  Group work is a prevalent activity in educational settings, where students
are often divided into topic-specific groups based on their preferences. The
grouping should reflect the students' aspirations as much as possible. Usually,
the resulting groups should also be balanced in terms of protected attributes
like gender or race since studies indicate that students might learn better in
a diverse group. Moreover, balancing the group cardinalities is also an
essential requirement for fair workload distribution across the groups. In this
paper, we introduce the multi-fair capacitated (MFC) grouping problem that
fairly partitions students into non-overlapping groups while ensuring balanced
group cardinalities (with a lower bound and an upper bound), and maximizing the
diversity of members in terms of protected attributes. We propose two
approaches: a heuristic method and a knapsack-based method to obtain the MFC
grouping. The experiments on a real dataset and a semi-synthetic dataset show
that our proposed methods can satisfy students' preferences well and deliver
balanced and diverse groups regarding cardinality and the protected attribute,
respectively.
