Heuristics for the rural postman problem

Abstract

When addressing the problem of snow removal for secondary roads, a tool for solving the rural postman problem can be very useful. We present some ideas for heuristics for this problem. The heuristics are of the same type as the classical Frederickson heuristic. The ideas concern the order of the main steps in such a method, namely constructing a connected graph with all vertices having even degree, containing all the required edges. We also propose two postprocessing heuristics for improving the tours and removing unnecessary detours. The computational tests show that the ideas are interesting alternatives to the classical approach, and that running times are acceptable. We study problem characteristics that may indicate which method to choose.