// This routine separates Benders' cuts violated by the current x solution.
// Violated cuts are found by solving the worker LP
//
IloBool
separate(const Arcs x, const IloNumArray2 xSol, IloCplex cplex,
const IloNumVarArray v, const IloNumVarArray u,
IloObjective obj, IloExpr cutLhs, IloNum& cutRhs)
{
IloBool violatedCutFound = IloFalse;
IloEnv env = cplex.getEnv();
IloModel mod = cplex.getModel();
IloInt numNodes = xSol.getSize();
IloInt numArcs = numNodes * numNodes;
IloInt i, j, k, h;
// Update the objective function in the worker LP:
// minimize sum(k in V0) sum((i,j) in A) x(i,j) * v(k,i,j)
// - sum(k in V0) u(k,0) + sum(k in V0) u(k,k)
mod.remove(obj);
IloExpr objExpr = obj.getExpr();
objExpr.clear();
for (k = 1; k < numNodes; ++k) {
for (i = 0; i < numNodes; ++i) {
for (j = 0; j < numNodes; ++j) {
objExpr += xSol[i][j] * v[(k-1)*numArcs + i*numNodes + j];
}
}
}
for (k = 1; k < numNodes; ++k) {
objExpr += u[(k-1)*numNodes + k];
objExpr -= u[(k-1)*numNodes];
}
obj.setExpr(objExpr);
mod.add(obj);
objExpr.end();
// Solve the worker LP
cplex.solve();
// A violated cut is available iff the solution status is Unbounded
if ( cplex.getStatus() == IloAlgorithm::Unbounded ) {
IloInt vNumVars = (numNodes-1) * numArcs;
IloNumVarArray var(env);
IloNumArray val(env);
// Get the violated cut as an unbounded ray of the worker LP
cplex.getRay(val, var);
// Compute the cut from the unbounded ray. The cut is:
// sum((i,j) in A) (sum(k in V0) v(k,i,j)) * x(i,j) >=
// sum(k in V0) u(k,0) - u(k,k)
cutLhs.clear();
cutRhs = 0.;
for (h = 0; h < val.getSize(); ++h) {
IloInt *index_p = (IloInt*) var[h].getObject();
IloInt index = *index_p;
if ( index >= vNumVars ) {
index -= vNumVars;
k = index / numNodes + 1;
i = index - (k-1)*numNodes;
if ( i == 0 )
cutRhs += val[h];
else if ( i == k )
cutRhs -= val[h];
}
else {
k = index / numArcs + 1;
i = (index - (k-1)*numArcs) / numNodes;
j = index - (k-1)*numArcs - i*numNodes;
cutLhs += val[h] * x[i][j];
}
}
var.end();
val.end();
violatedCutFound = IloTrue;
}
return violatedCutFound;
} // END separate
/** Separation function.
* This function is invoked whenever CPLEX finds an integer feasible
* solution. It then separates either feasibility or optimality cuts
* on this solution.
*/
void BendersOpt::LazyConstraintCallback::main() {
std::cout << "Callback invoked. Separate Benders cuts." << std::endl;
IloNumArray x(getEnv());
IloNumArray rayVals(getEnv());
IloNumVarArray rayVars(getEnv());
IloNumArray cutVal(getEnv());
IloNumVarArray cutVar(getEnv());
getValues(x, master->vars);
bool error = false;
// Iterate over blocks and trigger a separation on each of them.
// The separation is triggered asynchronously so that it can happen
// on different remote objects simultaneously.
for (BlockVector::size_type b = 0; b < blocks.size(); ++b) {
Block *const block = blocks[b];
// Remove current objective from the block's model.
IloModel model = block->cplex.getModel();
IloObjective obj = block->obj;
model.remove(obj);
IloExpr newObj = obj.getExpr();
// Iterate over the fixed master variables in this block to update
// the block's objective function.
// Each fixed variable goes to the right-hand side and therefore
// into the objective function.
for (std::vector<Block::FixData>::const_iterator it = block->fixed.begin(); it != block->fixed.end(); ++it)
newObj -= block->vars[it->row] * (it->val * x[it->col]);
obj.setExpr(newObj);
model.add(obj);
newObj.end();
// If the problem is unbounded we need to get an infinite ray in
// order to be able to generate the respective Benders cut. If
// CPLEX proves unboundedness in presolve then it will return
// CPX_STAT_INForUNBD and no ray will be available. So we need to
// disable presolve.
block->cplex.setParam(IloCplex::Param::Preprocessing::Presolve, false);
block->cplex.setParam(IloCplex::Param::Preprocessing::Reduce, 0);
// Solve the updated problem to optimality.
block->cplex.setParam(IloCplex::Param::RootAlgorithm, IloCplex::Primal);
try {
handles[b] = block->cplex.solve(true);
} catch (...) {
// If there is an exception then we need to kill and join
// all remaining solves. Otherwise we may leak handles.
while (--b > 0) {
handles[b].kill();
handles[b].join();
}
throw;
}
}
// Wait for the various LP solves to complete.
for (BlockVector::size_type b = 0; b < blocks.size(); ++b)
handles[b].join();
// See if we need to generate cuts.
for (BlockVector::size_type b = 0; b < blocks.size(); ++b) {
Block *const block = blocks[b];
cutVal.clear();
cutVar.clear();
double cutlb = -IloInfinity;
double cutub = IloInfinity;
// We ust STL types here since they are exception safe.
std::vector<double> tmp(master->vars.getSize(), 0);
std::map<IloNumVar,double,ExtractableLess<IloNumVar> > rayMap;
// Depending on the status either seperate a feasibility or an
// optimality cut.
switch (block->cplex.getStatus()) {
case IloAlgorithm::Unbounded:
{
// The subproblem is unbounded. We need to extract a feasibility
// cut from an unbounded ray of the problem (see also the comments
// at the top of this file).
std::cout << "unbounded ";
block->cplex.getRay(rayVals, rayVars);
cutub = 0.0;
for (IloInt j = 0; j < rayVars.getSize(); ++j) {
cutub -= rayVals[j] * block->objMap[rayVars[j]];
rayMap[rayVars[j]] = rayVals[j];
}
for (std::vector<Block::FixData>::const_iterator it = block->fixed.begin(); it != block->fixed.end(); ++it)
tmp[it->col] -= it->val * rayMap[block->vars[it->row]];
for (IloInt j = 0; j < master->vars.getSize(); ++j) {
if ( fabs (tmp[j]) > 1e-6 ) {
cutVar.add(master->vars[j]);
cutVal.add(tmp[j]);
}
}
}
break;
case IloAlgorithm::Optimal:
{
// The subproblem has a finite optimal solution.
// We need to check if this gives rise to an optimality cut (see
// also the comments at the top of this file).
std::cout << "optimal ";
double const objval = block->cplex.getObjValue();
double const eta = x[etaind + b];
block->cplex.getValues(block->vars, rayVals);
if ( objval > eta + 1e-6 ) {
cutub = 0.0;
for (IloInt j = 0; j < block->vars.getSize(); ++j)
cutub -= rayVals[j] * block->objMap[block->vars[j]];
for (std::vector<Block::FixData>::const_iterator it = block->fixed.begin(); it != block->fixed.end(); ++it)
tmp[it->col] -= it->val * rayVals[it->row];
for (IloInt j = 0; j < master->vars.getSize(); ++j) {
if ( fabs (tmp[j]) > 1e-6 ) {
cutVal.add(tmp[j]);
cutVar.add(master->vars[j]);
}
}
cutVal.add(-1.0);
cutVar.add(master->vars[etaind + b]);
}
}
break;
default:
std::cerr << "Unexpected status " << block->cplex.getStatus()
<< std::endl;
error = true;
break;
}
// If a cut was found then add that.
if ( cutVar.getSize() > 0 ) {
IloExpr expr(master->env);
for (IloInt i = 0; i < cutVar.getSize(); ++i)
expr += cutVar[i] * cutVal[i];
IloRange cut(getEnv(), cutlb, expr, cutub);
expr.end();
std::cout << "cut found: " << cut << std::endl;
add(cut).end();
}
else
std::cout << "no cuts." << std::endl;
}
cutVar.end();
cutVal.end();
rayVars.end();
rayVals.end();
x.end();
if ( error )
throw -1;
}
