This paper focuses on the development of new algorithms for the real-time train scheduling and routing problem in a complex and busy railway network. Since this is a strongly NP-hard problem and practical size instances are complex, simple heuristics are typically adopted in practice to compute feasible but low quality schedules in a short computation time. In order to compute good quality solutions, we consider a mixed-integer linear programming formulation of the problem and solve it with a commercial solver. However, the resolution of this formulation by a commercial solver often takes a too long computation time. Therefore, a new methodology based on the relaxation of some train routing constraints in the formulation is proposed for the quick computation of a good quality lower bound. The lower bound solution is then transformed via a constructive metaheuristic into a feasible schedule, representing a good quality upper bound to the problem. Computational experiments are performed on several disturbed traffic situations for two practical case studies from the Dutch and British railways. The results show that the new lower and upper bounds are computed in a few seconds and are often of similar quality to the ones computed by the commercial solver in hours of computation.

This paper focuses on the development of metaheuristic algorithms for the real-time traffic management problem of scheduling and routing trains in complex and busy railway networks. This key optimization problem can be formulated as a mixed integer linear program. However, since the problem is strongly NP-hard, heuristic algorithms are typically adopted in practice to compute good quality solutions in a short computation time. This paper presents a number of algorithmic improvements implemented in the AGLIBRARY optimization solver in order to improve the possibility of finding good quality solutions quickly. The optimization solver manages trains at the microscopic level of block sections and at a precision of seconds. The solver outcome is a detailed conflict-free train schedule, being able to avoid deadlock situations and to minimize train delays. The proposed algorithmic framework starts from a good initial solution for the train scheduling problem with fixed routes, obtained via a truncated branch-and-bound algorithm. Variable neighbourhood search or tabu search algorithms are then applied to improve the solution by re-routing some trains. The neighbourhood of a solution is characterized by the set of candidate trains to be re-routed and the available routes. Computational experiments are performed on railway networks from different countries and various sources of disturbance. The new algorithms often outperform a state-of-the-art tabu search algorithm and a commercial solver in terms of reduced computation times and/or train delays.