Create the Model

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The IloCplex object provides the functionality to create an optimization model that can be solved with IloCplex. The class IloCplex implements the ILOG Concert Technology interface IloModeler and its extensions IloMPModeler and IloCplexModeler. These interfaces define the constructors for modeling objects of the following types, which can be used with IloCplex:

Modeling variables are represented by objects implementing the IloNumVar interface defined by ILOG Concert Technology. Here is how to create three continuous variables, all with bounds 0 and 100:

  IloNumVar[] x = cplex.numVarArray(3, 0.0, 100.0);

There is a wealth of other methods for creating arrays or individual modeling variables. The documentation for IloModeler, IloCplexModeler, and IloMPModeler will give you the complete list.

Modeling variables build expressions, of type IloNumExpr, for use in constraints or the objective function of an optimization model. For example, the expression:

  x[0] + 2*x[1] + 3*x[2]

IloNumExpr expr = cplex.sum(x[0], 
                            cplex.prod(2.0, x[1]),
                            cplex.prod(3.0, x[2]));

Another way of creating an object representing the same expression is to use an expression of IloLinearNumExpr. Here is how:

  IloLinearNumExpr expr = cplex.linearNumExpr();
  expr.addTerm(1.0, x[0]);
  expr.addTerm(2.0, x[1]);
  expr.addTerm(3.0, x[2]);

The advantage of using IloLinearNumExpr over the first way is that you can more easily build up your linear expression in a loop, which is what is typically needed in more complex applications. Interface IloLinearNumExpr is an extension of IloNumExpr, and thus can be used anywhere an expression can be used.

  IloObjective obj = cplex.minimize(expr);

In addition to your creating an objective, you must also instruct IloCplex to use that objective in the model it solves. To do so, add the objective to IloCplex like this:

  cplex.add(obj);

Every modeling object that is to be used in a model must be added to the IloCplex object. The variables need not be explicitly added as they are treated implicitly when used in the expression of the objective. More generally, every modeling object that is referenced by another modeling object which itself has been added to IloCplex, is implicitly added to IloCplex as well.

There is a shortcut notation for creating and adding the objective to IloCplex:

  cplex.addMinimize(expr);

  cplex.addLe(cplex.sum(cplex.negative(x[0]), x[1], x[2]), 20);

Again, many methods are provided for adding other constraint types, including equality constraints, greater than or equal to constraints, and ranged constraints. Internally, they are all represented as IloRange objects with appropriate choices of bounds, which is why all these methods return IloRange objects. Also, note that the expressions above could have been created in many different ways, including the use of IloLinearNumExpr.