Local search algorithms for the vertex K-center problem

The vertex k-center problem is a classical NP-Hard problem with applications to Clustering and Facility Location. It has been shown that this problem cannot be solved within a ρ&2 approximation factor, unless P=NP. Although there are approximation algorithms that achieve that 2-approximation factor, their performance on most benchmark instances is poor. Because of this, many useful heuristic and metaheuristic algorithms have been designed to address this problem. In this paper we evaluate the performance of a representative set of local search algorithms for the vertex k-center problem that includes a new local search algorithm that takes ideas from the Metropolis algorithm. Our experimental results show that the proposed algorithm outperforms some of the most representative local search algorithms from the literature, such as Tabu Search and the Metropolis algorithm itself. The reason for its good performance is that our proposal takes advantage of the flexibility of the Metropolis algorithm as well as of some specific properties of the vertex k-center problem.