// This routine set up the IloCplex algorithm to solve the worker LP, and
// creates the worker LP (i.e., the dual of flow constraints and
// capacity constraints of the flow MILP)
//
// Modeling variables:
// forall k in V0, i in V:
// u(k,i) = dual variable associated with flow constraint (k,i)
//
// forall k in V0, forall (i,j) in A:
// v(k,i,j) = dual variable associated with capacity constraint (k,i,j)
//
// Objective:
// 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)
//
// Constraints:
// forall k in V0, forall (i,j) in A: u(k,i) - u(k,j) <= v(k,i,j)
//
// Nonnegativity on variables v(k,i,j)
// forall k in V0, forall (i,j) in A: v(k,i,j) >= 0
//
void
createWorkerLP(IloCplex cplex, IloNumVarArray v, IloNumVarArray u,
IloObjective obj, IloInt numNodes)
{
IloInt i, j, k;
IloEnv env = cplex.getEnv();
IloModel mod(env, "atsp_worker");
// Set up IloCplex algorithm to solve the worker LP
cplex.extract(mod);
cplex.setOut(env.getNullStream());
// Turn off the presolve reductions and set the CPLEX optimizer
// to solve the worker LP with primal simplex method.
cplex.setParam(IloCplex::Reduce, 0);
cplex.setParam(IloCplex::RootAlg, IloCplex::Primal);
// Create variables v(k,i,j) forall k in V0, (i,j) in A
// For simplicity, also dummy variables v(k,i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
IloInt numArcs = numNodes * numNodes;
IloInt vNumVars = (numNodes-1) * numArcs;
IloNumVarArray vTemp(env, vNumVars, 0, IloInfinity);
for (k = 1; k < numNodes; ++k) {
for (i = 0; i < numNodes; ++i) {
vTemp[(k-1)*numArcs + i *numNodes + i].setBounds(0, 0);
}
}
v.clear();
v.add(vTemp);
vTemp.end();
mod.add(v);
// Set names for variables v(k,i,j)
for (k = 1; k < numNodes; ++k) {
for(i = 0; i < numNodes; ++i) {
for(j = 0; j < numNodes; ++j) {
char varName[100];
sprintf(varName, "v.%d.%d.%d", (int) k, (int) i, (int) j);
v[(k-1)*numArcs + i*numNodes + j].setName(varName);
}
}
}
// Associate indices to variables v(k,i,j)
IloIntArray vIndex(env, vNumVars);
for (j = 0; j < vNumVars; ++j)
{
vIndex[j] = j;
v[j].setObject(&vIndex[j]);
}
// Create variables u(k,i) forall k in V0, i in V
IloInt uNumVars = (numNodes-1) * numNodes;
IloNumVarArray uTemp(env, uNumVars, -IloInfinity, IloInfinity);
u.clear();
u.add(uTemp);
uTemp.end();
mod.add(u);
// Set names for variables u(k,i)
for (k = 1; k < numNodes; ++k) {
for(i = 0; i < numNodes; ++i) {
char varName[100];
sprintf(varName, "u.%d.%d", (int) k, (int) i);
u[(k-1)*numNodes + i].setName(varName);
}
}
// Associate indices to variables u(k,i)
IloIntArray uIndex(env, uNumVars);
for (j = 0; j < uNumVars; ++j)
{
uIndex[j] = vNumVars + j;
u[j].setObject(&uIndex[j]);
}
// Initial objective function is empty
obj.setSense(IloObjective::Minimize);
mod.add(obj);
// Add constraints:
// forall k in V0, forall (i,j) in A: u(k,i) - u(k,j) <= v(k,i,j)
for (k = 1; k < numNodes; ++k) {
for(i = 0; i < numNodes; ++i) {
for(j = 0; j < numNodes; ++j) {
if ( i != j ) {
IloExpr expr(env);
expr -= v[(k-1)*numArcs + i*(numNodes) + j];
expr += u[(k-1)*numNodes + i];
expr -= u[(k-1)*numNodes + j];
mod.add(expr <= 0);
expr.end();
}
}
}
}
}// END createWorkerLP
ILOBRANCHCALLBACK1(SOSbranch, IloSOS1Array, sos) {
IloNumArray x;
IloNumVarArray var;
try {
IloInt i;
x = IloNumArray(getEnv());
var = IloNumVarArray(getEnv());
IloNum bestx = EPS;
IloInt besti = -1;
IloInt bestj = -1;
IloInt num = sos.getSize();
for (i = 0; i < num; i++) {
if ( getFeasibility(sos[i]) == Infeasible ) {
var.clear();
sos[i].getVariables(var);
getValues(x, var);
IloInt n = var.getSize();
for (IloInt j = 0; j < n; j++) {
IloNum inf = IloAbs(x[j] - IloRound(x[j]));
if ( inf > bestx ) {
bestx = inf;
besti = i;
bestj = j;
}
}
}
}
if ( besti >= 0 ) {
IloCplex::BranchDirectionArray dir;
IloNumArray val;
try {
dir = IloCplex::BranchDirectionArray(getEnv());
val = IloNumArray(getEnv());
var.clear();
sos[besti].getVariables(var);
IloInt n = var.getSize();
for (IloInt j = 0; j < n; j++) {
if ( j != bestj ) {
dir.add(IloCplex::BranchDown);
val.add(0.0);
} else {
dir.add(IloCplex::BranchUp);
val.add(1.0);
}
}
makeBranch(var, val, dir, getObjValue());
makeBranch(var[bestj], 0.0, IloCplex::BranchDown, getObjValue());
}
catch (...) {
dir.end();
val.end();
throw;
}
dir.end();
val.end();
}
}
catch (...) {
var.end();
x.end();
throw;
}
var.end();
x.end();
}