A Weighted Vertex Cover-Based Intensification Tabu Search for the Capacitated Dispersion Problem

The dispersion problem consists of selecting a subset of elements from a data set in order to maximize its diversity, which has many applications in real-world scenarios. For the capacitated dispersion problem (CDP), it seeks for a subset such that the minimum distance among the selected elements is as large as possible while satisfying a demand constraint. In this paper, we propose a weighted vertex cover-based intensification tabu search algorithm (WVC-ITS) for solving this challenging optimization problem. First, it transforms the CDP into a series of decision version subproblems, i.e., the weighted vertex cover problem. Then, it tackles each subproblem with an intensification tabu search-based algorithm. Computational experiments on 100 benchmark instances used in the literature and 20 newly generated challenging instances show that WVC-ITS is highly competitive in terms of both solution quality and computational efficiency. Compared with the state-of-the-art algorithms, WVC-ITS is able to obtain the best results for all the 120 instances within very short computational time and improve the previous best known results for 17 benchmark instances.