Topological Constraints in Periodic Train Scheduling

It is well known that many scheduling problems can be modeled as constraint optimization problems. The scheduling of train services can be considered as a problem subject to a number of constraints describing railway infrastructure, required train services and reasonable time-intervals for waiting and transits. Railway optimization problems are known to be hard problems and a good solution or the best solution is a rather difficult task. In this work, we propose a topological constraint optimization technique for solving periodic train scheduling, developed in collaboration with the National Network of Spanish Railways (RENFE). This topological technique transforms the railway optimization problem in subproblems such that a traffic pattern is generated for each subproblem. These traffic patterns will be periodically repeated to compose the entire running map. The results show that this technique improve the results obtained by well known tools as LINGO and ILOG Concert Technology (CPLEX).