Trying to model a Turntable event

[ikus060]

Hello, I have some basic knowledge about MILP but I'm far from being an expert on the subjet. For that reason, I need some help to modeling a turntable event to maximize the number of relationship between individual.

Here a minified version of the problem.

1. We have 32 persons
2. We have 4 Tables (so 8 person per tables)
3. We 3 different round where people may need to switch tables

I want to maximize the number of people that met each other at the same table during the event.

If a person A sit with person B at round 1 and 2, this count as only one relationship.

Thanks for helping. If it's not the right place to ask this kind of help, don't hesitate to point me into the right direction.