Tabu search for the Max-Mean Dispersion Problem

In this paper, we address a variant of a classical optimization problem in the context of selecting elements in a set, while maximizing their diversity. In particular, we maximize their mean dispersion. This NP-hard problem was recently introduced as the maximum mean dispersion problem (MaxMeanDP), and it models several real problems, from pollution control to capital investment or web page ranking. In this paper, we first review the previous methods for the MaxMeanDP and then explore different tabu search approaches and their influence on the quality of the solutions obtained. As a result, we propose a dynamic tabu algorithm based on three different neighborhoods, which is able to attain high quality solutions. Experimentation on previously reported instances shows that the proposed procedure outperforms existing methods in terms of solution quality. Additionally, we believe that our findings on the use of different memory structures invites further consideration of the interplay between short and long term memory to enhance simple forms of tabu search.