Improving the modulo simplex algorithm for large-scale periodic timetabling

The Periodic Event Scheduling Problem (PESP), in which events have to be scheduled repeatedly over a given period, is a complex and wellknown discrete problem with numerous real-world applications. One of them is to find periodic timetables which is economically important, but difficult to handle mathematically, since even finding a feasible solution to this problem is known to be NP-hard. On the other hand, recent achievements demonstrate the applicability and practicability of the mathematical model. In this paper we propose different approaches to improve the modulo network simplex algorithm [11], which is a powerful heuristic for the PESP problem, by exploiting improved search methods in the modulo simplex tableau and larger classes of cuts to escape from the many local optima. Numerical experiments on large-scale railway instances show that our algorithms not only perform better than the original method, but even outperform state-of-the-art commercial MIP solver.