There have been a multitude of heuristic algorithms proposed for the solution of large scale traveling salesman problems. Our intent in this paper is to examine some of these well known heuristics, to introduce some new heuristics, and to compare these approximate techniques on the basis of efficiency and accuracy. We emphasize the strengths and weaknesses of each algorithm tested. One of our major conclusions is that it is not difficult to get within 2–3% of optimality using a composite heuristic which requires on the order of n3 computations where n is the number of nodes in the network.