Iterating over a CPLEX Model

Periodically a question arises about how to parse an LP (or QP or MIP) in CPLEX after it has been constructed. CPLEX provides iterators in at least the C++ and Java APIs, and probably in the other APIs as well. In C++ the iterators are classes; in Java they implement the standard Java Iterator interface. I'll give a small Java example here (using CPLEX 12; there may be some differences with earlier versions).

To illustrate the process, I'll create a CPLEX model for the following linear program:\begin{eqnarray*}\textrm{maximize} & x+2y+3z\\\textrm{s.t.} & x+y+z & \le 5\\ & y+2z & \le 3\\ & x-z & =0\\ & x,y,z & \ge 0.\end{eqnarray*} Ignoring, as usual, any need to deal with exceptions, here is the code to create the model:

IloNumVar[] vars = new IloNumVar[3];
vars[0] = cplex.numVar(0, Double.MAX_VALUE, "x");
vars[1] = cplex.numVar(0, Double.MAX_VALUE, "y");
vars[2] = cplex.numVar(0, Double.MAX_VALUE, "z");
cplex.addMaximize(
  cplex.scalProd(
    new double[] {1., 2., 3.}, vars), "Obj");
// first constraint: x + y + z <= 5
cplex.addLe(cplex.sum(vars), 5., "Con1");
// second constraint: y + 2z <= 3
cplex.addLe(
  cplex.scalProd(
    new double[] {0., 1., 2.}, vars), 3., "Con2");
// third constraint: x = z
cplex.addEq(vars[0], vars[2], "Con3");

There are several choices for how I iterate over the model.  I'll focus specifically on constraints by using a rangeIterator. (With a more general iterator, I might need to rely on instanceOf comparisons to interpret what the iterator was giving me.) Here is the rest of the code:

Iterator it = cplex.rangeIterator();
while (it.hasNext()) {
  IloRange r = (IloRange) it.next();
  System.out.println("Constraint: " + r.getName());
  IloLinearNumExprIterator it2 =
    ((IloLinearNumExpr) r.getExpr()).linearIterator();
  while (it2.hasNext()) {
    System.out.println("\tVariable "
                       + it2.nextNumVar().getName()
                       + " has coefficient "
                       + it2.getValue());
  }
  // get range bounds, checking for +/- infinity
  // (allowing for some rounding)
  String lb = (r.getLB() <= Double.MIN_VALUE + 1) ?
              "-infinity" : Double.toString(r.getLB());
  String ub = (r.getUB() >= Double.MAX_VALUE - 1) ?
              "+infinity" : Double.toString(r.getUB());
  System.out.println("\t" + lb + " <= LHS <= " + ub);

The output is as follows:

Constraint: Con1
        Variable x has coefficient 1.0
        Variable y has coefficient 1.0
        Variable z has coefficient 1.0
        -infinity <= LHS <= 5.0
Constraint: Con2
        Variable y has coefficient 1.0
        Variable z has coefficient 2.0
        -infinity <= LHS <= 3.0
Constraint: Con3
        Variable x has coefficient 1.0
        Variable z has coefficient -1.0
        -infinity <= LHS <= 0.0

The outer iterator it (and instance of rangeIterator) iterates over all ranges (constraints) in the model, but its next() method returns the generic type Object, which needs to be cast to IloRange. The inner iterator it2 iterates over the expression portion of a constraint, and returns a variable (via nextNumVar()) and its coefficient (via getValue()) at each step.  The iterator exploits any sparsity in the model: only terms with non-zero coefficients are returned.

Suppose that, for some reason, I need to be able to associate the coefficients with their corresponding column indices in the original constraint matrix. I'll add a bit of code near the top to map each variable to its column index. (Add the following after the variable declarations and immediately before the declaration of the objective function.)

HashMap<IloNumVar, Integer> map =
 new HashMap<IloNumVar, Integer>();
for (int i = 0; i < 3; i++) {
  map.put(vars[i], i);
}

I replace the contents of the inner while loop with the following:

    IloNumVar v = it2.nextNumVar();
    System.out.println("\tVariable " + v.getName()
                       + " (column " + map.get(v) + ")"
                       + " has coefficient "
                       + it2.getValue());
 

The relevant portion of the output now reads as follows:

Constraint: Con1
        Variable x (column 0) has coefficient 1.0
        Variable y (column 1) has coefficient 1.0
        Variable z (column 2) has coefficient 1.0
        -infinity <= LHS <= 5.0
Constraint: Con2
        Variable y (column 1) has coefficient 1.0
        Variable z (column 2) has coefficient 2.0
        -infinity <= LHS <= 3.0
Constraint: Con3
        Variable x (column 0) has coefficient 1.0
        Variable z (column 2) has coefficient -1.0
        -infinity <= LHS <= 0.0

Note that I have to save the value of nextNumVar() in a temporary variable (v) because I need it in two places, and if I called it twice it would advance the iterator too often.