A Genetic Algorithm for the Undirected Rural Postman Problem

This paper introduces a new method to deal with the Undirected Rural Postman Problem (RPP), based on Genetic Algorithms. The RPP is a particular Arc Routing Problem which consists of determining a minimum cost circuit on a graph so that it is possible to traverse a given subset of required edges. The RPP is known to be an NP-hard problem and it has some interesting real-life applications. The authors are aware of only one publication using Genetic Algorithms alone in this type of problems. The new method – the RPGA algorithm – will be described in detail and tested with different groups of problems, the results being compared with those gathered from other publications. A comparison is also made with several crossovers frequently used in TSP problems. A new case based on the city of Porto is also solved. The simplicity of RPGA and the computational experiments suggest that it can be a good choice to solve (undirected) RPP, in a short period of time.