Using choco solver for solving equations

Question

I am looking for a way to encode mathematical equations on Choco Solver. I see there's a way to encode constraints like:

x + y < 9

But I am trying to encode something like

3x + 4y < 9

where x and y are int vars.

Any help would be greatly appreciated.

Answer 1

I am also new to Choco but I can solve this one.

To do that you can use the constraint scalar (see docs).

First you just need to define the x and the y in two IntVar variables. You can use VariableFactory.bounded or Variable.enumerated. They are pretty similar when you just want to use a domain with a lower bound and an upper bound, but the difference is explained in the user guide.

Then you need to define an array with the coefficients of the equation, in this case { 3, 4 }.

Here is how you do it:

Solver solver = new Solver();

IntVar x = VariableFactory.bounded("x", 0, 50, solver);
IntVar y = VariableFactory.bounded("y", 0, 50, solver);

int[] coefficients = new int[]{ 3, 4 };

solver.post(IntConstraintFactory.scalar(new IntVar[]{ x,  y }, coefficients, "<", VariableFactory.fixed(9, solver)));

if (solver.findSolution()) {
    do {
        System.out.println("x = " + x.getValue() + ", y = " + y.getValue());
    } while (solver.nextSolution());
} else {
    System.out.println("The equation has no solutions.");
}