Abstract
A local search framework for the (undirected) Rural Postman Problem (RPP) is presented in this paper. The framework allows local search approaches that have been applied successfully to the well–known Travelling Salesman Problem also to be applied to the RPP. New heuristics for the RPP, based on this framework, are introduced and these are capable of solving significantly larger instances of the RPP than have been reported in the literature. Test results are presented for a number of benchmark RPP instances in a bid to compare efficiency and solution quality against known methods.
Highlights
Consider a weighted graph G = (V, E), with vertex set V = {v1, . . . , vp}, edge set E, and edge weights denoted by c(i, j) for all vivj ∈ E
Perhaps the best known heuristic for the undirected Rural Postman Problem (RPP) is Frederickson’s heuristic (Frederickson, 1979). This heuristic is similar to Christofides’ heuristic for the Travelling Salesman Problem[1] (TSP), and operates by adding artificial edges to the subgraph induced by Er in a way that yields a connected, Eulerian graph
In a local search framework moves are performed on candidate solutions to the RPP that directly specify the order in which required edges are traversed in the transformed solution
Summary
The above CPP and RPP definitions for undirected graphs have been generalised in many ways, and algorithms catering for directed and mixed graphs, for example, have been introduced — see Ball et al (1995), Dror (2000) and Eiselt et al (1995a, 1995b) for an overview. Perhaps the best known heuristic for the undirected RPP is Frederickson’s heuristic (Frederickson, 1979) This heuristic is similar to Christofides’ heuristic for the Travelling Salesman Problem[1] (TSP), and operates by adding artificial edges (representing shortest paths between the relevant vertices in G) to the subgraph induced by Er in a way that yields a connected, Eulerian graph (i.e., one in which it is possible to find a closed route traversing each edge exactly once).
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