/
if (nuseless_rows) {
next = useless_constraint_action::presolve(prob,
useless_rows,nuseless_rows,next) ;
}
/*
Hand off the job of dealing with the fixed columns to a specialist.
Note that there *cannot* be duplicates in this list or we'll get in trouble
`unfixing' a column multiple times. The code above now adds a variable
to fixed_cols only if it's not already fixed. If that ever changes,
the disabled code (sort, unique) will need to be reenabled.
*/
if (nfixed_cols) {
if (false && nfixed_cols > 1) {
std::sort(fixed_cols,fixed_cols+nfixed_cols) ;
int *end = std::unique(fixed_cols,fixed_cols+nfixed_cols) ;
nfixed_cols = static_cast<int>(end-fixed_cols) ;
}
next = remove_fixed_action::presolve(prob,fixed_cols,nfixed_cols,next) ;
}
} else {
// delete arrays
for (int i=0;i<nactions;i++) {
deleteAction(actions[i].rowcols,int *) ;
deleteAction(actions[i].bounds,double *) ;
}
}
deleteAction(actions,action*) ;
delete [] useless_rows ;
delete [] fixed_cols ;
# if COIN_PRESOLVE_TUNING
if (prob->tuning_) double thisTime = CoinCpuTime() ;
# endif
# if PRESOLVE_DEBUG > 0 || PRESOLVE_CONSISTENCY > 0
presolve_check_sol(prob) ;
presolve_check_nbasic(prob) ;
# endif
# if PRESOLVE_DEBUG > 0 || COIN_PRESOLVE_TUNING
int droppedRows = prob->countEmptyRows()-startEmptyRows ;
int droppedColumns = prob->countEmptyCols()-startEmptyColumns ;
std::cout
<< "Leaving forcing_constraint_action::presolve: removed " << droppedRows
<< " rows, " << droppedColumns << " columns" ;
# if COIN_PRESOLVE_TUNING > 0
if (prob->tuning_)
std::cout << " in " << (thisTime-prob->startTime_) << "s" ;
# endif
std::cout << "." << std::endl ;
# endif
return (next) ;
}
const CoinPresolveAction
*forcing_constraint_action::presolve(CoinPresolveMatrix *prob,
const CoinPresolveAction *next)
{
double startTime = 0.0;
int startEmptyRows=0;
int startEmptyColumns = 0;
if (prob->tuning_) {
startTime = CoinCpuTime();
startEmptyRows = prob->countEmptyRows();
startEmptyColumns = prob->countEmptyCols();
}
double *clo = prob->clo_;
double *cup = prob->cup_;
double *csol = prob->sol_ ;
const double *rowels = prob->rowels_;
const int *hcol = prob->hcol_;
const CoinBigIndex *mrstrt = prob->mrstrt_;
const int *hinrow = prob->hinrow_;
const int nrows = prob->nrows_;
const double *rlo = prob->rlo_;
const double *rup = prob->rup_;
// const char *integerType = prob->integerType_;
const double tol = ZTOLDP;
const double inftol = prob->feasibilityTolerance_;
const int ncols = prob->ncols_;
int *fixed_cols = new int[ncols];
int nfixed_cols = 0;
action *actions = new action [nrows];
int nactions = 0;
int *useless_rows = new int[nrows];
int nuseless_rows = 0;
int numberLook = prob->numberRowsToDo_;
int iLook;
int * look = prob->rowsToDo_;
bool fixInfeasibility = (prob->presolveOptions_&16384)!=0;
# if PRESOLVE_DEBUG
std::cout << "Entering forcing_constraint_action::presolve." << std::endl ;
presolve_check_sol(prob) ;
# endif
/*
Open a loop to scan the constraints of interest. There must be variables
left in the row.
*/
for (iLook=0;iLook<numberLook;iLook++) {
int irow = look[iLook];
if (hinrow[irow] > 0) {
CoinBigIndex krs = mrstrt[irow];
CoinBigIndex kre = krs + hinrow[irow];
/*
Calculate upper and lower bounds on the row activity based on upper and lower
bounds on the variables. If these are finite and incompatible with the given
row bounds, we have infeasibility.
*/
double maxup, maxdown;
implied_row_bounds(rowels, clo, cup, hcol, krs, kre,
&maxup, &maxdown);
if (maxup < PRESOLVE_INF && maxup + inftol < rlo[irow]&&!fixInfeasibility) {
/* max row activity below the row lower bound */
prob->status_|= 1;
prob->messageHandler()->message(COIN_PRESOLVE_ROWINFEAS,
prob->messages())
<<irow
<<rlo[irow]
<<rup[irow]
<<CoinMessageEol;
break;
} else if (-PRESOLVE_INF < maxdown && rup[irow] < maxdown - inftol&&!fixInfeasibility) {
/* min row activity above the row upper bound */
prob->status_|= 1;
prob->messageHandler()->message(COIN_PRESOLVE_ROWINFEAS,
prob->messages())
<<irow
<<rlo[irow]
<<rup[irow]
<<CoinMessageEol;
break;
}
// ADD TOLERANCE TO THESE TESTS
else if ((rlo[irow] <= -PRESOLVE_INF ||
(-PRESOLVE_INF < maxdown && rlo[irow] <= maxdown)) &&
(rup[irow] >= PRESOLVE_INF ||
(maxup < PRESOLVE_INF && rup[irow] >= maxup))) {
/*
Original comment: I'm not sure that these transforms don't intefere with
each other. We can get it next time.
Well, I'll argue that bounds are never really loosened (at worst, they're
transferred onto some other variable, or inferred to be unnecessary.
Once useless, always useless. Leaving this hook in place allows for a sort
of infinite loop where this routine keeps queuing the same constraints over
and over. -- lh, 040901 --
if (some_col_was_fixed(hcol, krs, kre, clo, cup)) {
prob->addRow(irow);
continue;
}
*/
// this constraint must always be satisfied - drop it
useless_rows[nuseless_rows++] = irow;
} else if ((maxup < PRESOLVE_INF && fabs(rlo[irow] - maxup) < tol) ||
(-PRESOLVE_INF < maxdown && fabs(rup[irow] - maxdown) < tol)) {
// the lower bound can just be reached, or
// the upper bound can just be reached;
// called a "forcing constraint" in the paper (p. 226)
const int lbound_tight = (maxup < PRESOLVE_INF &&
fabs(rlo[irow] - maxup) < tol);
/*
Original comment and rebuttal as above.
if (some_col_was_fixed(hcol, krs, kre, clo, cup)) {
// make sure on next time
prob->addRow(irow);
continue;
}
*/
// out of space - this probably never happens (but this routine will
// often put duplicates in the fixed column list)
if (nfixed_cols + (kre-krs) >= ncols)
break;
double *bounds = new double[hinrow[irow]];
int *rowcols = new int[hinrow[irow]];
int lk = krs; // load fix-to-down in front
int uk = kre; // load fix-to-up in back
CoinBigIndex k;
for ( k=krs; k<kre; k++) {
int jcol = hcol[k];
prob->addCol(jcol);
double coeff = rowels[k];
PRESOLVEASSERT(fabs(coeff) > ZTOLDP);
// one of the two contributed to maxup - set the other to that
if (lbound_tight == (coeff > 0.0)) {
--uk;
bounds[uk-krs] = clo[jcol];
rowcols[uk-krs] = jcol;
if (csol != 0) {
csol[jcol] = cup[jcol] ;
}
clo[jcol] = cup[jcol];
} else {
bounds[lk-krs] = cup[jcol];
rowcols[lk-krs] = jcol;
++lk;
if (csol != 0) {
csol[jcol] = clo[jcol] ;
}
cup[jcol] = clo[jcol];
}
fixed_cols[nfixed_cols++] = jcol;
}
PRESOLVEASSERT(uk == lk);
action *f = &actions[nactions];
nactions++;
f->row = irow;
f->nlo = lk-krs;
f->nup = kre-uk;
f->rowcols = rowcols;
f->bounds = bounds;
}
}
}
if (nactions) {
#if PRESOLVE_SUMMARY
printf("NFORCED: %d\n", nactions);
#endif
next = new forcing_constraint_action(nactions,
CoinCopyOfArray(actions,nactions), next);
}
deleteAction(actions,action*);
if (nuseless_rows) {
next = useless_constraint_action::presolve(prob,
useless_rows, nuseless_rows,
next);
}
delete[]useless_rows;
/*
We need to remove duplicates here, or we get into trouble in
remove_fixed_action::postsolve when we try to reinstate a column multiple
times.
*/
if (nfixed_cols)
{ if (nfixed_cols > 1)
{ std::sort(fixed_cols,fixed_cols+nfixed_cols) ;
int *end = std::unique(fixed_cols,fixed_cols+nfixed_cols) ;
nfixed_cols = static_cast<int>(end-fixed_cols) ; }
next = remove_fixed_action::presolve(prob,fixed_cols,nfixed_cols,next) ; }
delete[]fixed_cols ;
if (prob->tuning_) {
double thisTime=CoinCpuTime();
int droppedRows = prob->countEmptyRows() - startEmptyRows ;
int droppedColumns = prob->countEmptyCols() - startEmptyColumns;
printf("CoinPresolveForcing(32) - %d rows, %d columns dropped in time %g, total %g\n",
droppedRows,droppedColumns,thisTime-startTime,thisTime-prob->startTime_);
}
# if PRESOLVE_DEBUG
presolve_check_sol(prob) ;
std::cout << "Leaving forcing_constraint_action::presolve." << std::endl ;
# endif
return (next);
}