No abstract

The General Routing Problem (GRP) is a fundamental N P-hard vehicle routing problem, first defined by Orloff in 1974. It contains as special cases the Chinese Postman Problem, the Rural Postman Problem, the Graphical TSP and the Steiner TSP. We examine in detail a known constructive heuristic for the GRP, due to Christofides and others. We show how to speed it up, in both theory and practice, while obtaining solutions that are at least as good. Computational results show that, for large instances, our implementation is faster than the original by several orders of magnitude.

Matchings and T-joins are fundamental and much-studied concepts in graph theory and combinatorial optimization. One important application of matchings and T-joins is in the computation of strong lower bounds for arc routing problems (ARPs). An ARP is a special kind of vehicle routing problem, in which the demands are located along edges or arcs, rather than at nodes. We point out that the literature on applying matchings and T-joins to ARPs does not fully exploit the structure of real-life road networks. We propose some ways to exploit this structure. Computational results show significant running time improvements, without deteriorating the quality of the lower bounds.

No abstract

Arc Routing Problems (ARPs) are a special kind of Vehicle Routing Problem (VRP), in which the demands are located on edges or arcs, instead of nodes. There is a huge literature on ARPs, and a variety of exact and heuristic algorithms are available. Recently, however, we encountered some real-life ARPs with over ten thousand roads, which is much larger than those usually considered in the literature. For these problems, we develop fast upper-and lower-bounding procedures. We also present extensive computational results.