An iterative bi-level hierarchical approach for train scheduling

Abstract

This paper presents an iterative bi-level hierarchical approach for train scheduling based on the concept of decentralized operational control in railway operations. The entire railway network is divided into a number of subnetworks connected at boundary stations, called interchange points. The planning of this decomposed network is done by two types of planners, namely, low and high level, handling subnetworks and interchange points respectively. The plan of the entire network is generated using an iterative approach, where at each step the low level planners generate feasible schedules for each subnetwork independently and share their version of the schedule of interchange point with the high level planners. The high level planners analyze individual schedules of the interchange point for possible conflicts, devise resolutions of the found conflicts and send back updated schedules to low level planners. On receipt, the low level planners adjust schedules to comply with boundary conditions subject to internal constraints. The iterative process continues until a global feasible solution is obtained. In current implementation, both planners use greedy heuristics to generate schedules of subnetworks and to resolve conflicts at interchange points respectively. We illustrate the concept of iterative bi-level hierarchical approach for train scheduling on a test network extracted from Indian Railways. This approach succeeds in generating feasible solutions for all tested instances in a finite number of iterations. Even though unified approach outperforms decomposed approach both in terms of schedule quality as well as response time, the use of suggested approach will become relevant where time taken by the algorithm to generate schedule of a railway network increases non-linearly with its size.