static void
solveanddisplay (IloEnv env, IloCplex cplex, IloNumVarArray var,
IloRangeArray con)
{
// Optimize the problem and obtain solution.
if ( !cplex.solve() ) {
env.error() << "Failed to optimize LP" << endl;
throw(-1);
}
IloNumArray vals(env);
env.out() << "Solution status = " << cplex.getStatus() << endl;
env.out() << "Solution value = " << cplex.getObjValue() << endl;
cplex.getValues(vals, var);
env.out() << "Values = " << vals << endl;
cplex.getSlacks(vals, con);
env.out() << "Slacks = " << vals << endl;
cplex.getDuals(vals, con);
env.out() << "Duals = " << vals << endl;
cplex.getReducedCosts(vals, var);
env.out() << "Reduced Costs = " << vals << endl;
} // END solveanddisplay
// 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
bool FrontalSolverWithoutConnexity::solve(int borne_max, bool warmstart) {
LOG(INFO) << name_ << " :: " << description_;
//Extracting data
VLOG(2) << "Extracting data";
int n = data_.n;
int m = data_.m;
double Ba = data_.Ba;
double Bp = data_.Bp;
const vector<vector<double> >& Ha = data_.Ha;
const vector<vector<double> >& Ca = data_.Ca;
const vector<vector<double> >& Hp = data_.Hp;
const vector<vector<double> >& Cp = data_.Cp;
//Environement
VLOG(2) << "Creating environment";
IloEnv env;
IloModel model = IloModel (env);
IloCplex cplex = IloCplex(model);
//Variables
VLOG(2) << "Creating variables";
BoolVarMatrix x(env);
NumVarMatrix y(env);
NumVarMatrix z(env);
VLOG(2) << "Creating variables";
for (int i = 0; i < m ; ++i) {
x.add(IloBoolVarArray(env,n));
y.add(IloNumVarArray(env,n,0,Bp));
z.add(IloNumVarArray(env,n,0,Ba));
}
IloNumVar ha_var(env);
model.add(ha_var);
IloNumVar hp_var(env);
model.add(hp_var);
//Objective function
VLOG(2) << "Processing objective function";
IloExpr objective(env,0);
for (int i = 0; i < m ; ++i) {
for (int j = 0; j < n ; ++j) {
objective += x[i][j];
}
}
model.add(IloMaximize(env, objective ));
VLOG(2) << "Creating constraint expressions";
IloExpr sum_Cy(env,0);
IloExpr sum_HCPx(env,0);
IloExpr sum_Cz(env,0);
IloExpr sum_HCAx(env,0);
VLOG(2) << "Computing constraint expressions";
for (int i = 0; i < m ; ++i) {
for (int j = 0; j < n ; ++j) {
VLOG(5) << i << " " << j << " " << Cp[i][j] << endl;
sum_Cy += y[i][j]*Cp[i][j];
sum_Cz += z[i][j]*Ca[i][j];
sum_HCPx += x[i][j]*Hp[i][j]*Cp[i][j];
sum_HCAx += x[i][j]*Ha[i][j]*Ca[i][j];
}
}
VLOG(2) << "Adding constraints";
//Selection of an admissible area
model.add(sum_Cy == sum_HCPx);
model.add(sum_Cz == sum_HCAx);
model.add(ha_var + hp_var >= 2);
for (int i = 0; i < m ; ++i) {
for (int j = 0; j < n ; ++j) {
//Defining y
model.add(y[i][j] <= Bp*x[i][j]);
model.add(y[i][j] <= hp_var);
model.add(y[i][j] >= hp_var - Bp*(1-x[i][j]));
model.add(y[i][j] >= 0);
//Defining z
model.add(z[i][j] <= Ba*x[i][j]);
model.add(z[i][j] <= ha_var);
model.add(z[i][j] >= ha_var - Ba*(1-x[i][j]));
model.add(z[i][j] >= 0);
//Constraint on x
if (Cp[i][j] == 0)
model.add(x[i][j]==0);
}
}
// Warmstart
if (warmstart) {
// Setting Warmstart from solution
VLOG(2) << "Setting informations for warmstart";
IloNumVarArray startVar(env);
IloNumArray startVal(env);
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) {
startVar.add(x[i][j]);
startVal.add(sol_.x_[i][j]);
if (sol_.x_[i][j] == 0){
startVar.add(y[i][j]);
startVal.add(sol_.x_[i][j]);
startVar.add(z[i][j]);
startVal.add(sol_.x_[i][j]);
}
}
cplex.addMIPStart(startVar, startVal);
startVal.end();
startVar.end();
}
//Solve
VLOG(2) << "Resolution...";
cplex.solve();
//Output
VLOG(2) << "Solution status = " << cplex.getStatus() << endl;
VLOG(2) << "Solution value = " << cplex.getObjValue() << endl;
for (int i = 0; i < data_.m; ++i) {
for (int j = 0; j < data_.n; ++j) {
sol_.x_[i][j] = cplex.getValue(x[i][j]);
}
}
env.end();
return false;
}
/** Get the solution status for this worker.
* Calling this function before calling join() is an error.
*/
IloAlgorithm::Status getStatus() const { return cplex.getStatus(); }
std::string CPLEX_LP_MSTSolverIF::getCPLEXStatus(IloCplex& cplex) {
std::ostringstream oss { };
oss << cplex.getStatus() << std::flush;
return oss.str();
}