Construction heuristics and domination analysis for the asymmetric TSP

Non-Euclidean TSP construction heuristics, and especially asymmetric TSP construction heuristics, have been neglected in the literature by comparison with the extensive eorts devoted to studying Euclidean TSP construction heuristics. 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 requiring 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 dierent families of TSP instances, disclosing that our combined heuristic clearly outperforms well-known TSP construction methods and proves signicantly more robust in obtaining high quality solutions over a wide range of problems. We also provide a short overview of recent results ..