Coin Branch and Cut uses a generic OsiSolverInterface and its resolve capability. This does not give much flexibility so advanced users can inherit from the interface of choice. This describes such a solver for a long thin problem e.g. fast0507 again. As with all these examples it is not guaranteed that this is the fastest way to solve any of these problems - they are to illustrate techniques. The full code is in CbcSolver2.hpp and CbcSolver2.cpp (this code can be found in the CBC Samples directory, see Chapter 5, More Samples ). initialSolve is called a few times so although we will not gain much this is a simpler place to start. The example derives from OsiClpSolverInterface and the code is:
Example 3.10. initialSolve
// modelPtr_ is of type ClpSimplex *
modelPtr_->setLogLevel(1); // switch on a bit of printout
modelPtr_->scaling(0); // We don't want scaling for fast0507
setBasis(basis_,modelPtr_); // Put basis into ClpSimplex
// Do long thin by sprint
ClpSolve options;
options.setSolveType(ClpSolve::usePrimalorSprint);
options.setPresolveType(ClpSolve::presolveOff);
options.setSpecialOption(1,3,15); // Do 15 sprint iterations
modelPtr_->initialSolve(options); // solve problem
basis_ = getBasis(modelPtr_); // save basis
modelPtr_->setLogLevel(0); // switch off printout
The resolve method is more complicated. The main pieces of data are a counter count_ which is incremented each solve and an int array node_ which stores the last time a variable was active in a solution. For the first few times normal dual is called and node_ array is updated.
Example 3.11. First few solves
if (count_<10) {
OsiClpSolverInterface::resolve(); // Normal resolve
if (modelPtr_->status()==0) {
count_++; // feasible - save any nonzero or basic
const double * solution = modelPtr_->primalColumnSolution();
for (int i=0;i<numberColumns;i++) {
if (solution[i]>1.0e-6||modelPtr_->getStatus(i)==ClpSimplex::basic) {
node_[i]=CoinMax(count_,node_[i]);
howMany_[i]++;
}
}
} else {
printf("infeasible early on\n");
}
}
After the first few solves we only use those which took part in a solution in the last so many solves. As fast0507 is a set covering problem we can also take out any rows which are already covered.
Example 3.12. Create small problem
int * whichRow = new int[numberRows]; // Array to say which rows used
int * whichColumn = new int [numberColumns]; // Array to say which columns used
int i;
const double * lower = modelPtr_->columnLower();
const double * upper = modelPtr_->columnUpper();
setBasis(basis_,modelPtr_); // Set basis
int nNewCol=0; // Number of columns in small model
// Column copy of matrix
const double * element = modelPtr_->matrix()->getElements();
const int * row = modelPtr_->matrix()->getIndices();
const CoinBigIndex * columnStart = modelPtr_->matrix()->getVectorStarts();
const int * columnLength = modelPtr_->matrix()->getVectorLengths();
int * rowActivity = new int[numberRows]; // Number of columns with entries in each row
memset(rowActivity,0,numberRows*sizeof(int));
int * rowActivity2 = new int[numberRows]; // Lower bound on row activity for each row
memset(rowActivity2,0,numberRows*sizeof(int));
char * mark = (char *) modelPtr_->dualColumnSolution(); // Get some space to mark columns
memset(mark,0,numberColumns);
for (i=0;i<numberColumns;i++) {
bool choose = (node_[i]>count_-memory_&&node_[i]>0); // Choose if used recently
// Take if used recently or active in some sense
if ((choose&&upper[i])
||(modelPtr_->getStatus(i)!=ClpSimplex::atLowerBound&&
modelPtr_->getStatus(i)!=ClpSimplex::isFixed)
||lower[i]>0.0) {
mark[i]=1; // mark as used
whichColumn[nNewCol++]=i; // add to list
CoinBigIndex j;
double value = upper[i];
if (value) {
for (j=columnStart[i];
j<columnStart[i]+columnLength[i];j++) {
int iRow=row[j];
assert (element[j]==1.0);
rowActivity[iRow] ++; // This variable can cover this row
}
if (lower[i]>0.0) {
for (j=columnStart[i];
j<columnStart[i]+columnLength[i];j++) {
int iRow=row[j];
rowActivity2[iRow] ++; // This row redundant
}
}
}
}
}
int nOK=0; // Use to count rows which can be covered
int nNewRow=0; // Use to make list of rows needed
for (i=0;i<numberRows;i++) {
if (rowActivity[i])
nOK++;
if (!rowActivity2[i])
whichRow[nNewRow++]=i; // not satisfied
else
modelPtr_->setRowStatus(i,ClpSimplex::basic); // make slack basic
}
if (nOK<numberRows) {
// The variables we have do not cover rows - see if we can find any that do
for (i=0;i<numberColumns;i++) {
if (!mark[i]&&upper[i]) {
CoinBigIndex j;
int good=0;
for (j=columnStart[i];
j<columnStart[i]+columnLength[i];j++) {
int iRow=row[j];
if (!rowActivity[iRow]) {
rowActivity[iRow] ++;
good++;
}
}
if (good) {
nOK+=good; // This covers - put in list
whichColumn[nNewCol++]=i;
}
}
}
}
delete [] rowActivity;
delete [] rowActivity2;
if (nOK<numberRows) {
// By inspection the problem is infeasible - no need to solve
modelPtr_->setProblemStatus(1);
delete [] whichRow;
delete [] whichColumn;
printf("infeasible by inspection\n");
return;
}
// Now make up a small model with the right rows and columns
ClpSimplex * temp = new ClpSimplex(modelPtr_,nNewRow,whichRow,nNewCol,whichColumn);
If the variables cover the rows then we know that the problem is feasible (We are not using cuts). If the rows were E rows then this might not be the case and we would have to do more work. When we have solved then we see if there are any negative reduced costs and if there are then we have to go to the full problem and use primal to clean up.
Example 3.13. Check optimal solution
temp->setDualObjectiveLimit(1.0e50); // Switch off dual cutoff as problem is restricted
temp->dual(); // solve
double * solution = modelPtr_->primalColumnSolution(); // put back solution
const double * solution2 = temp->primalColumnSolution();
memset(solution,0,numberColumns*sizeof(double));
for (i=0;i<nNewCol;i++) {
int iColumn = whichColumn[i];
solution[iColumn]=solution2[i];
modelPtr_->setStatus(iColumn,temp->getStatus(i));
}
double * rowSolution = modelPtr_->primalRowSolution();
const double * rowSolution2 = temp->primalRowSolution();
double * dual = modelPtr_->dualRowSolution();
const double * dual2 = temp->dualRowSolution();
memset(dual,0,numberRows*sizeof(double));
for (i=0;i<nNewRow;i++) {
int iRow=whichRow[i];
modelPtr_->setRowStatus(iRow,temp->getRowStatus(i));
rowSolution[iRow]=rowSolution2[i];
dual[iRow]=dual2[i];
}
// See if optimal
double * dj = modelPtr_->dualColumnSolution();
// get reduced cost for large problem
// this assumes minimization
memcpy(dj,modelPtr_->objective(),numberColumns*sizeof(double));
modelPtr_->transposeTimes(-1.0,dual,dj);
modelPtr_->setObjectiveValue(temp->objectiveValue());
modelPtr_->setProblemStatus(0);
int nBad=0;
for (i=0;i<numberColumns;i++) {
if (modelPtr_->getStatus(i)==ClpSimplex::atLowerBound
&&upper[i]>lower[i]&&dj[i]<-1.0e-5)
nBad++;
}
// If necessary claen up with primal (and save some statistics)
if (nBad) {
timesBad_++;
modelPtr_->primal(1);
iterationsBad_ += modelPtr_->numberIterations();
}
We then update node_ array as for the first few solves. To give some idea of the effect of this tactic fast0507 has 63,009 variables and the small problem never has more than 4,000 variables. In just over ten percent of solves did we have to resolve and then the average number of iterations on full problem was less than 20. To give another example - again only for illustrative purposes it is possible to do quadratic mip. In this case we make resolve the same as initialSolve. The full code is in ClpQuadInterface.hpp and ClpQuadInterface.cpp (this code can be found in the CBC Samples directory, see Chapter 5, More Samples ).
Example 3.14. Solve a quadratic mip
// save cutoff
double cutoff = modelPtr_->dualObjectiveLimit();
modelPtr_->setDualObjectiveLimit(1.0e50);
modelPtr_->scaling(0);
modelPtr_->setLogLevel(0);
// solve with no objective to get feasible solution
setBasis(basis_,modelPtr_);
modelPtr_->dual();
basis_ = getBasis(modelPtr_);
modelPtr_->setDualObjectiveLimit(cutoff);
if (modelPtr_->problemStatus())
return; // problem was infeasible
// Now pass in quadratic objective
ClpObjective * saveObjective = modelPtr_->objectiveAsObject();
modelPtr_->setObjectivePointer(quadraticObjective_);
modelPtr_->primal();
modelPtr_->setDualObjectiveLimit(cutoff);
if (modelPtr_->objectiveValue()>cutoff)
modelPtr_->setProblemStatus(1);
modelPtr_->setObjectivePointer(saveObjective);