[gecode-users] Newbie: Cost function with squared variables propagation trouble

[Pieter Thysebaert]

Hello,

I'm using Gecode 1.2.2 on Debian sarge.

While modelling a scheduling problem I have stumbled across the following:

Let's say the decision variables of my problem are X_ijk, binary.
Let integer variables Y_i >= 0 be related to the X_ij by  Y_i = k <=>
X_ijk = 1 for some range of j, expressed by using constraints like
eq(this, Y_i, k, X_ijk); for that range of j

The cost function I want to minimize is
sum_over_i  (Y_i - Constant_i)^2

Clearly, if for some i, Constant_i < 0 the cost is at least (Y_i -
Constant_i)^2.

However, for all but the most trivial instances of my problem, the
minimal cost after initial propagation is smaller than this "intuitive"
lower bound.
I believe (but I can be wrong) that this is partly due to my feable
modelling skills: in order to implement the cost function above, I have

1. expanded each square term into a polynomial
2. introduced auxiliary variables Z_i = sqr(Y_i)
3. written the cost as a sum of Z_i and Y_i terms

Is there a more concise way to express the cost function above without
introducing explicit extra constraints stating the obvious (i.e. cost >=
intuitive lower bound for Constant_i < 0) that will nevertheless
propagate and find these "intuitive" cost bounds?
If not, can someone point me to an exmaple which would show me how to
implement my own propagator for such a cost function?

As a side note, I have also been caught by the following oddity (well
that's how it seemed to me at first).
If I want to build a MiniModel::LinExpr using the following code

LinExpr myExpr;

for (int i = 0; i < ...; i++) {
    myExpr = myExpr + some_term(i);
}

On my machine, this code fails upon the first assignment to the empty
LinExpr, and only works when explicitly initializing myExpr with the
first term and then adding the others.
Is this standard behavior?

Thx,
Pieter