Exact and heuristic algorithms for the Hamiltonian p-median problem

• Published in: European journal of operational research 2016-09, Vol.253 (2), p.280-289
• Main Authors: Erdoğan, Güneş, Laporte, Gilbert, Rodríguez Chía, Antonio M.
• Format: Article
• Language: English
• Subjects: Algorithms; Branch-and-cut; Construction; Dynamic programming; Exact solutions; Formulations; Hamiltonian; Heuristic; Heuristic methods; Mathematical analysis; Mathematical problems; Metaheuristic; Optimization; p-median; Studies
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2016.02.012

•We provide three algorithms for the Hamiltonian p-median problem.•The first algorithm is an exact branch-and-cut algorithm.•The others are a constructive heuristic and an iterated local search metaheuristic.•The exact algorithm can solve 100-vertex instances.•The ILS metaheuristic solves the problem to near-optimality. 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.