Tabu search with strategic oscillation for the maximally diverse grouping problem

Abstract

We propose new heuristic procedures for the maximally diverse grouping problem (MDGP). This NP-hard problem consists of forming maximally diverse groups—of equal or different size—from a given set of elements. The most general formulation, which we address, allows for the size of each group to fall within specified limits. The MDGP has applications in academics, such as creating diverse teams of students, or in training settings where it may be desired to create groups that are as diverse as possible. Search mechanisms, based on the tabu search methodology, are developed for the MDGP, including a strategic oscillation that enables search paths to cross a feasibility boundary. We evaluate construction and improvement mechanisms to configure a solution procedure that is then compared to state-of-the-art solvers for the MDGP. Extensive computational experiments with medium and large instances show the advantages of a solution method that includes strategic oscillation.

Keywords:

• diversity problems
• metaheuristics
• strategic oscillation

Acknowledgements

This research has been partially supported by the Ministerio de Education y Ciencia of Spain (Grant Ref. TIN2009-07516) and by the University Rey Juan Carlos (in the program ‘Ayudas a la Movilidad 2010’).