assigning values to IntVar if and only if BoolVar, else zero [or-tools]

Question

If I have an IntVar s[j] stored in a vector s, is it possible to iterate for (a period of time) t and create a BoolVar b such that b[t] is true if and only if s[j]==t? I tried setting some restrictions:

    for (int j = 0; j < nbTasks; ++j)
    {
        for (int t = 0; t < tmax; ++t)
        {
            const IntVar expr = cp_model.NewIntVar(Domain(-1000000000,100000000000));
            const IntVar actual_t = cp_model.NewConstant(t).WithName("actual_t");
            const BoolVar b = cp_model.NewBoolVar().WithName("b");
            const IntVar value = cp_model.NewConstant(w[j][t]);

            obj_final.push_back(expr);
            actuals[j].push_back(actual_t);
            expressions[j].push_back(expr);
            values[j].push_back(value);

            cp_model.AddEquality(b, starts[j]==actual_t);
            cp_model.AddProductEquality(expr, {value, b});
        }
    }  

I created the BoolVar b and then set an equality to the bool value of s[j]==t, then I used the constraint expr == value*b and added the expression to the vector obj_final, and finally set the objective: cp_model.Maximize(LinearExpr::Sum(obj_final)); The problem is that my solution is optimal but the objective is zero, so I guess b is always false.

My goal is to assign a value to an expression if and only if s[j]==t. Enforce constraints isn't what i need because the other expressions must be zero. I'll be thankful for any help.

Answer 1

To create an intermediate boolean that is true iff s[j] == t you just have to create 2 constraints:

cp_model.AddEquality(s[j], t).OnlyEnforceIf(b);
cp_model.AddNotEqual(s[j], t).OnlyEnforceIf(Not(b));

The problem with this line:

cp_model.AddEquality(b, starts[j]==actual_t);

is that starts[j]==actual_t "always" evaluates to false.

To learn more about channeling, see:

• https://github.com/google/or-tools/blob/stable/ortools/sat/doc/channeling.md
• https://github.com/google/or-tools/blob/stable/ortools/sat/doc/integer_arithmetic.md#step-function