I am trying to implement a constraint for non overlapping rectangles. I found this link: http://yetanothermathprogrammingconsultant.blogspot.com/2017/07/rectangles-no-overlap-constraints.html
But I dont quite understand why the sum of the binary variable should be less or equal to 3 like in the picture below. Shouldn't it be only two of the constraints that should be true at the same time so that the sum should be less or equal to two?
These constraints state that at least one of the inequalities should hold. If sum(delta)=4 then all restrictions are relaxed. That we want to prevent. So we need to forbid sum(delta)=4. We do that by stating sum(delta)<4 or sum(delta)<=3. In other words: at least one delta=0 so at least one constraint should hold.
The stated approach basically implements:
constraint 1 OR constraint 2 OR constraint 3 OR constraint 4.
or in words:
rectangle i should be to the left of rectangle j
or rectangle i should be to the right of rectangle j
or rectangle i should be above rectangle j
or rectangle i should be below rectangle j
Not sure why you want two constraints to hold.