Look-Ahead Approaches for Integrated Planning in Public Transportation

In this paper we deal with three consecutive planning stages in public transportation: Line planning (including line pool generation), timetabling, and vehicle scheduling. These three steps are traditionally performed one after another in a sequential way often leading to high costs in the (last) vehicle scheduling stage. In this paper we propose three different ways to "look ahead", i.e., to include aspects of vehicle scheduling already earlier in the sequential process: an adapted line pool generation algorithm, a new cost structure for line planning, and a reordering of the sequential planning stages. We analyze these enhancements experimentally and show that they can be used to decrease the costs significantly

Towards Improved Robustness of Public Transport by a Machine-Learned Oracle

The design and optimization of public transport systems is a highly complex and challenging process. Here, we focus on the trade-off between two criteria which shall make the transport system attractive for passengers: their travel time and the robustness of the system. The latter is time-consuming to evaluate. A passenger-based evaluation of robustness requires a performance simulation with respect to a large number of possible delay scenarios, making this step computationally very expensive. For optimizing the robustness, we hence apply a machine-learned oracle from previous work which approximates the robustness of a public transport system. We apply this oracle to bi-criteria optimization of integrated public transport planning (timetabling and vehicle scheduling) in two ways: First, we explore a local search based framework studying several variants of neighborhoods. Second, we evaluate a genetic algorithm. Computational experiments with artificial and close to real-word benchmark datasets yield promising results. In all cases, an existing pool of solutions (i.e., public transport plans) can be significantly improved by finding a number of new non-dominated solutions, providing better and different trade-offs between robustness and travel time

Cost-Minimal Public Transport Planning

In this paper we discuss what a cost-optimal public transport plan looks like, i.e., we determine a line plan, a timetable and a vehicle schedule which can be operated with minimal costs while, at the same time, allowing all passengers to travel between their origins and destinations. We are hereby interested in an exact solution of the integrated problem. In contrast to a passenger-optimal transport plan, in which there is a direct connection for every origin-destination pair, the structure or model for determining a cost-optimal transport plan is not obvious and has not been researched so far. We present three models which differ with respect to the structures we are looking for. If lines are directed and may contain circles, we prove that a cost-optimal schedule can (under weak assumptions) already be obtained by first distributing the passengers in a cost-optimal way. We are able to streamline the resulting integer program such that it can be applied to real-world instances. The model gives bounds for the general case. In the second model we look for lines operated in both directions, but allow only simplified vehicle schedules. This model then yields stronger bounds than the first one. Our most realistic model looks for lines operated in both directions, and allows all structures for the vehicle schedules. This model, however, is only computable for small instances. Finally, the results of the three models and their respective bounds are compared experimentally

A New Sequential Approach to Periodic Vehicle Scheduling and Timetabling

When evaluating the operational costs of a public transport system, the most important factor is the number of vehicles needed for operation. In contrast to the canonical sequential approach of first fixing a timetable and then adding a vehicle schedule, we consider a sequential approach where a vehicle schedule is determined for a given line plan and only afterwards a timetable is fixed. We compare this new sequential approach to a model that integrates both steps. To represent various operational requirements, we consider multiple possibilities to restrict the vehicle circulations to be short, as this can provide operational benefits. The sequential approach can efficiently determine public transport plans with a low number of vehicles. This is evaluated theoretically and empirically demonstrated for two close-to real-world instances

Robustness Tests for Public Transport Planning

The classical planning process in public transport planning focuses on the two criteria operating costs and quality for passengers. Quality mostly considers quantities like average travel time and number of transfers. Since public transport often suffers from delays caused by random disturbances, we are interested in adding a third dimension: robustness. We propose passenger-oriented robustness indicators for public transport networks and timetables. These robustness indicators are evaluated for several public transport plans which have been created for an artificial urban network with the same demand. The study shows that these indicators are suitable to measure the robustness of a line plan and a timetable. We explore different trade-offs between operating costs, quality (average travel time of passengers), and robustness against delays. Our results show that the proposed robustness indicators give reasonable results

Delay Management with Integrated Decisions on the Vehicle Circulations

The task of delay management in public transport is to decide whether a vehicle should wait for a delayed vehicle in order to maintain the connection for transferring passengers. So far, the vehicle circulations are often ignored in the optimization process, although they have an influence on the propagation of the delay through the network. In this paper we consider different ways from literature to incorporate vehicle circulations in the delay management stage of public transport planning. Since the IP formulation for the integrated problem is hard to solve, we investigate bounds and develop several heuristics for the integrated problem. Our experiments on close-to real-world instances show that integrating delay management and decisions on vehicle circulations may reduce the overall delay by up to 39 percent. We also compare the runtimes and objective function values of the different heuristics. We conclude that we can find competitive solutions in a reasonable amount of time

Robustness as a Third Dimension for Evaluating Public Transport Plans

Providing attractive and efficient public transport services is of crucial importance due to higher demands for mobility and the need to reduce air pollution and to save energy. The classical planning process in public transport tries to achieve a reasonable compromise between service quality for passengers and operating costs. Service quality mostly considers quantities like average travel time and number of transfers. Since daily public transport inevitably suffers from delays caused by random disturbances and disruptions, robustness also plays a crucial role. While there are recent attempts to achieve delay-resistant timetables, comparably little work has been done to systematically assess and to compare the robustness of transport plans from a passenger point of view. We here provide a general and flexible framework for evaluating public transport plans (lines, timetables, and vehicle schedules) in various ways. It enables planners to explore several trade-offs between operating costs, service quality (average perceived travel time of passengers), and robustness against delays. For such an assessment we develop several passenger-oriented robustness tests which can be instantiated with parameterized delay scenarios. Important features of our framework include detailed passenger flow models, delay propagation schemes and disposition strategies, rerouting strategies as well as vehicle capacities. To demonstrate possible use cases, our framework has been applied to a variety of public transport plans which have been created for the same given demand for an artificial urban grid network and to instances for long-distance train networks. As one application we study the impact of different strategies to improve the robustness of timetables by insertion of supplement times. We also show that the framework can be used to optimize waiting strategies in delay management

The line planning routing game

In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a system- optimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples