Robust optimization of train scheduling with consideration of response actions to primary and secondary risks

Nowadays, with the rapid development of rail transportation systems, passenger demand and the possibility of the risks occurring in this industry have increased. These conditions cause uncertainty in passenger demand and the development of adverse impacts as a result of risks, which put the assurance of precise planning in jeopardy. To deal with uncertainty and lessen negative impacts, robust optimization of the train scheduling problem in the presence of risks is crucial. A two-stage mixed integer programming model is suggested in this study. In the first stage, the objective of the nominal train scheduling problem is to minimize the total travel time function and optimally determine the decision variables of the train timetables and the number of train stops. A robust optimization model is developed in the second stage with the aim of minimizing unsatisfied demand and reducing passenger dissatisfaction. Additionally, programming is carried out and the set of optimal risk response actions is identified in the proposed approach for the presence of primary and secondary risks in the train scheduling problem. A real-world example is provided to demonstrate the model's effectiveness and to compare the developed models. The results demonstrate that secondary risk plays a significant role in the process of optimal response actions selection. Furthermore, in the face of uncertainty, robust solutions can significantly and effectively minimize unsatisfied demand by a slightly rise in the travel time and the number of stops obtained from the nominal problem

A flexible metro train scheduling approach to minimize energy cost and passenger waiting time

This paper aims to propose a flexible method for optimizing the service-oriented train timetable and utilization of different service trains in an urban rail transit line, in which the inhomogeneous passenger demands in two directions are taken into consideration. Different types of trains with various loading capacities are scheduled to satisfy passenger demands, such that the energy cost and passenger waiting time can be minimized. We first formulate a nonlinear integer programming model by considering a variety of system constraints, including inventory train constraints, train loading capacity constraints, train type constraints, etc. Then, complexity analyses and decomposition methods are specifically discussed to solve the model. A modified tabu search algorithm (MTS) with prior enumeration methods (PE) is then designed to find approximately optimal solutions for the formulated model. A set of numerical examples are implemented to verify the effectiveness and performance of the proposed approaches on a simple metro line and the Beijing Metro Yizhuang Line

A novel two-stage approach for energy-efficient timetabling for an urban rail transit network

Urban rail transit (URT) is the backbone transport mode in metropolitan areas to accommodate large travel demands. The high energy consumption of URT becomes a hotspot problem due to the ever-increasing operation mileages and pressing agendas of carbon neutralization. The high model complexity and inconsistency in the objectives of minimizing passenger travel time and operational energy consumption are the main challenges for energy-efficient timetabling for a URT network with multiple interlinked lines. This study proposes a general model framework of timetabling and passenger path choice in a URT network to minimize energy consumption under passenger travel time constraints. To obtain satisfactory energy-efficient nonuniform timetables, we suggest a novel model reformulation as a tree knapsack problem to determine train running times by a pseudo-polynomial dynamic programming algorithm in the first stage. Furthermore, a heuristic sequencing method is developed to determine nonuniform headways and dwell times in the second stage. The suggested model framework and solution algorithm are tested using a real-world URT network, and the results show that energy consumption can be considerably reduced given certain travel time increments

Real-time passenger flow oriented metro operation without timetables

With the increased population in large cities, the demand for urban passenger transport increases every year. Because of their high speed, high capacity and low energy consumption characteristics, urban metro systems are considered to play an essential role in urban transportation. Generally, unpredictable fluctuating passenger flow usually exists in urban metro operations, so traditional predetermined metro timetables cannot always meet the variation of real-time passenger flow, and the service quality of the metro system can be impacted profoundly. Nowadays, many researchers make efforts to propose suitable metro operation strategies to satisfy the constantly changing passenger demands and ensure the system’s service quality. In this situation, the author of this thesis deals with the dynamic metro scheduling problem and proposes a real-time metro operation method according to the variation of passenger flow. An innovative methodology has been proposed to model and solve the dynamic passenger flow oriented metro scheduling and real-time optimisation problem, and derived to propose passenger flow-based real-time operation strategies based on real-life operation without predetermined timetables. First, a formal mathematical model, the Passenger Flow-Oriented Scheduling Model (POSM) has been proposed, based on nonlinear integer programming to minimise the service quality index (SQI) and also optimise the scheduling strategy with real-time passenger flow variation. An innovative algorithm GA_POSM, based on a genetic algorithm and integrated macroscopic metro and passenger flow simulator, has been designed to solve the scheduling and real-time optimisation problems formulated by POSM. Then, the performance of GA_POSM has been evaluated based on the system data of Beijing Metro Line 19 with typical passenger flow distribution scenarios and Poisson distribution scenarios. The results show that, compared with traditional periodic timetables, the SQI can be significantly reduced by the scheduling method based on POSM; with real-time passenger flow variation, POSM can also optimise generated scheduling method flexibly. Based on a field study in the London Underground Bakerloo Line Operation Department, the author also extended the proposed mathematical model to deal with different objectives in real-life operation, and integrated GA_POSM with a decision tree algorithm to improve its calculation speed for real-time application. Based on these extensions, a real-time passenger flow-oriented metro operation method without timetables, RPOM, has been proposed, and the system architecture and infrastructure requirements have been introduced. Compared to traditional timetable-based metro operation, the method can significantly improve the metro operation flexibility and the service quality according to further case studies