Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling

Abstract

Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to use slight shifts in the departure times from the stations to avoid too many simultaneous departures. This limits peak consumption and can help to improve the stability of the power supply. To this end, we derive efficient formulations for the problem of an optimal timetable adjustment based on a given timetable draft, two of which even allow for totally unimodular polyhedral descriptions. The proper choice of the objective function allows the incorporation of the priorities of either the train operating companies or the infrastructure manager. These include the avoidance of large peaks in average or instantaneous consumption and the improved use of recuperated braking energy. To solve the arising optimization models efficiently, we develop specially tailored exact Benders decomposition schemes that allow for the computation of high-quality solutions within a very short time. In an extensive case study for German railway passenger traffic, we show that our methods are capable of solving the problem on a nationwide scale. We see that the optimal adjustment of timetables entails a tremendous potential for reducing energy consumption.

EETTlib—Energy‐efficient train timetabling library

“…To this end, it is also necessary to keep instantaneous peaks in consumption, lasting up to several seconds, under control. Details about the technical background and typical pricing schemes can be found in [7].…”

“…We will now define several possible metrics according to which the energy-efficiency of a railway timetable can be optimized. First, we introduce the objective functions we used in our projects with Deutsche Bahn AG for the German railway network and VAG for the Nürnberg underground network as we studied them in [4,7], respectively. For these two fine-tuned objective functions, we will provide reference computational results in Section 6.…”

“…For these two fine-tuned objective functions, we will provide reference computational results in Section 6. Furthermore, we present a few alternative choices from [6,7] which can be combined with the first two objectives as seen fit by the planners of a railway undertaking. In Appendix B, we show that they can all easily be stated as mixed-integer linear programs (MIPs).…”

Set characterizations and convex extensions for geometric convex-hull proofs

“…Staircase compatibility is a special case of CPMC which arises especially in scheduling applications with precedence constraints (see e.g. [SZ15,BMS20b]), but also when considering flow problems with piecewise linear costs, for example ( [LM16]). Here, each subset of nodes V i ∈ V is equipped with a total order < i , which we assume to be the case in the following.…”

The Bipartite Boolean Quadric Polytope with Multiple-Choice Constraints

“…A substructure like this is prevalent in many applications when competing choices or compatibilities between decision are involved. This includes the knapsack problem with multiple-choice constraints ([Nau87, KPP04]), with applications in investment planning, among others, or the clique problem with multiple-choice constraints ([BGMS18, BGM20]), which arises, for example, in scheduling problems ( [BMS20]) and flow problems with piecewise linear routing costs ( [LM16]). In the case of the boolean quadric polytope, the multiple-choice structure models given, fixed proportions between the multiplied quantities.…”