Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 95060, 28 pages

ACS-TS: train scheduling using ant colony system

Keivan Ghoseiri and Fahimeh Morshedsolouk

School of Railway Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran

Received 6 July 2005; Revised 15 January 2006; Accepted 18 January 2006

Copyright © 2006 Keivan Ghoseiri and Fahimeh Morshedsolouk. 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.


This paper develops an algorithm for the train scheduling problem using the ant colony system metaheuristic called ACS-TS. At first, a mathematical model for a kind of train scheduling problem is developed and then the algorithm based on ACS is presented to solve the problem. The problem is considered as a traveling salesman problem (TSP) wherein cities represent the trains. ACS determines the sequence of trains dispatched on the graph of the TSP. Using the sequences obtained and removing the collisions incurred, train scheduling is determined. Numerical examples in small and medium sizes are solved using ACS-TS and compared to exact optimum solutions to check for quality and accuracy. Comparison of the solutions shows that ACS-TS results in good quality and time savings. A case study is presented to illustrate the solution.