// Print out the objective function.
// Note that the quadratic expression in the objective
// is normalized: i.E., for all i != j, terms
// c(i,j)*x[i]*x[j] + c(j,i)*x[j]*x[i] is normalized as
// (c(i,j) + c(j,i)) * x[i]*x[j], or
// (c(i,j) + c(j,i)) * x[j]*x[i].
internal static void PrintObjective(IObjective obj)
{
System.Console.WriteLine("obj: " + obj);
// Count the number of linear terms
// in the objective function.
int nlinterms = 0;
ILinearNumExprEnumerator len = ((ILQNumExpr)obj.Expr).GetLinearEnumerator();
while (len.MoveNext())
{
++nlinterms;
}
// Count the number of quadratic terms
// in the objective function.
int nquadterms = 0;
int nquaddiag = 0;
IQuadNumExprEnumerator qen = ((ILQNumExpr)obj.Expr).GetQuadEnumerator();
while (qen.MoveNext())
{
++nquadterms;
INumVar var1 = qen.GetNumVar1();
INumVar var2 = qen.GetNumVar2();
if (var1.Equals(var2))
{
++nquaddiag;
}
}
System.Console.WriteLine("number of linear terms in the objective : " + nlinterms);
System.Console.WriteLine("number of quadratic terms in the objective : " + nquadterms);
System.Console.WriteLine("number of diagonal quadratic terms in the objective : " + nquaddiag);
System.Console.WriteLine();
}
// This method separates Benders' cuts violated by the current x solution.
// Violated cuts are found by solving the worker LP
//
public IRange Separate(double[][] xSol, IIntVar[][] x)
{
int i, j, k;
IRange cut = null;
// 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)
ILinearNumExpr objExpr = cplex.LinearNumExpr();
for (k = 1; k < numNodes; ++k)
{
for (i = 0; i < numNodes; ++i)
{
for (j = 0; j < numNodes; ++j)
{
objExpr.AddTerm(v[k - 1][i][j], xSol[i][j]);
}
}
}
for (k = 1; k < numNodes; ++k)
{
objExpr.AddTerm(u[k - 1][k], 1.0);
objExpr.AddTerm(u[k - 1][0], -1.0);
}
cplex.GetObjective().Expr = objExpr;
// Solve the worker LP
cplex.Solve();
// A violated cut is available iff the solution status is Unbounded
if (cplex.GetStatus().Equals(Cplex.Status.Unbounded))
{
// Get the violated cut as an unbounded ray of the worker LP
ILinearNumExpr rayExpr = cplex.Ray;
// 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)
ILinearNumExpr cutLhs = cplex.LinearNumExpr();
double cutRhs = 0.0;
ILinearNumExprEnumerator rayEnum = rayExpr.GetLinearEnumerator();
while (rayEnum.MoveNext())
{
INumVar var = rayEnum.NumVar;
bool varFound = false;
for (k = 1; k < numNodes && !varFound; ++k)
{
for (i = 0; i < numNodes && !varFound; ++i)
{
for (j = 0; j < numNodes && !varFound; ++j)
{
if (var.Equals(v[k - 1][i][j]))
{
cutLhs.AddTerm(x[i][j], rayEnum.Value);
varFound = true;
}
}
}
}
for (k = 1; k < numNodes && !varFound; ++k)
{
for (i = 0; i < numNodes && !varFound; ++i)
{
if (var.Equals(u[k - 1][i]))
{
if (i == 0)
{
cutRhs += rayEnum.Value;
}
else if (i == k)
{
cutRhs -= rayEnum.Value;
}
varFound = true;
}
}
}
}
cut = cplex.Ge(cutLhs, cutRhs);
}
return(cut);
} // END Separate