Tabu search and GRASP for the capacitated clustering problem

The Capacitated Clustering Problem (CCP) consists of forming a specified number of clusters or groups from a set of elements in such a way that the sum of the weights of the elements in each cluster is within some capacity limits, and the sum of the benefits between the pairs of elements in the same cluster is maximized. This problem— which has been recently tackled with a GRASP/VNS approach— arises in the context of facility planners at mail processing and distribution. We propose a tabu search and several GRASP variants to find high quality solutions to this NP-hard problem. These variants are based on several neighborhoods, including a new one, in which we implement a one-for-two swapping strategy. We also hybridize both methodologies to achieve improved outcomes. The Maximally Diverse Grouping Problem (MDGP) is a special case of the CCP in which all the elements have a weight of one unit. This problem has been recently studied in the academic context when forming student groups, and we adapt the best method reported in the literature, a tabu search with strategic oscillation (TS_SO), to the CCP. Our empirical study with 50 large instances shows the superiority of the new GRASP with tabu search for the CCP with respect to both the previous GRASP/VNS approach and the adapted TS_SO.