Optimization Methods in Modern Transportation Systems

One of the greatest challenges in the public transportation network is the optimization of the passengers waiting time, where it is necessary to find a compromise between the satisfaction of the passengers and the requirements of the transport companies. This paper presents a detailed review of the available literature dealing with the problem of passenger transport in order to optimize the passenger waiting time at the station and to meet the requirements of companies (maximize profits or minimize cost). After a detailed discussion, the paper clarifies the most important objectives in solving a timetabling problem: the requirements and satisfaction of passengers, passenger waiting time and capacity of vehicles. At the end, the appropriate algorithms for solving the set of optimization models are presented

Passenger Centric Train Timetabling Problem with elastic demand

A wide taxonomy of the adopted design criterion in models for Train Timetabling Problem (TTP), considers two kinds of models: operations-centric models, which are focused on railway operations and assume the demand has been considered and modeled in the design stage of the railway network, and passenger-centric models, which tries to maximize customers satisfaction. The first models have been widely studied since historically, the train operating companies (TOC) had a monopoly in the railway market. Currently, and because of the European directive (EU Directive 91/440) which allows the competition between different TOC, the research interest in the second kind of models is increasing. This paper proposes a mathematical model for TTP which includes the elasticity of the demand against the characteristics of supply. To do that, the proposed model is based on the concept of strategy and by means of the use of radial-basis functions, the demand model allows to estimate the number of passengers in each strategy on the network, taking into account the existing correlation between strategies

User perspectives in public transport timetable optimisation

The present paper deals with timetable optimisation from the perspective of minimising the waiting time experienced by passengers when transferring either to or from a bus. Due to its inherent complexity, this bi-level minimisation problem is extremely difficult to solve mathematically, since timetable optimisation is a non-linear non-convex mixed integer problem, with passenger flows defined by the route choice model, whereas the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach is developed in this paper, based on the idea of varying and optimising the offset of the bus lines. Varying the offset for a bus line impacts the waiting time passengers experience at any transfer stop on the bus line.In the bi-level timetable optimisation problem, the lower level is a transit assignment calculation yielding passengers' route choice. This is used as weight when minimising waiting time by applying a Tabu Search algorithm to adapt the offset values for bus lines. The updated timetable then serves as input in the following transit assignment calculation. The process continues until convergence.The heuristic solution approach was applied on the large-scale public transport network in Denmark. The timetable optimisation approach yielded a yearly reduction in weighted waiting time equivalent to approximately 45 million Danish kroner (9 million USD)

An Optimization to Schedule Train Operations with Phase-Regular Framework for Intercity Rail Lines

The most important operating problem for intercity rail lines, which are characterized with the train operations at rapid speed and high frequency, is to design a service-oriented schedule with the minimum cost. This paper proposes a phase-regular scheduling method which divides a day equally into several time blocks and applies a regular train-departing interval and the same train length for each period under the period-dependent demand conditions. A nonlinear mixed zero-one programming model, which could accurately calculate the passenger waiting time and the in-train crowded cost, is developed in this study. A hybrid genetic algorithm associated with the layered crossover and mutation operation is carefully designed to solve the proposed model. Finally, the effectiveness of the proposed model and algorithm is illustrated through the application to Hefei-Wuhan intercity rail line in China

An optimization model for line planning and timetabling in automated urban metro subway networks

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networksComment: 30 pages, 6 figures, 9 table

Train Timetabling Optimisation Model Considering Headway Coordination between Mainline and Depot

This paper proposes an optimisation model for an urban rail transit line timetable considering headway coordination between the mainline and the depot during the transition period. The model accounts for the tracking operation scenario of trains inserted from the depot onto the mainline and related train operation constraints. The optimisation objectives are the number of trains inserted, maximum train capacity rate and average headway deviation. Second-generation non-dominated sorting genetic algorithm is designed to solve the model. A case study shows that optimisation achieves a total of 25 trains inserted, a maximum train capacity rate of 0.975 and an average headway deviation of 9.5 s, resulting in significant improvements in train operations and passenger satisfaction. Compared with the current train timetable before optimisation, the average dwell time and the maximum train capacity rate at various stations have been reduced after optimisation. The proposed model and approach can be used for train timetabling optimisation and managing the operations of urban rail transit lines

Planning of Truck Platoons: a Literature Review and Directions for Future Research

A truck platoon is a set of virtually linked trucks that drive closely behind one another using automated driving technology. Benefits of truck platooning include cost savings, reduced emissions, and more efficient utilization of road capacity. To fully reap these benefits in the initial phases requires careful planning of platoons based on trucks’ itineraries and time schedules. This paper provides a framework to classify various new transportation planning problems that arise in truck platooning, surveys relevant operations research models for these problems in the literature and identifies directions for future research

A multi-agent-based approach for the impacts analysis of passenger flow on platforms in metro stations considering train operations

Impacts analysis of train operation on passenger flow in metro stations is an important and fundamental requirement to improve the operational efficiency and ensure passengers a high level of service. This study aims at large metro stations where thousands of passengers are moving, boarding or alighting and the complicated interactions among passengers and between passengers and other entities like stairways or trains take place all the time. A multi-agent-based approach is developed from the investigation of movement characteristics of passengers to meet the above requirement and deal with such interactions. The simulation scenarios considering the various conditions of train operations are performed in the case studies of a metro station in Beijing (China) to prove the feasibility of the proposed approach, which is useful to formulate and evaluate the operation schemes of trains

Designing robust schedule coordination scheme for transit networks with safety control margins

We propose a robust schedule coordination scheme which combines timetable planning with a semi-flexible departure delayed control strategy in case of disruptions. The flexibility is provided by allowing holding for the late incoming bus within a safety control margin (SCM). In this way, the stochastic travel time is addressed by the integration of real-time control and slacks at the planning phase. The schedule coordination problem then jointly optimises the planning headways and slack times in the timetable subject to SCM. Analytical formulations of cost functions are derived for three types of operating modes: uncoordinated operation, departure punctual control and departure delayed control. The problem is formulated as a stochastic mixed integer programming model and solved by a branch-and-bound algorithm. Numerical results provide an insight into the interaction between SCM and slack times, and demonstrate that the proposed model leads to cost saving and higher efficiency when SCM is considered. Compared to the conventional operating modes, the proposed method also presents advantages in transfer reliability and robustness to delay and demand variation