void Callback::constructRHS( GraphVariables const & vars
, NodeSet const & dS
, NodeSet const & S
, IloExpr & rhs
) const {
rhs.clear();
for ( Graph::Node const & j : dS ) {
rhs += vars.xVars[vars.nodeToIndex[j]];
}
for ( Graph::Node const & j : S ) {
rhs += vars.yVars[vars.nodeToIndex[j]];
}
}
int CProblem::setModel() {
//time_t start, end;
numvar = 1+n; // lambda + all c;
IloEnv env;
try {
IloModel model(env);
IloCplex cplex(env);
/*Variables*/
IloNumVar lambda(env, "lambda");
IloNumVarArray c(env, n);//
for (unsigned int u=0; u<n; u++) {
std::stringstream ss;
ss << u;
std::string str = "c" + ss.str();
c[u]=IloNumVar(env, str.c_str());
}
IloArray<IloIntVarArray> z(env,n);
for (unsigned int u=0; u<n; u++) {
z[u]= IloIntVarArray(env, n);
for (unsigned int v=0; v<n; v++) {
std::stringstream ss;
ss << u;
ss << v;
std::string str = "z" + ss.str();
z[u][v] = IloIntVar(env, 0, 1, str.c_str());
}
}
/* Constant M*/
int M=n*max_d;
UB = M;
/* Objective*/
model.add(IloMinimize(env, lambda));
//model.add(IloMinimize(env, IloSum(c)));
/*Constrains*/
model.add(lambda - UB <= 0);
/* d=function of the distance */
IloArray<IloNumArray> Par_d(env,n);
for (unsigned int u=0; u<n; u++) {
Par_d[u]=IloNumArray(env,n);
for (unsigned int v=0; v<n; v++) {
Par_d[u][v]=d[u][v];
}
}
for (unsigned u=0; u<n; u++) {
for (unsigned v=0; v<u; v++) {
model.add(c[v]-c[u]+M* z[u][v] >= Par_d[u][v] );
model.add(c[u]-c[v]+M*(1-z[u][v]) >= Par_d[u][v]);
numvar++; // + z[u][v]
}
}
/*
for (unsigned i=0; i<sqrt(n)-1; i=i+1) {
for (unsigned j=0; j<sqrt(n)-1; j=j+1) {
//square lattice
model.add (c[i*sqrt(n)+j] +c[i*sqrt(n)+j+1] +
c[(i+1)*sqrt(n)+j] +c[(i+1)*sqrt(n)+j+1]>= 16-4*sqrt(2)); // Bedingung fuer Quadratischen Gridgraph und d(x) = 3-x
//
// triangular lattice
// model.add (c[i*5+j]+c[i*5+j+1] +
// c[(i+1)+j] >= 4); // Bedingung fuer Quadratischen Gridgraph und d(x) = 3-x
// model.add (c[i*sqrt(n)+j]+c[i*sqrt(n)+j+1] +
// c[(i+1)*sqrt(n)+j]+c[(i+1)*sqrt(n)+j+1] >= 22 - 4*sqrt(2)); // Bedingung fuer Quadratischen Gridgraph und d(x) = 4-x
}
}
*/
/*
for (unsigned i=0; i<sqrt(n)-2; i+=3) {
for (unsigned j=0; j<sqrt(n)-2; j+=3) {
// model.add (c[i*sqrt(n)+j] + c[i*sqrt(n)+j+1] + c[i*sqrt(n)+j+2] +
// c[(i+1)*sqrt(n)+j]+ c[(i+1)*sqrt(n)+j+1]+ c[(i+1)*sqrt(n)+j+2] +
// c[(i+2)*sqrt(n)+j]+ c[(i+2)*sqrt(n)+j+1]+ c[(i+2)*sqrt(n)+j+2]
// >= 60-17*sqrt(2)-3*sqrt(5)); // Bedingung fuer Quadratischen Gridgraph und d(x) = 3-x
// model.add (c[i*sqrt(n)+j] + c[i*sqrt(n)+j+1] + c[i*sqrt(n)+j+2] +
// c[(i+1)*sqrt(n)+j]+ c[(i+1)*sqrt(n)+j+1]+ c[(i+1)*sqrt(n)+j+2] +
// c[(i+2)*sqrt(n)+j]+ c[(i+2)*sqrt(n)+j+1]+ c[(i+2)*sqrt(n)+j+2]
// >= 82-8*sqrt(2)-2*sqrt(5)); // Bedingung fuer Quadratischen Gridgraph und d(x) = 4-x
}
}
*/
for (unsigned int v=0; v<n; v++) {
IloExpr expr;
model.add (c[v] <= lambda);
model.add (c[v] >= 0);
expr.end();
}
std::cout << "Number of variables " << numvar << "\n";
/* solve the Model*/
cplex.extract(model);
cplex.exportModel("L-Labeling.lp");
/*
start = clock();
int solveError = cplex.solve();
end = clock ();
*/
IloTimer timer(env);
timer.start();
int solveError = cplex.solve();
timer.stop();
if ( !solveError ) {
std::cout << "STATUS : "<< cplex.getStatus() << "\n";
env.error() << "Failed to optimize LP \n";
exit(1);
}
//Info.time = (double)(end-start)/(double)CLOCKS_PER_SEC;
Info.time = timer.getTime();
std::cout << "STATUS : "<< cplex.getStatus() << "\n";
/* get the solution*/
env.out() << "Solution status = " << cplex.getStatus() << "\n";
numconst = cplex.getNrows();
env.out() << " Number of constraints = " << numconst << "\n";
lambda_G_d=cplex.getObjValue();
env.out() << "Solution value = " << lambda_G_d << "\n";
for (unsigned int u=0; u<n; u++) {
C.push_back(cplex.getValue(c[u]));
std::cout << "c(" << u << ")=" << C[u]<< " ";
}
std::cout <<"\n";
/*
for (unsigned int u=0; u<n; u++) {
for (unsigned int v=0; v<u; v++) {
std::cout<< "z[" << u <<"][" << v << "]="<< cplex.getValue( z[u][v]) << " ";
Z.push_back(cplex.getValue( z[u][v]));
}
std::cout << "\n";
}
std::cout <<"\n";
*/
} // end try
catch (IloException& e) {
std::cerr << "Concert exception caught: " << e << std::endl;
}
catch (...) {
std::cerr << "Unknown exception caught" << std::endl;
}
env.end();
return 0;
}
// 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;
}
int CProblem::setModel() {
//time_t start, end;
numvar = 1+n; // lambda + all c;
IloEnv env;
try {
IloModel model(env);
IloCplex cplex(env);
/*Variables*/
IloNumVar lambda(env, "lambda");
IloNumVarArray c(env, n);//
for (unsigned int u=0; u<n; u++) {
std::stringstream ss;
ss << u;
std::string str = "c" + ss.str();
c[u]=IloNumVar(env, str.c_str());
}
IloArray<IloIntVarArray> z(env,n);
for (unsigned int u=0; u<n; u++) {
z[u]= IloIntVarArray(env, n);
for (unsigned int v=0; v<n; v++) {
std::stringstream ss;
ss << u;
ss << v;
std::string str = "z" + ss.str();
z[u][v] = IloIntVar(env, 0, 1, str.c_str());
}
}
/* Constant M*/
int M=n*max_d;
UB = M;
/* Objective*/
model.add(IloMinimize(env, lambda));
/*Constrains*/
model.add(lambda - UB <= 0);
/* d=function of the distance */
IloArray<IloNumArray> Par_d(env,n);
for (unsigned int u=0; u<n; u++) {
Par_d[u]=IloNumArray(env,n);
for (unsigned int v=0; v<n; v++) {
Par_d[u][v]=d[u][v];
}
}
for (unsigned u=0; u<n; u++) {
for (unsigned v=0; v<u; v++) {
model.add(c[v]-c[u]+M* z[u][v] >= Par_d[u][v] );
model.add(c[u]-c[v]+M*(1-z[u][v]) >= Par_d[u][v]);
numvar++; // + z[u][v]
}
}
for (unsigned int v=0; v<n; v++) {
IloExpr expr;
model.add (c[v] <= lambda);
model.add (c[v] >= 0);
expr.end();
}
std::cout << "Number of variables " << numvar << "\n";
/* solve the Model*/
cplex.extract(model);
cplex.exportModel("L-Labeling.lp");
/*
start = clock();
int solveError = cplex.solve();
end = clock ();
*/
// cplex.setParam(IloCplex::Threads, 1);
cplex.setParam(IloCplex::ClockType , 1 ); // CPU time
IloTimer timer(env);
const double startt = cplex.getTime();
timer.start();
int solveError = cplex.solve();
timer.stop();
const double stopt = cplex.getTime() - startt;
if ( !solveError ) {
std::cout << "STATUS : "<< cplex.getStatus() << "\n";
env.error() << "Failed to optimize LP \n";
exit(1);
}
//Info.time = (double)(end-start)/(double)CLOCKS_PER_SEC;
Info.time = timer.getTime();
std::cout << "STATUS : "<< cplex.getStatus() << "\n";
/* get the solution*/
env.out() << "Solution status = " << cplex.getStatus() << "\n";
env.out() << "Time cplex.getTime " << stopt << "\n";
numconst = cplex.getNrows();
env.out() << " Number of constraints = " << numconst << "\n";
lambda_G_d=cplex.getObjValue();
env.out() << "Solution value = " << lambda_G_d << "\n";
for (unsigned int u=0; u<n; u++) {
C.push_back(cplex.getValue(c[u]));
std::cout << "c(" << u << ")=" << C[u]<< " ";
}
std::cout <<"\n";
/*
for (unsigned int u=0; u<n; u++) {
for (unsigned int v=0; v<u; v++) {
std::cout<< "z[" << u <<"][" << v << "]="<< cplex.getValue( z[u][v]) << " ";
Z.push_back(cplex.getValue( z[u][v]));
}
std::cout << "\n";
}
std::cout <<"\n";
*/
} // end try
catch (IloException& e) {
std::cerr << "Concert exception caught: " << e << std::endl;
}
catch (...) {
std::cerr << "Unknown exception caught" << std::endl;
}
env.end();
return 0;
}
int CProblem::setModel() {
//time_t start, end;
numvar = 1+n; // lambda + all c;
IloEnv env;
try {
IloModel model(env);
IloCplex cplex(env);
/*Variables*/
IloNumVar lambda(env, "lambda");
IloNumVarArray c(env, n);//
for (unsigned int u=0; u<n; u++) {
std::stringstream ss;
ss << u;
std::string str = "c" + ss.str();
c[u]=IloNumVar(env, str.c_str());
}
IloArray<IloIntVarArray> z(env,n);
for (unsigned int u=0; u<n; u++) {
z[u]= IloIntVarArray(env, n);
for (unsigned int v=0; v<n; v++) {
std::stringstream ss;
ss << u;
ss << v;
std::string str = "z" + ss.str();
z[u][v] = IloIntVar(env, 0, 1, str.c_str());
}
}
/* Constant M*/
int UB, LB;
switch (lattice){
case 1: // hexagonal_lattice
if (max_d==3) {LB = 5; UB = 10;} //d(x) = 3 -x
else {LB = 9; UB = 27;}
break;
case 2:// triangular_lattice
if (max_d==3) { LB = 8; UB = 16;} //d(x) = 3 -x
else {LB = 18; UB = 54;}
break;
case 3:// square_lattice
if (max_d==3) { LB = 6; UB = 12;} //d(x) = 3 -x
else { LB = 11; UB = 33;}
break;
default: UB=n*max_d;break;
}
std::cout << "Lattice " << lattice << "\n";
std::cout << "UB for lambda " << UB << "\n";
/* Objective*/
model.add(IloMinimize(env, lambda));
/*Constrains*/
model.add(lambda - UB <= 0);
model.add(lambda - LB >= 0);
/* d=function of the distance */
IloArray<IloNumArray> Par_d(env,n);
for (unsigned int u=0; u<n; u++) {
Par_d[u]=IloNumArray(env,n);
for (unsigned int v=0; v<n; v++) {
Par_d[u][v]=d[u][v];
}
}
int M = INT_MAX;//Par_d[0][0] + UB;
for (unsigned u=0; u<n; u++) {
for (unsigned v=0; v<u; v++) {
model.add(c[v]-c[u]+M* z[u][v] >= Par_d[u][v] );
model.add(c[u]-c[v]+M*(1-z[u][v]) >= Par_d[u][v]);
numvar++; // + z[u][v]
}
}
for (unsigned int v=0; v<n; v++) {
IloExpr expr;
model.add (c[v] <= lambda);
model.add (c[v] >= 0);
expr.end();
}
std::cout << "Number of variables " << numvar << "\n";
/* solve the Model*/
cplex.extract(model);
cplex.exportModel("L-Labeling.lp");
IloTimer timer(env);
timer.start();
int solveError = cplex.solve();
timer.stop();
if ( !solveError ) {
std::cout << "STATUS : "<< cplex.getStatus() << "\n";
env.error() << "Failed to optimize LP \n";
exit(1);
}
//Info.time = (double)(end-start)/(double)CLOCKS_PER_SEC;
Info.time = timer.getTime();
std::cout << "STATUS : "<< cplex.getStatus() << "\n";
/* get the solution*/
env.out() << "Solution status = " << cplex.getStatus() << "\n";
numconst = cplex.getNrows();
env.out() << " Number of constraints = " << numconst << "\n";
lambda_G_d=cplex.getObjValue();
env.out() << "Solution value = " << lambda_G_d << "\n";
for (unsigned int u=0; u<n; u++) {
C.push_back(cplex.getValue(c[u]));
std::cout << "c(" << u << ")=" << C[u]<< " ";
}
std::cout <<"\n";
/*
for (unsigned int u=0; u<n; u++) {
for (unsigned int v=0; v<u; v++) {
std::cout<< "z[" << u <<"][" << v << "]="<< cplex.getValue( z[u][v]) << " ";
Z.push_back(cplex.getValue( z[u][v]));
}
std::cout << "\n";
}
std::cout <<"\n";
*/
} // end try
catch (IloException& e) {
std::cerr << "Concert exception caught: " << e << std::endl;
}
catch (...) {
std::cerr << "Unknown exception caught" << std::endl;
}
env.end();
return 0;
}
int
main(int argc, char **argv)
{
IloEnv env;
try {
IloInt i, j;
IloNumArray capacity(env), fixedCost(env);
FloatMatrix cost(env);
IloInt nbLocations;
IloInt nbClients;
const char* filename = "../../../examples/data/facility.dat";
if (argc > 1)
filename = argv[1];
ifstream file(filename);
if (!file) {
cerr << "ERROR: could not open file '" << filename
<< "' for reading" << endl;
cerr << "usage: " << argv[0] << " <file>" << endl;
throw(-1);
}
file >> capacity >> fixedCost >> cost;
nbLocations = capacity.getSize();
nbClients = cost.getSize();
IloBool consistentData = (fixedCost.getSize() == nbLocations);
for(i = 0; consistentData && (i < nbClients); i++)
consistentData = (cost[i].getSize() == nbLocations);
if (!consistentData) {
cerr << "ERROR: data file '"
<< filename << "' contains inconsistent data" << endl;
throw(-1);
}
IloNumVarArray open(env, nbLocations, 0, 1, ILOINT);
NumVarMatrix supply(env, nbClients);
for(i = 0; i < nbClients; i++)
supply[i] = IloNumVarArray(env, nbLocations, 0, 1, ILOINT);
IloModel model(env);
for(i = 0; i < nbClients; i++)
model.add(IloSum(supply[i]) == 1);
for(j = 0; j < nbLocations; j++) {
IloExpr v(env);
for(i = 0; i < nbClients; i++)
v += supply[i][j];
model.add(v <= capacity[j] * open[j]);
v.end();
}
IloExpr obj = IloScalProd(fixedCost, open);
for(i = 0; i < nbClients; i++) {
obj += IloScalProd(cost[i], supply[i]);
}
model.add(IloMinimize(env, obj));
obj.end();
IloCplex cplex(env);
cplex.extract(model);
cplex.solve();
cplex.out() << "Solution status: " << cplex.getStatus() << endl;
IloNum tolerance = cplex.getParam(
IloCplex::Param::MIP::Tolerances::Integrality);
cplex.out() << "Optimal value: " << cplex.getObjValue() << endl;
for(j = 0; j < nbLocations; j++) {
if (cplex.getValue(open[j]) >= 1 - tolerance) {
cplex.out() << "Facility " << j << " is open, it serves clients ";
for(i = 0; i < nbClients; i++) {
if (cplex.getValue(supply[i][j]) >= 1 - tolerance)
cplex.out() << i << " ";
}
cplex.out() << endl;
}
}
}
catch(IloException& e) {
cerr << " ERROR: " << e << endl;
}
catch(...) {
cerr << " ERROR" << endl;
}
env.end();
return 0;
}
