A fast heuristic for the train scheduling problem
Computers and Operations Research
A Graph-based Ant system and its convergence
Future Generation Computer Systems
Heuristic Techniques for Single Line Train Scheduling
Journal of Heuristics
A Combined Constraint-Based Search Method for Single-Track Railway Scheduling Problem
EPIA '01 Proceedings of the10th Portuguese Conference on Artificial Intelligence on Progress in Artificial Intelligence, Knowledge Extraction, Multi-agent Systems, Logic Programming and Constraint Solving
Ant Colony Optimization
A Lagrangian heuristic algorithm for a real-world train timetabling problem
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
A short convergence proof for a class of ant colony optimizationalgorithms
IEEE Transactions on Evolutionary Computation
Ant system: optimization by a colony of cooperating agents
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
The hyper-cube framework for ant colony optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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In this paper we study a train scheduling problem on a single line that may be traversed in both directions by trains with different priorities travelling with different speeds. We propose an ACO approach to provide decision support for tackling this problem. Our results show the strong performance of ACO when compared to optimal solutions provided by CPLEX for small instances as well as to other heuristics on larger instances.