Optimizing Schedule of Trains in Context of a Large Railway Network

The Train Timetabling Problem (TTP) is a complex problem where the objective is to find a conflict-free schedule for trains on a given railway network satisfying some operational constraints and maximize the efficiency of infrastructure usage. We deal with a railway network at the scale of a large national railway. With a route longer than 50,000 Km, a weekly schedule with several tens of thousands in passenger trains and many more freight trains with thousands of control points, such large scale railway problems pose a grand computational challenge for finding an optimal schedule. We present two flexible heuristics based on a Mixed Integer Program (MIP) formulation for local optimization to improve infrastructure utilization. These methods provide flexibility in scheduling new trains with varying speed and delays at each section line on the route. The two methods provide a robust solution with hundreds of trains being scheduled over a portion of the railway network yielding 100% improvement in throughput. We additionally present methods, based on linear programming to validate this nominal schedule over global correlated variations in travel times (satisfying linear constraints) without making any probabilistic assumptions. The global validity, based on linear programming, takes the order of a few minutes for a portion of the network, and is computationally efficient to handle the entire network.