Engineering the modulo network simplex heuristic for the periodic timetabling problem

Abstract

The Periodic Event Scheduling Problem (PESP), in which events have to be scheduled repeatedly over a given period, is a complex and well-known 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, there are recent achievements like the computation of the timetable of the Dutch railway system that impressively demonstrate the applicability and practicability of the mathematical model. In this paper we propose different approaches to improve the modulo network simplex algorithm [8], 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 railway instances show that our algorithms are able to handle problems of the size of the German intercity railway network. © 2011 Springer-Verlag.