} // END WorkerLP
// This method creates the master ILP (arc variables x and degree constraints).
//
// Modeling variables:
// forall (i,j) in A:
// x(i,j) = 1, if arc (i,j) is selected
// = 0, otherwise
//
// Objective:
// minimize sum((i,j) in A) c(i,j) * x(i,j)
//
// Degree constraints:
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
//
// Binary constraints on arc variables:
// forall (i,j) in A: x(i,j) in {0, 1}
//
internal static void CreateMasterILP(IModeler model,
Data data,
IIntVar[][] x)
{
int i, j;
int numNodes = data.numNodes;
// Create variables x(i,j) for (i,j) in A
// For simplicity, also dummy variables x(i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
for (i = 0; i < numNodes; ++i)
{
x[i] = new IIntVar[numNodes];
for (j = 0; j < numNodes; ++j)
{
x[i][j] = model.BoolVar("x." + i + "." + j);
model.Add(x[i][j]);
}
x[i][i].UB = 0;
}
// Create objective function: minimize sum((i,j) in A ) c(i,j) * x(i,j)
ILinearNumExpr objExpr = model.LinearNumExpr();
for (i = 0; i < numNodes; ++i)
{
objExpr.Add(model.ScalProd(x[i], data.arcCost[i]));
}
model.AddMinimize(objExpr);
// Add the out degree constraints.
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j)
{
expr.AddTerm(x[i][j], 1.0);
}
for (j = i + 1; j < numNodes; ++j)
{
expr.AddTerm(x[i][j], 1.0);
}
model.AddEq(expr, 1.0);
}
// Add the in degree constraints.
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j)
{
expr.AddTerm(x[j][i], 1.0);
}
for (j = i + 1; j < numNodes; ++j)
{
expr.AddTerm(x[j][i], 1.0);
}
model.AddEq(expr, 1.0);
}
} // END CreateMasterILP
// This method creates the master ILP (arc variables x and degree constraints).
//
// Modeling variables:
// forall (i,j) in A:
// x(i,j) = 1, if arc (i,j) is selected
// = 0, otherwise
//
// Objective:
// minimize sum((i,j) in A) c(i,j) * x(i,j)
//
// Degree constraints:
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
//
// Binary constraints on arc variables:
// forall (i,j) in A: x(i,j) in {0, 1}
//
internal static void CreateMasterILP(IModeler model,
Data data,
IIntVar[][] x)
{
int i, j;
int numNodes = data.numNodes;
// Create variables x(i,j) for (i,j) in A
// For simplicity, also dummy variables x(i,i) are created.
// Those variables are fixed to 0 and do not partecipate to
// the constraints.
for (i = 0; i < numNodes; ++i)
{
x[i] = new IIntVar[numNodes];
for (j = 0; j < numNodes; ++j)
{
x[i][j] = model.BoolVar("x." + i + "." + j);
model.Add(x[i][j]);
}
x[i][i].UB = 0;
}
// Create objective function: minimize sum((i,j) in A ) c(i,j) * x(i,j)
ILinearNumExpr objExpr = model.LinearNumExpr();
for (i = 0; i < numNodes; ++i)
objExpr.Add(model.ScalProd(x[i], data.arcCost[i]));
model.AddMinimize(objExpr);
// Add the out degree constraints.
// forall i in V: sum((i,j) in delta+(i)) x(i,j) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j) expr.AddTerm(x[i][j], 1.0);
for (j = i + 1; j < numNodes; ++j) expr.AddTerm(x[i][j], 1.0);
model.AddEq(expr, 1.0);
}
// Add the in degree constraints.
// forall i in V: sum((j,i) in delta-(i)) x(j,i) = 1
for (i = 0; i < numNodes; ++i)
{
ILinearNumExpr expr = model.LinearNumExpr();
for (j = 0; j < i; ++j) expr.AddTerm(x[j][i], 1.0);
for (j = i + 1; j < numNodes; ++j) expr.AddTerm(x[j][i], 1.0);
model.AddEq(expr, 1.0);
}
}