A fast variable neighborhood search for p-hub median problem using social network analysis concepts

This study will contribute to the uncapacitated single allocation p-hub median problem (USApHMP) which is known as an NP-hard problem in the literature. This problem is concerned with locating of hub facilities in a network and allocating of each non-hub node to just one hub in order to minimize total transportation costs in the network. A hybrid variable neighborhood search (VNS) algorithm is proposed considering three structures of local search which are used as a combination of nested VNS and sequential VNS in the algorithm. For reduction of the dimensions in the nested part, social network analysis centrality measures for the node are used to choose elite points instead of all existing points in the local search structures. The obtained results demonstrate that this will not only retain quality of the solutions, but also reduce run time of the algorithm significantly. Three standard data sets (AP, CAB, and URAND) were used for numerical analysis. Computational results show that quality of the obtained solutions is good and able to compete with other heuristics addressed in the literature. From the viewpoint of execution time, it considerably outperforms all other algorithms. The intelligent search embedded in this algorithm makes it robust and efficient on networks with up to 400 nodes.