int
main (void)
{
IloEnv env;
int retval = -1;
try {
// Create the model.
IloModel model(env);
IloCplex cplex(env);
IloObjective obj(env);
IloNumVarArray vars(env);
IloRangeArray rngs(env);
IloIntArray cone(env);
createmodel(model, obj, vars, rngs, cone);
// Extract model.
cplex.extract(model);
// Solve the problem. If we cannot find an _optimal_ solution then
// there is no point in checking the KKT conditions and we throw an
// exception.
cplex.setParam(IloCplex::Param::Barrier::QCPConvergeTol, CONVTOL);
if ( !cplex.solve() || cplex.getStatus() != IloAlgorithm::Optimal )
throw string("Failed to solve problem to optimality");
// Test the KKT conditions on the solution.
if ( !checkkkt (cplex, obj, vars, rngs, cone, TESTTOL) ) {
env.error() << "Testing of KKT conditions failed." << endl;
}
else {
env.out() << "Solution status: " << cplex.getStatus() << endl;
env.out() << "KKT conditions are satisfied." << endl;
retval = 0;
}
env.end();
} catch (IloException &e) {
cerr << "IloException: " << e << endl;
if (env.getImpl())
env.end();
::abort();
} catch (string& e) {
cerr << e << endl;
if (env.getImpl())
env.end();
::abort();
}
return retval;
}
vector<array<double,3>> solveLP(int size, graph g){
double EPS = 1;
int bigM = 200;
auto type = IloNumVar::Bool;
vector<array<double,3>> result;
IloEnv env;
try {
IloModel model(env);
IloNumVarArray vars(env);
IloConstraintArray cons(env);
unordered_map<string,int> v;
int counter = 0;
//setup easy access to variables!
variable_access x(name_x, vars, v);
variable_access t(name_t, vars, v);
variable_access y(name_y, vars, v);
variable_access e1(name_e1, vars, v);
variable_access e2(name_e2, vars, v);
variable_access n1(name_n1, vars, v);
variable_access n2(name_n2, vars, v);
variable_access a1(name_a1, vars, v);
variable_access a2(name_a2, vars, v);
variable_access z1(name_z1, vars, v);
variable_access z2(name_z2, vars, v);
//variables: lower and upper bound and the name!
//add varibles
for(int i=1; i<= size; ++i){
//t
v[name_t(i)] = counter++;
vars.add( IloNumVar(env, 0, bigM, IloNumVar::Float, name_t(i).c_str() ) );
//x
v[name_x(i)] = counter++;
vars.add( IloNumVar(env, 0, bigM, IloNumVar::Float, name_x(i).c_str() ) );
//y
v[name_y(i)] = counter++;
vars.add( IloNumVar(env, 0, bigM, IloNumVar::Float, name_y(i).c_str() ) );
for(int j=1; j<=size; ++j){
if(i==j) continue;
//e1
v[name_e1(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_e1(i,j).c_str() ) );
//e2
v[name_e2(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_e2(i,j).c_str() ) );
//n1
v[name_n1(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_n1(i,j).c_str() ) );
//n2
v[name_n2(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_n2(i,j).c_str() ) );
//a1
v[name_a1(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_a1(i,j).c_str() ) );
//a2
v[name_a2(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_a2(i,j).c_str() ) );
//z1
v[name_z1(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_z1(i,j).c_str() ) );
//z2
v[name_z2(i,j)] = counter++;
vars.add( IloNumVar(env, 0, 1, type, name_z2(i,j).c_str() ) );
}
}
//add all constraints
model.add(vars);
//subject: feasibility
model.add(IloMaximize(env, 0));
//add constraints
//add constraints for arcs
for(int i=1; i<= size; ++i){
for(int j=1; j<= size; ++j){
if(i==j) continue;
if(g.is_arc(i,j)){
cout<< "constr. for arc ("<<i<<":"<<j<<")" <<endl;
//xi < xj
cons.add( x(i) <= x(j) - EPS );
//|ti-tj| < |xi - xj|
cons.add( t(j) - t(i) <= x(j) - x(i) + (1-a1(i,j))*bigM -EPS);
cons.add( t(i) - t(j) <= x(j) - x(i) + (1-a1(i,j))*bigM -EPS);
cons.add( t(j) - t(i) <= x(i) - x(j) + (1-a2(i,j))*bigM -EPS);
cons.add( t(i) - t(j) <= x(i) - x(j) + (1-a2(i,j))*bigM -EPS);
cons.add( a1(i,j) + a2(i,j) >= 1 );
}
}
}
//constraints for edges
for(int i=1; i<= size; ++i){
for(int j=1; j<= size; ++j){
if(i==j) continue;
if (g.is_edge(i,j)){
cout<< "constr. for edge ("<<i<<":"<<j<<")" <<endl;
// |t1-t2| < |y1-y2|
cons.add( t(j) - t(i) <= y(j) - y(i) + (1-e1(i,j))*bigM -EPS);
cons.add( t(i) - t(j) <= y(j) - y(i) + (1-e1(i,j))*bigM -EPS);
cons.add( t(j) - t(i) <= y(i) - y(j) + (1-e2(i,j))*bigM -EPS);
cons.add( t(i) - t(j) <= y(i) - y(j) + (1-e2(i,j))*bigM -EPS);
cons.add( e1(i,j) + e2(i,j) >= 1 );
//|x1-x2| <= |t1-t2|
cons.add( x(j) - x(i) <= t(j) - t(i) + (1-z1(i,j))*bigM );
cons.add( x(i) - x(j) <= t(j) - t(i) + (1-z1(i,j))*bigM);
cons.add( x(j) - x(i) <= t(i) - t(j) + (1-z2(i,j))*bigM);
cons.add( x(i) - x(j) <= t(i) - t(j) + (1-z2(i,j))*bigM);
cons.add( z1(i,j) + z2(i,j) >= 1 );
}
}
}
//constraints for non-existing edges
for(int i=1; i<= size; ++i){
for(int j=1; j<= size; ++j){
if(i==j) continue;
if (g.is_no_edge(i,j)){
cout<< "constr. for non_edge ("<<i<<":"<<j<<")" <<endl;
// |y1-y2| <= |t1-t2|
cons.add( y(j) - y(i) <= t(j) - t(i) + (1-n1(i,j))*bigM);
cons.add( y(i) - y(j) <= t(j) - t(i) + (1-n1(i,j))*bigM);
cons.add( y(j) - y(i) <= t(i) - t(j) + (1-n2(i,j))*bigM);
cons.add( y(i) - y(j) <= t(i) - t(j) + (1-n2(i,j))*bigM);
cons.add( n1(i,j) + n2(i,j) >= 1 );
//|x1-x2| <= |t1-t2|
cons.add( x(j) - x(i) <= t(j) - t(i) + (1-z1(i,j))*bigM );
cons.add( x(i) - x(j) <= t(j) - t(i) + (1-z1(i,j))*bigM);
cons.add( x(j) - x(i) <= t(i) - t(j) + (1-z2(i,j))*bigM);
cons.add( x(i) - x(j) <= t(i) - t(j) + (1-z2(i,j))*bigM);
cons.add( z1(i,j) + z2(i,j) >= 1 );
}
}
}
//add all constraints to the model
model.add(cons);
//solve the model
IloCplex cplex(model);
cplex.extract(model);
cout<< model<<endl;
//solve silently
//cplex.setOut(env.getNullStream());
bool solved = cplex.solve();
if ( !solved ) {
cerr<<"MIP model is infeasible!"<<endl;
//conflict refiner
IloConstraintArray infeas(env);
IloNumArray preferences(env);
infeas.add(cons );
for (IloInt i = 0; i<vars.getSize(); i++) {
if ( vars[i].getType() != IloNumVar::Bool ) {
infeas.add(IloBound(vars[i], IloBound::Lower));
infeas.add(IloBound(vars[i], IloBound::Upper));
}
}
for (IloInt i = 0; i<infeas.getSize(); i++) {
preferences.add(1.0); // user may wish to assign unique preferences
}
if ( cplex.refineConflict(infeas, preferences) ) {
IloCplex::ConflictStatusArray conflict = cplex.getConflict(infeas);
env.getImpl()->useDetailedDisplay(IloTrue);
cout << "Conflict :" << endl;
for (IloInt i = 0; i<infeas.getSize(); i++) {
if ( conflict[i] == IloCplex::ConflictMember)
cout << "Proved : " << infeas[i] << endl;
if ( conflict[i] == IloCplex::ConflictPossibleMember)
cout << "Possible: " << infeas[i] << endl;
}
}
else
cout << "Conflict could not be refined" << endl;
cout << endl;
env.end();
return result;
}
for(int i=1; i<= size; ++i){
array<double,3> coord = {{cplex.getValue(x(i)),
cplex.getValue(y(i)),
cplex.getValue(t(i))}};
result.push_back(coord);
}
//print variables
for(int i=1; i<= size; ++i){
cout<< x(i).getName() << " = "<< cplex.getValue(x(i));
cout<<"\t\t"<< y(i).getName() << " = "<< cplex.getValue(y(i));
cout<<"\t\t"<< t(i).getName() << " = "<< cplex.getValue(t(i))<<endl;
}
cout<<endl;
for(int i=1; i<= size; ++i)
for(int j=1; j<= size; ++j){
if(i==j) continue;
cout<< z1(i,j).getName() << " = "<< cplex.getValue(z1(i,j));
cout<<"\t"<< z2(i,j).getName() << " = "<< cplex.getValue(z2(i,j))<<endl;
}
for(int i=1; i<= size; ++i)
for(int j=1; j<= size; ++j){
if(i==j) continue;
if (not g.is_edge(i,j)) continue;
cout<< e1(i,j).getName() << " = "<< cplex.getValue(e1(i,j));
cout<<"\t"<< e2(i,j).getName() << " = "<< cplex.getValue(e2(i,j))<<endl;
}
for(int i=1; i<= size; ++i)
for(int j=1; j<= size; ++j){
if(i==j) continue;
if (g.is_edge(i,j)) continue;
cout<< n1(i,j).getName() << " = "<< cplex.getValue(n1(i,j));
cout<<"\t"<< n2(i,j).getName() << " = "<< cplex.getValue(n2(i,j))<<endl;
}
for(int i=1; i<= size; ++i)
for(int j=1; j<= size; ++j){
if(i==j) continue;
if (not g.is_arc(i,j)) continue;
cout<< a1(i,j).getName() << " = "<< cplex.getValue(a1(i,j));
cout<<"\t"<< a2(i,j).getName() << " = "<< cplex.getValue(a2(i,j))<<endl;
}
}
catch (IloException& e) {
cerr << "Concert exception caught: " << e << endl;
}
catch (...) {
cerr << "Unknown exception caught" << endl;
}
env.end();
return result;
}