Cream: Class Library for Constraint Programming in Java

FAQ of Cream

How disjunctive constraints can be expressed in Cream?

Cream has no disjunctive constraints, such as (x > 0) or (y > 0). However, you can encode it in Cream as follows. Or, you can simply use x.max(y).gt(0) in this case.

        Network net = new Network();
        IntVariable x = new IntVariable(net, -1, 1, "x");
        IntVariable y = new IntVariable(net, -1, 1, "y");
        // x > 0 or y > 0
        IntVariable c1 = x.sign().max(0);
        IntVariable c2 = y.sign().max(0);
        // c1 or c2 --> c1 max c2
        c1.max(c2).gt(0);

How conditional constraints can be expressed in Cream?

Cream has no conditional constraints, such as if (x > 0) then (y > 0) else (z > 0). However, you can encode it in Cream as follows.

        Network net = new Network();
        IntVariable x = new IntVariable(net, 0, 1, "x");
        IntVariable y = new IntVariable(net, 0, 1, "y");
        IntVariable z = new IntVariable(net, 0, 1, "z");
        // if x > 0 then y > 0 else z > 0
        IntVariable c1 = x.sign().max(0);
        IntVariable c2 = y.sign().max(0);
        IntVariable c3 = z.sign().max(0);
        // if c1 then c2 else c3
        // --> (c1 and c2) or (not c1 and c3)
        // --> (c1 min c2) max (1-c1 min c3)
        c1.min(c2).max(c1.negate().add(1).min(c3)).gt(0);

Can Cream handle soft constraints?

Cream does not support soft constraints directly. However, you can encode them in some cases. Suppose you have a set of soft constraints x1<=0, x2<=0, ..., xn<=0. They can be expressed in Cream as follows (but, perhaps not efficient).

        IntVariable w1 = x1.sign().max(0);
        IntVariable w2 = x2.sign().max(0);
        ...
        IntVariable wn = x3.sign().max(0);
        IntVariable w = w1.add(w2)....add(wn);
        net.setObjective(w);
        int opt = Solver.MAXIMIZE | Solver.BETTER;
        Solver solver = new DefaultSolver(net, opt);

Is it possible to add constraints dynamically?
Yes, but you need to start a new solver after adding constraints. If you want to find a similar solution after adding constraints, please refer to neighborhoodSearchExample() in Examples.java.
Is it possible to use non-contiguous values for domains?
Yes. The following example declares an integer variable "x" with the domain {1,2,4,8}.
```
        IntDomain d = new IntDomain(1, 7).delete(3).delete(5, 7);
        IntVariable x = new IntVariable(net, d, "x");
  
```

Naoyuki Tamura