Which algorithm for game matchmaking in tournament

Question

I organize amateur tournaments every week with random players. Every week, players sign up, and I get a list with:

• Name
• Rank (1, 2 or 3)
• Role (s) (DPS, TANK and HEALER)

I need to get balanced teams of 6. Ideally, there are 2 DPS, 2 TANKS and 2 HEALERS but in practice there are not enough healers and I have to make 3 DPS, 2 TANKS and 1 HEALER.

The other problem is that some players register together, up to 3 players grouped.

The process is currently done by hand but I would like to automate it.

I learned about the algorithm Knapsack problem, is this a good track?

Do you have any advice to help me in my research?

Thanks you.