Construction heuristics for the asymmetric TSP

Non Euclidean TSP construction heuristics and especially asymmetric TSP construc tion heuristics have been neglected in the literature by comparison with the extensive e orts devoted to studying Euclidean TSP construction heuristics This state of a airs is at odds with the fact that asymmetric models are relevant to a wider range of applica tions and indeed are uniformly more general that symmetric models Moreover common construction approaches for the Euclidean TSP have been shown to produce poor quality solutions for non Euclidean instances Motivation for remedying this gap in the study of construction approaches is increased by the fact that such methods are a great deal faster than other TSP heuristics which can be important for real time problems requir ing continuously updated response The purpose of this paper is to describe two new construction heuristics for the asymmetric TSP and a third heuristic based on combining the other two Extensive computational experiments are performed for several di er ent families of TSP instances disclosing that our combined heuristic clearly outperforms well known TSP construction methods and proves signi cantly more robust in obtaining relatively high quality solutions over a wide range of problems