Exact and heuristic approaches for the cycle hub location problem

Abstract

In this paper, we present solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch-and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a metaheuristic based on greedy randomized adaptive search procedure to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes and 8 hubs confirm the efficiency of the proposed solution algorithms.