How to generate all set assignations in a random order

First off, I'm not even sure the terminology is the right one, as I havent found anything similar (especially since I dont even know what keywords to use)

The problem: There is a population of people, and I want to assign them into groups. I have a set of rules to give each assignation a score. I want to find the best one (or at least a very good one).

For example, with a population of four {A,B,C,D} and assigning to two groups of two, the possible assignations are:

{A,B},{C,D}

{A,C},{B,D}

{A,D},{B,C}

And for example, {B,A},{C,D} and {C,D},{A,B} are both the same as the first one (i dont care about the order inside the groups and the order of the groups themselves).

The number of people, the amount of groups and how many people fit in each group are all inputs.

My idea was to list each possible assignation, calculate their score and keep track of the best one. That is, to brute force it. As the population can be big, I was thinking on going through them in a random order and return the best one found when time runs out (probably when the user gets bored or thinks it is a good enough find).

The population is big enough that listing all the assignations to be able to shuffle them doesent fit into memory. So I need either a method to find all the possible assignations in a random order, or a method to, given an index, generate the corresponding assignation, and use an index array and shuffle that (the second would be better because I can then easily distribute the tasks into multiple servers).