Tabu Search for the Maximum Diversity Problem

In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NPhard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have been largely ignored and most tabu search applications restrict themselves to the local search framework. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for this problem. This construction can be coupled with a local search procedure or a short-term tabu search for improved outcomes. Extensive computational experiments with medium and large instances show that the proposed procedure outperforms the best heuristics reported in the literature within short computational times.