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CBC uses a generic OsiSolverInterface and its resolve capability. This does not give much flexibility so advanced users can inherit from their interface of choice. This section illustrates how to implement a specialized solver for a long thin problem, e.g., fast0507 again. As with the other examples in the Guide, the sample code is not guaranteed to be the fastest way to solve the problem. The main purpose of the example is to illustrate techniques. The full source is in CbcSolver2.hpp and CbcSolver2.cpp located in the CBC Samples directory, see Chapter 8, More Samples .
The method initialSolve is called a few times in CBC, and provides a convenient starting point. The modelPtr_ derives from OsiClpSolverInterface.
Example 7.1. 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 than initialSolve(). The main pieces of data are a counter count_ which is incremented each solve and an integer array node_ which stores the last time a variable was active in a solution. For the first few solves, the normal Dual Simplex is called and node_ array is updated.
Example 7.2. 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, only those variables which took part in a solution in the last so many solves are used. As fast0507 is a set covering problem, any rows which are already covered can be taken out.
Example 7.3. Create Small Sub-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 the problem is feasible (no cuts are being used). (If the rows were equality constraints, then this might not be the case. More work would be needed.) After the solution to the subproblem, the reduced costs of the full problem are checked. If the reduced cost of any variable not in the subproblem is negative, the code goes back to the full problem and cleans up with Primal Simplex.
Example 7.4. 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 clean up with primal (and save some statistics)
if (nBad) {
timesBad_++;
modelPtr_->primal(1);
iterationsBad_ += modelPtr_->numberIterations();
}
The array node_ is updated, as for the first few solves. To give some idea of the effect of this tactic, the problem fast0507 has 63,009 variables but the small problem never has more than 4,000 variables. In only about ten percent of solves was it necessary to resolve, and then the average number of iterations on full problem was less than 20.