LS-MAX-QAP Testing Data

Test instance results for the corresponding manuscript, with abstract as follows. "This research examines a new variant of the maximal quadratic assignment problem, motivated by the challenge of assigning students to a series of project groups of fixed sizes over the duration of an academic course. The primary objective is to maximize the number of unique collaboration experiences, as measured by pairwise student interactions, subject to minor restrictions to prevent group homogeneity. A secondary objective is to minimize the maximum number of repeated interactions between any pair of students, as a method to balance such experiences. This research models this problem as a lexicographic, mixed-integer linear program, and it proposes three exact solution methods and three corresponding heuristics based on model decomposition to improve scalability. Testing assessed each method’s relative efficacy and computational efficiency using 900 synthetic instances and a larger, real-world case study. Results show that, whereas exact methods struggle with larger instances, the heuristic approaches deliver stronger empirical performance. In particular, the preemptive weighting approach yields the best outcomes for lexicographic optimization across the two objectives. Notably, each heuristic produced high-quality solutions for the large-scale instances within 4 hours of computational effort, whereas exact methods performed poorly, even with up to 16 hours of effort."