Stable Roommate Generalised

A heuristic algorithm for solving generalised stable-roommate problem, inspired by the difficulty in forming groups for group projects.

The algorithm uses cardinal method (rating each member on a scale) instead of the usual preference ordering, because it carries more information, is easier to collect, and makes aggregating preferences easier.

Input

• A square matrix pref where pref[i][j] is preference (or rating) of i for j
• group_size: Number of members in each group.

Output

• List of groups.

How does it work?

• number of groups = ceil(num_members/group_size)
• Randomly initialize each group with a single member.
• Let left over members propose to each group in order of their preference (Step is similar to Gale-Shapley algorithm). Each group accepts one new member in each iteration.
• At end of each iteration, swap members between groups if swapping improves overall score (Step executed iter_count no of times).
• Continue the process till the last member is grouped.
• Finally, iterate one last time to check if swapping members improves overall score (no of times looped is final_iter_count).

Note

• Increasing iter_count and final_iter_count improves the matching but also increases execution time significantly.
• Each run of algorithm will give slightly different results (as initial step involves choosing random members). So, looping till a desired score threshold is reached is possible.

Got a web app for this?

• Yes