The Railway Traveling Salesman Problem

Abstract

We consider the Railway Traveling Salesman Problem (RTSP) in which a salesman using the railway network wishes to visit a certain number of cities to carry out his/her business, starting and ending at the same city, and having as goal to minimize the overall time of the journey. RTSP is an $\mathcal{NP}$-hard problem. Although it is related to the Generalized Asymmetric Traveling Salesman Problem, in this paper we follow a direct approach and present a modelling of RTSP as an integer linear program based on the directed graph resulted from the timetable information. Since this graph can be very large, we also show how to reduce its size without sacrificing correctness. Finally, we conduct an experimental study with real-world and synthetic data that demonstrates the superiority of the size reduction approach.

This work was partially supported by the Human Potential Programme of EU under contract no. HPRN-CT-1999-00104 (AMORE), by the IST Programme (6th FP) of EC under contract No. IST-2002-001907 (integrated project DELIS), and by the Action PYTHAGORAS funded by the European Social Fund (Operational Program for Educational and Vocational Training II) and the Greek Ministry of Education.