Modeling Network Transition Constraints with Hypergraphs

Abstract

Discrete time dynamic graphs are frequently used to model multicommodity flows or activity paths through constrained resources, but simple graphs fail to capture the interaction effects of resource transitions. The resulting schedules are not operationally feasible, and return inflated objective values. A directed hypergraph formulation is derived to address railway network sequencing constraints, and an experimental problem sample solved to estimate the magnitude of objective inflation when interaction effects are ignored. The model is used to demonstrate the value of advance scheduling of train paths on a busy North American railway.

An Exact Decomposition Approach for the Real-Time Train Dispatching Problem

“…Actually, the lack of real-life implementations of theoretical studies regards all known approaches, exact or approximated, as recently observed in [20]. However, in the same paper the author conjectures that the application of optimization to regular dispatching activities is imminent: in this paper we somehow con rm his conjecture.…”

“…Con icts between operations are prevented by simple packing constraints. Examples of applications of (TI) to train optimization can be found in [7], [8], [10], [11], [20], [30], [34]: actually the literature is much wider, and we refer to [14], [23] and [31] for extensive surveys. To our knowledge, basically all these works deal with the track allocation problem, which is solved o -line and where the feasible time periods associated with train routes are strongly limited by the tentative timetable.…”

“…Consequently, the number of feasible time periods grows too large to be handled e ectively by time-indexed formulations within the stringent times imposed by the application, as extensively discussed in [26]. Another problem with (TI) formulations is that, if the time step is not chosen carefully, they may easily lead to solutions which are practically unrealizable (see [20]). …”

Time-Indexed Formulations for the Runway Scheduling Problem

“…Larger step sizes correspond to smaller time-indexed formulations and consequently faster computations. However, the final solution may be suboptimal (with respect to the optimal continuous time solution); or, even worse, feasible instances may become infeasible (see, e.g., Harrod (2011)). It is not difficult to see that, if separations are integer (time units), then a time step size of 1 time unit would ensure that the final solution is also optimal for the original problem.…”

A simulated annealing algorithm for first train transfer problem in urban railway networks

“…Some recent studies on this area include Carey and Lockwood [20], Higgins et al [21], Caprara et al [13], Zhou and Zhong [22], Caprara et al [23], Carey and Crawford [24], Zhou and Zhong [25], D'Ariano et al [26], Burdett and Kozan [27], Liu and Kozan [28], Burdett and Kozan [8], Cacchiani et al [29], Castillo et al [15], Liu and Kozan [6], Harrod [30], Narayanaswami and Rangaraj [31], etc. The non-periodical timetables are more practical for real-time scheduling or rescheduling.…”