Heuristics for the Mixed Rural Postman Problem

Abstract

The Rural Postman Problem on a mixed graph (MRPP) consists of finding a minimum cost tour which traverses, at least once, the arcs and edges of a given subset of the arcs and edges of the graph. This problem is known to be NP-hard. This paper presents two heuristic approaches to solve it. An approximate algorithm based on the resolution of some flow and matching problems and a tabu search implementation is presented. The tabu search algorithm seeks high-quality tours by means of a switching mechanism in an intensification phase and two levels of diversification. Computational results are presented to assess the merits of the method. Scope and purpose Routing Problems arise in several areas of distribution management and logistics and their practical significance has been well documented in the literature. Arc Routing Problems are routing problems where a single vehicle or a fleet of vehicles must service the arcs of a transportation network. Such problems occur in a variety of practical contexts, such as garbage collection, mail delivery, snow removal and school bus routing. In this paper we focus on the Mixed Rural Postman Problem (MRPP), an NP-hard problem that includes, as special cases, the well-known Chinese Postman Problem and the Rural Postman Problem. The MRPP fits real-world situations more closely than other simpler problems. In this paper we present heuristic procedures for the MRPP, where the effectiveness of the procedures is measured by the combination of solution quality and speed.