Review of Length Approximations for Tours with Few Stops

Abstract

The shortest tour distance for visiting all points exactly once and returning to the origin is computed by solving the well-known traveling salesman problem (TSP). Owing to the large computational effort needed for optimizing TSP tours, researchers have developed approximations that relate the average length of TSP tours to the number of points, n, visited per tour. The existing approximations are used in transportation system planning and evaluation for estimating the distance for vehicles with large capacities (e.g., delivery trucks) where n is relatively large. However, the average TSP tour lengths would be inaccurately estimated if the approximations were derived for a wide range of n values since the tour lengths increase at a decreasing rate (i.e., with [Formula: see text]) as n increases. A comprehensive review is presented here of existing studies approximating TSP tour lengths for low n values, which have become important for some recently favored delivery alternatives (e.g., deliveries by bikes, drones, and robots).