Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 728916, 19 pages
Research Article

Mathematical Solutions for Solving Periodic Railway Transportation

Instituto Universitario de Automática e Informática Industrial, Universidad Politécnica de Valencia, 46022 Valencia, Spain

Received 28 November 2008; Revised 28 January 2009; Accepted 9 February 2009

Academic Editor: J. Jiang

Copyright © 2009 Miguel A. Salido and Federico Barber. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Train scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to compute railway scheduling. In this paper, we present a set of heuristics for a constraint-based train scheduling tool, which is a project in collaboration with the National Network of Spanish Railways (RENFE), Spain. We formulate train scheduling as constraint optimization problems. Three heuristics are developed to speed up and direct the search toward suboptimal solutions in periodic train scheduling problems. The feasibility of our problem-oriented heuristics is confirmed with experimentation using real-life data. The results show that these techniques enable MIP solvers such as LINGO and ILOG Concert Technology (CPLEX) to terminate earlier with good solutions.