Using a Divide and Conquer Method for Routing in a PC Vehicle Routing Application

Vehicle routing is an area of both practical and theoretical importance. Unfortunately, routing problems are notably difficult to solve since almost all vehicle routing problems are NP-hard. However, we have discovered that when reduced to its simplest form, solving a single vehicle routing problem, without capacity and time window constraints is quite similar to the Traveling Salesman Problem (TSP). In this paper, we studied various well-known traveling salesman heuristics such as the Nearest Neighbor, the Space-Filling Curve, and the 2-Opt. In addition, we proposed a hybrid that can trade off the quality of a solution with computing time. The input to any TSP heuristic is the all-pairs shortest paths of the points to be visited. We have found the Floyd-Warshall algorithm, a traditional method to compute all-pairs shortest paths, to be too time-consuming, especially for large data sets. Hence, in this paper, we also proposed an algorithm that generates approximate all-pairs shortest paths. Our experimental results showed that our algorithm’s errors are quite small. More importantly, these estimated shortest paths information is sufficient for TSP heuristics to produce good tours especially for geometric graphs like road networks. In addition, our approximate all-pairs shortest paths also allowed pre-computation, thus speeding up shortest path computations tremendously. Finally, our algorithms were implemented and integrated into a vehicle routing application that can be run on a PC.