This paper presents an exact algorithm, a constructive heuristic algorithm, and a metaheuristic for the Hamiltonian p-Median Problem (HpMP). The exact algorithm is a branch-and-cut algorithm based on an enhanced p-median based formulation, which is proved to dominate an existing p-median based formulation. The constructive heuristic is a giant tour heuristic, based on a dynamic programming formulation to optimally split a given sequence of vertices into cycles. The metaheuristic is an iterated local search algorithm using 2-exchange and 1-opt operators. Computational results show that the branch-and-cut algorithm outperforms the existing exact solution methods.
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