The element expression

The constraint propagation algorithm for element expressions reduces domains efficiently.

The element expression indexes an array of values with a decision variable. This expression is used to associate a cost or a distance to the value of a variable, for example.

Suppose there is a decision variable x that chooses a delivery customer and suppose that the distances to the customers are:

• 7 for customer 1,

• 12 for customer 2,

• 5 for customer 3 and

• 21 for customer 4.

If the variable y is to be equal to the distance of the chosen customer, you can write:

    IloIntArray distance(env, 4, 7, 12, 5, 21);
    model.add(y == IloElement(distance, x));

This constraint states that y is equal to the x-th element of the distance array. In the C++ API, another way to state the same constraint is to write:

    model.add(y == distance[x]);

This constraint achieves full domain reduction. In other words, after domain reduction, for each value of x there is a value for y that satisfies the constraint and vice-versa.

Here is an example of a model with one element expression:

    IloIntVar x(env, 0, 3);
    IloIntVar y(env, 0, 20);
    IloModel model(env);
    model.add(y == IloElement(IloIntArray(env, 4, 7, 12, 5, 21), x));
    IloCP cp(model);
    if ( cp.propagate() ) {
      cp.out() << " Domains reduced: " << std::endl;
      cp.out() << " Domain of x is " << cp.domain(x) << std::endl;
      cp.out() << " Domain of y is " << cp.domain(y) << std::endl;
    } else
      cp.out() << " Model has no solution." << std::endl;

Running this code produces the output:

 Domains reduced:
 Domain of x is [0..2]
 Domain of y is [5 7 12]

The value 3 is removed from the domain of x because the fourth element in the array is 21, which does not belong to the domain of y. The domain of y is reduced to the set of values that are indexed by values of x, that is 5, 7 and 12.