Solving the p-second center problem with variable neighborhood search

The p-center problem is a well-known and highly studied problem pertaining to
 the identification of p of the potential n center locations in such a way as
 to minimize the maximum distance between the users and the closest center.
 As opposed to the p-center, the p-second center problem minimizes the
 maximum sum of the distances from the users to the closest and the second
 closest centers. In this paper, we propose a new Variable Neighborhood
 Search based algorithm for solving the p-second center problem. Its
 performance is assessed on the benchmark instances from the literature.
 Moreover, to further evaluate the algorithm?s performance, we generated
 larger instances with 1000, 1500, 2000, and 2500 nodes and instances defined
 over graphs up to 1000 nodes with different densities. The obtained results
 clearly demonstrate the effectiveness and efficiency of the proposed
 algorithm.