What are the best criteria to take into account when creating groups of students, to maximize their efficiency? This is my first post to the community. I am currently researching on the criteria that make grouping of students as efficient as possible. There are many methods that a professor in an international university program could use to sort the groups of students in class. Nationality, age, educational background, GPA so far, age, level of interest on the course, genre, combinations of them etc. I am creating this post, to try and gather all the opinions on what criteria you use in your classrooms to make your groups as efficient as possible and if you have tried any different scenarios of grouping, what are the results you came across?
Having seen this be done in various ways, I'll suggest 2 successful approaches I have seen used. 

The first is to split students into groups based on a combination of class performance to date (from mini tests or assignments), and attendance at class. Obviously this requires we have attendance records, but these are available on account of the main class activity being a programming lab, where attendance on lab computers is recorded during a scheduled class. 

We found the by considering class performance alone, students could end up in groups where they were of similar ability, yet one (or more) had significantly better work ethic and attendance than the others. I won't go into correlation between attendance and work ethic here as I feel it's off topic for this question. I will add that we see a clear and undeniable correlation between attendance and class performance, but work ethic is obviously difficult to quantify or measure. 

I suggest you also group students by course for logistical reasons, as it makes it easier for students with similar timetables to meet outwith the class. This may be less appropriate or indeed unnecessary if your students have free choice in classes, or if you use the American style "major" system, rather than the UK-style where a "course" is the major, following a somewhat prescribed curriculum. 

An alternative approach (to which I do not claim any credit over whatsoever, but alas am unsure of the originator of), which I shall not express an opinion on, is to offer the class a choice - either I (instructor) assign your groups, or you can. If you pick your own groups, that's it - final. No mark reallocation and negotiation and peer assessment. Alternatively, I (instructor) pick groups, but we have a peer assessment phase and divide marks according to contribution. 

The rationale of the latter approach (which I again highlight I unfortunately don't know the originator of) is that it forces students to think more carefully as to who they work with, rather than just a friend. Obviously your own policies may prelude this, or require peer assessment of contribution etc. 

My experience is that in the latter case, students prefer to have the instructor assign groups, when faced with the prospect of having to select groups based on ability, rather than blind loyalty and friendship. By giving the students the choice over how the groups are decided, they have had input into the process, and we receive significantly less complaints regarding group allocations when doing this, compared to setting groups without offering the "choice". In the event the students chose to pick their own groups (which is incredibly rare), you simply need to ensure everyone has a group, and that you stick to your policy on the group mark being final (note there are many considerations as to if this is valid or if it perhaps allows weak students to be carried, but I shall avoid discussing them for now as I feel they are relatively obvious to any instructor) 

In terms of student efficiency, I find the ability/attendance composite works nicely. I don't have experience of the other criteria for grouping on, other than anecdotally where (by coincidence) a group of international exchange students asked if they could be split up, as they wanted the chance to try working with other people than their own cohort (from the same university and course). In that case it was simply a coincidence due to a group of exchange students performing best in the class.