The balanced maximally diverse grouping problem with block constraints

The paper investigates the assignment of items to groups such that all groups are balanced, i.e. all groups contain the same number of items and all pairs of groups are as homogeneous as possible regarding the attribute values of the assigned items. Therefore, we adapt the maximally diverse grouping problem (MDGP). It is especially known in the context of students being assigned to groups. We describe the set of optimal solutions for the MDGP for realistic input data and develop a new linear objective function to determine the best balanced solution amongst all optimal solutions for the MDGP by weighting the biggest diversity between two groups with a higher value than the second biggest and so on. Furthermore, an integer program, a detailed complexity analysis, and a computational study are presented. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the problem of maximally diverse grouping, describing optimal solutions for realistic input data and developing a new linear objective function for determining the best balanced solution. An integer program, detailed complexity analysis, and computational study are presented in the research.