An adjustable robust optimization approach for periodic timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing a periodic timetable that can easily be adjusted in case of small periodic disturbances. We develop a solution method for a parametrized class of uncertainty regions. This class relates closely to uncertainty regions known in the robust optimization literature, and naturally defines a metric for the robustness of the timetable. The proposed solution method combines a linear decision rule with well-known reformulation techniques and cutting-plane methods. We show that the RPTP can be solved for practical-sized instances by applying the solution method to practical cases of Netherlands Railways (NS). In particular, we show that the trade-off between the efficiency and robustness of a timetable can be analyzed using our solution method

New Models and Applications for Railway Timetabling

A timetable is a crucial element for the daily operations of a railway operator. At the same time, designing such a timetable is an extremely complex puzzle, and years of investigations are necessary to design a timetable from scratch. Amongst several other aspects, planners should take the travel demand, connections between trains, capacity on the tracks and in the train, and daily disturbances into account when designing a timetable. Next to this, there are often too many restrictions that a timetable has to satisfy, such that no longer a timetable can exist satisfying all these restrictions. In this thesis, methods are developed that can support the design of a timetable such that the timetable is as good as possible. For example, we can compute an ideal timetable, matching with travel demand as good as possible. Using this ideal timetable, one can make clear whether regular departure patterns are useful or not, and how this is related with the expected travel time of passengers. This can also be used to determine infrastructure-bottlenecks. Other methods in this thesis aim at relaxing a set of restrictions, if there are too many restrictions, or to make a timetable that is robust against minor disturbances

Soft-core meson-baryon interactions. II. πN\pi N and K+NK^+ N scattering

The $\pi N$ potential includes the t-channel exchanges of the scalar-mesons $\sigma$ and f_0, vector-meson $\rho$, tensor-mesons f_2 and f_2' and the Pomeron as well as the s- and u-channel exchanges of the nucleon N and the resonances $\Delta$, Roper and S_{11}. These resonances are not generated dynamically. We consider them as, at least partially, genuine three-quark states and we treat them in the same way as the nucleon. The latter two resonances were needed to find the proper behavior of the phase shifts at higher energies in the corresponding partial waves. The soft-core $\pi N$-model gives an excellent fit to the empirical $\pi N$ S- and P-wave phase shifts up to T_{lab}=600 MeV. Also the scattering lengths have been reproduced well and the soft-pion theorems for low-energy $\pi N$ scattering are satisfied. The soft-core model for the $K^+ N$ interaction is an SU_f(3)-extension of the soft-core $\pi N$-model. The $K^+ N$ potential includes the t-channel exchanges of the scalar-mesons a_0, $\sigma$ and f_0, vector-mesons $\rho$, $\omega$ and $\phi$, tensor-mesons a_2, f_2 and f_2' and the Pomeron as well as u-channel exchanges of the hyperons $\Lambda$ and $\Sigma$. The fit to the empirical $K^+ N$ S-, P- and D-wave phase shifts up to T_{lab}=600 MeV is reasonable and certainly reflects the present state of the art. Since the various $K^+ N$ phase shift analyses are not very consistent, also scattering observables are compared with the soft-core $K^+ N$-model. A good agreement for the total and differential cross sections as well as the polarizations is found.Comment: 24 pages, 20 PostScript figures, revtex4, submitted to Phys. Rev.

To bind or not to bind: The H-dibaryon in light of chiral effective field theory

We analyse the quark mass dependence of the binding energy of the H-dibaryon in the framework of chiral effective field theory. We show that the SU(3) breaking effects induced by the differences of the pertinent two-baryon thresholds (Lambda-Lambda, Xi-N, Sigma-Sigma) have a very pronounced impact that need to be incorporated properly in future lattice QCD simulations. We also point out that if the H-dibaryon is a two-baryon bound state, its dominant component is Xi-N rather than Lambda-Lambda, which is a consequence of the approximate SU(3) flavor symmetry of the two-baryon interactions.Comment: 8 pages, 2 figures; Results updated to the new H binding energy reported by NPLQCD, conclusions remain unchanged, several references adde

Strangeness S=-2 baryon-baryon interactions using chiral effective field theory

We derive the leading order strangeness S=-2 baryon-baryon interactions in chiral effective field theory. The potential consists of contact terms without derivatives and of one-pseudoscalar-meson exchanges. The contact terms and the couplings of the pseudoscalar mesons to the baryons are related via SU(3) flavor symmetry to the S=-1 hyperon-nucleon channels. We show that the chiral effective field theory predictions with natural values for the low-energy constants agree with the experimental information in the S=-2 sector.Comment: 10 pages, 2 PostScript figure

Soft-core meson-baryon interactions. I. One-hadron-exchange potentials

The Nijmegen soft-core model for the pseudoscalar-meson baryon interaction is derived, analogous to the Nijmegen NN and YN models. The interaction Hamiltonians are defined and the resulting amplitudes for one-meson-exchange and one-baryon-exchange in momentum space are given for the general mass case. The partial wave projection is carried through and explicit expressions for the momentum space partial wave meson-baryon potentials are presented.Comment: 25 pages, 2 PostScript figures, revtex4, submitted to Phys. Rev.

An iterative heuristic for passenger-centric train timetabling with integrated adaption times

In this paper we present a method to construct a periodic timetable from a tactical planning perspective. We aim at constructing a timetable that is feasible with respect to infrastructure constraints and minimizes average perceived passenger travel time. In addition to in-train and transfer times, our notion of perceived passenger time includes the adaption time (waiting time at the origin station). Adaption time minimization allows us to avoid strict frequency regularity constraints and, at the same time, to ensure regular connections between passengers’ origins and destinations. The combination of adaption time minimization and infrastructure constraints satisfaction makes the problem very challenging. The described periodic timetabling problem can be modelled as an extension of a Peri- odic Event Scheduling Problem (PESP) formulation, but requires huge computing times if it is directly solved by a general-purpose solver for instances of realistic size. In this paper, we propose a heuristic approach consisting of two phases that are executed iteratively. First, we solve a mixed-integer linear program to determine an ideal timetable that mini- mizes the average perceived passenger travel time but neglects infrastructure constraints. Then, a Lagrangian-based heuristic makes the timetable feasible with respect to infras- tructure constraints by modifying train departure and arrival times as little as possible. The obtained feasible timetable is then evaluated to compute the resulting average per- ceived passenger travel time, and a feedback is sent to the Lagrangian-based heuristic so as to possibly improve the obtained timetable from the passenger perspective, while still respecting infrastructure constraints. We illustrate the proposed iterative heuristic approach on real-life instances of Netherlands Railways and compare it to a benchmark approach, showing that it finds a feasible timetable very close to the ideal one

Resolving infeasibilities in railway timetabling instances

One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes

Timetabling for strategic passenger railway planning

In research and practice, public transportation planning is executed in a series of steps, which are often divided into the strategic, the tactical, and the operational planning phase. Timetables are normally designed in the tactical phase, taking into account a given line plan, safety restrictions arising from infrastructural constraints, as well as regularity requirements and bounds on transfer times. In this paper, however, we propose a timetabling approach that is aimed at decision making in the strategic phase of public transportation planning and to determine an outline of a timetable that is good from the passengers’ perspective. Instead of including explicit synchronization constraints between train runs (as most timetabling models do), we include the adaption time (waiting time at the origin station) in the objective function to ensure regular connections between passengers’ origins and destinations. We model the problem as a mixed integer quadratic program and linearize it. Furthermore we propose a heuristic to generate starting solutions. We illustrate the trade-offs between dwell times and regularity of trains in two case studies based on the Dutch railway network

An Adjustable Robust Optimization Approach for Periodic Timetabling

In this paper, we consider the Robust Periodic Timetabling Problem (RPTP), the problem of designing an adjustable robust periodic timetable. We develop a solution method for a parametrized class of uncertainty regions. This class relates closely to uncertainty regions known in the robust optimization literature, and naturally denes a metric for the robustness of the timetable. The proposed solution method combines a linear decision rule with well-known reformulation techniques and cutting-plane methods. We show that the RPTP can be solved for practical-sized instances by applying the solution method to practical cases of Netherlands Railways (NS). In particular, we show that the trade-o between the e- ciency and robustness of a timetable can be analyzed using our solution method