Generation of the transport service offer with application to timetable planning considering constraints due to maintenance work

Line planning is an important step in strategic timetable planning in public transport. In this step the transport offer for the customer is generated by the public transport operator, whereby the resulting costs for the operator should be as deep as possible. Mathematical models for line planning allow to create optimized line plans quickly. Planners can use these models to rate and select different alternatives. This is particularly valuable under the aspect of increasing maintenance and construction tasks of the railway infrastructure. We show, that in this case, it is possible to create functional requirements for automated timetable creation from the result of line planning step. The practical use of the involved models is illustrated by a real application example

Optimization in railway timetabling for regional and intercity trains in Zealand: A case of study of DSB

The Train Timetabling Problem is one of the main tactical problems in the railway planning process. Depending on the size of the network, the problem can be hard to solve directly and alternative methods should be studied. In this thesis, the Train Timetabling Problem is formulated using a graph formu-lation that takes advantage of the symmetric timetabling strategy and assumed fixed running times between station. The problem is formulated for the morning rush hour period of the Regional and InterCity train network of Zealand. The solution method implemented is based on a Large Neighborhood Search model that iteratively applies a dive-and-cut-and-price procedure. An LP relax version of the problem is solved using Column Generation considering only a subset of columns and constraints. Each column corresponds to the train paths of a line that are found by shortest paths in the graphs. Then, violated constraints are added by separation and an heuristic process is applied to help finding integer solutions. Last, the passengers are routed on the network based on the found timetable and the passenger travel time calculated. The process is repeated taking into account the best transfers from the solution found. A parameter tuning is conducted to find the best algorithm setting. Then, the model is solved for different scenarios where the robustness and quality of the solution is analyzed. The model shows good performance in most of the scenarios being able to find good quality solutions relatively fast. The way the best transfers are considered between timetable solutions does not add significant value in terms of solution quality but could be useful from a planning perspective. In addition, most of the real-life conflicts are taken into account in the model but not all of them. As a result, the model can still be improved in order to provide completely conflict-free timetables. In general, the model appears to be useful for the timetabling planning process of DSB. It allows to test different network requirements and preferences easily. The model not only generates a timetable but also estimates the passenger travel time and the occupancy of the trains quite accurately. Also, any modification in the line plan can easily be included without affecting the core model.Outgoin

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

An Overview and Categorization of Approaches for Train Timetable Generation

A train timetable is a crucial component of railway transportation systems as it directly impacts the system’s performance and the customer satisfaction. Various approaches can be found in the literature that deal with timetable generation. However, the approaches proposed in the literature differ significantly in terms of the use case for which they are in tended. Differences in objective function, timetable periodicity, and solution methods have led to a confusing number of works on this topic. Therefore, this paper presents a com pact literature review of approaches to train timetable generation. The reviewed papers are briefly summarized and categorized by objective function and periodicity. Special emphasis is given to approaches that have been applied to real-world railway data

Network optimization in railway transport planning

This work is dealing with train timetabling problem. In the first chapter, one can find an introduction to network flows which is needed for understanding deeper concepts later on. Namely, basic graph theory definitions are stated as well as core problems like the minimum cost flow and shortest path problem. Furthermore, two equivalent representations of network flows are described, including some useful properties connected to each of them. At the end of the chapter, linear programming and simplex method are introduced into some detail. In the second chapter more complex theory is introduced. At the beginning, multi-commodity flow problem is stated and few solutions approaches are briefly described. Once we settled for one of them, the rest of the chapter is dealing with Lagrangian relaxation and column generation techniques. Since column generation is the main result needed for solving our problem, some finer results, like determining lower and upper bounds, are stated. In the last, third chapter, one can find a model for representing train timetabling problem for a single line network. That model was introduced by Valentina Cacchiani in her Ph.D. thesis. In this work, periodicity of timetable is assumed because it makes computations way quicker, as well as it has some other benefits. At the end, one can find an algorithm based on column generation technique for solving introduced model. That algorithm is based on 6 steps, and after reading this work, one should be able to fully understand each of them.Ovaj rad bavi se problemom rasporeda vožnje u željezničkom prometu. U prvom poglavlju nalazi se uvod u mrežne tokove koji je potreban za razumijevanje naprednijih koncepata. Konkretno, iskazane su osnovne definicije teorije grafova kao i neki temeljni problemi poput problema najjeftinijeg toka i problema najkraćeg puta. Nadalje, opisana su dva ekvivalenta prikaza mrežnih tokova, uključujući neka korisna svojstva za svaki od njih. Na kraju poglavlja, linearno programiranje i simpleks metoda, objašnjeni su na razini razumijevanja. U drugom poglavlju nalazi se naprednija teorija koja se nadovezuje na prvo poglavlje. Na početku poglavlja prikazan je problem više dobara, kao i nekoliko pristupa rješavanju navedenog problema. Nakon što smo se odlučili za jedan od pristupa, ostatak poglavlja bavi se Lagrangeovom relaksacijom i metodom generacije stupaca. Kako je upravo metoda generacije stupaca najvažniji rezultat za rješavanje našega problema, napredniji rezultati vezani uz određivanje donjih i gornjih granica su detaljno objasnjeni. U posljednjem, trećem poglavlju, nalazi se model za prikazivanje problema rasporeda vožnje za mreže s jednom tračnicom. Navedeni model prvi puta je predstavljen u doktorskom radu Valentine Cacchiani. U ovom radu također pretpostavljamo periodičnost rasporeda vožnje kako bismo, između ostalih, ostvarili prednost poput bržeg vremena računanja. Na kraju rada nalazi se algoritam, temeljen na metodi generacije stupaca, za rješavanje predstavljenog modela. Navedeni algoritam sastoji se od 6 koraka, od kojih je svaki detaljno opisan u ovome radu

Almost 20 Years of Combinatorial Optimization for Railway Planning: from Lagrangian Relaxation to Column Generation

We summarize our experience in solving combinatorial optimization problems arising in railway planning, illustrating all of these problems as integer multicommodity flow ones and discussing the main features of the mathematical programming models that were successfully used in the 1990s and in recent years to solve them