Originally posted by: qtbgo

Hi, Suppose we have a interval variable itv. I want that if it overlap with a time period, say [3,5], a penalty should imposed in the objective function.

How to model this?

thanks in advance.

Originally posted by: qtbgo

I guess I can use overlapLength, that is in the objective function we have penalty term minimize overLapLength(ivt, 3,5).

Now, another question.

Suppose we have an interval variable array x[i in 1..10] in 0..1000 size 1..5, which are not overlaped (we impose noOverlap(x)).

and we have some hole such as [3,5], [10,11], [21,24], which are implemented as tuples and included in a set called Holes ({<3,5>,<10,11>, <21,24>, } ) etc. any coverage on these holes will be penalize in the objective. So, we have:

minimize  sum( i in 10, j in Holes)overLapLength(x[i], j.t1, j.t2)

But I guess this objective is not the best way to model this case, because it compares all pairs of i, j which is not necessary . it seems we can use a piecewise linear function to model the cost of holes,but I cannot figured it out.

Can anyone help me?

Originally posted by: PhilippeLaborie

You can use the notion of intensity function as follows:

1. You define a stepFunction h with value 100 (100%) during the holes and value 0 outside the holes.

2. Your intervals in the noOverlap constraint are defined with this intensity function. the intensity function will ensure the following relation between the size and the start/end/length of each interval variable:

size = sum(start->end) h(t) / 100

length = end-start

So 'size' will be the total duration of the interval variable executed inside the holes, this is what you want.

Be careful then that you need to specify a 'length' and not a 'size' when defining the "duration" of the interval variable.

So instead of doing:

dvar interval x[i in 1..10] in 0..1000 size 1..5;

You need:

dvar interval x[i in 1..10] in 0..1000 intensity h;

forall(i in 1..10) {
 1 <= lengthOf(x[i],1) <= 5;
}

Then you can directly minimize:

minimize sum(i in 1..10) sizeOf(x[i],0);

Two remarks:
1- there is an example of manipulation of step functions and intensity functions in the delivered example sched_calendar

2- of course if your interval variables already have some intensity function defined for other reasons, you will need to duplicate the variables and synchronize them (with startAtStart/endAtEnd constraints).

Originally posted by: qtbgo

Very interesting, I didn't know that size can be 0 when length is not 0 before.