Lixing Yang

Train Timetable Problem on a Single-Line Railway With Fuzzy Passenger Demand

The aim of the train timetable problem is to determine arrival and departure times at each station so that no collisions will happen between different trains and the resources can be utilized effectively. Due to uncertainty of real systems, train timetables have to be made under an uncertain environment under most circumstances. This paper mainly investigates a passenger train timetable problem with fuzzy passenger demand on a single-line railway in which two objectives, i.e., fuzzy total passengers time and total delay time, are considered. As a result, an expected value goal-programming model is constructed for the problem. A branch-and-bound algorithm based on the fuzzy simulation is designed in order to obtain an optimal solution. Finally, some numerical experiments are given to show applications of the model and the algorithm.

Saving Energy and Improving Service Quality: Bicriteria Train Scheduling in Urban Rail Transit Systems

This paper formulates a two-objective model to optimize the timetables of urban rail transit systems based on energy-saving strategies and service quality levels. With time-dependent passenger demands, the calculation process of passenger travel time simulates boarding and alighting activities with some constraints to guarantee traffic capacity and meet passenger requirements, particularly in the oversaturated conditions. Traction and auxiliary energy consumption are considered in the operational energy consumption calculation. The regenerative energy, which is generated from braking trains and simultaneously used by traction trains, is also taken into account in the calculation with transmission loss. Through adjusting the headway, this model makes a tradeoff between passenger travel time and operational energy consumption with guaranteed traffic capability. Furthermore, a genetic algorithm with the binary encoding method is designed to obtain high-quality timetables. Based on the operational data of the Beijing Yizhuang subway line, we implement some numerical experiments to demonstrate the effectiveness of the proposed approaches.

Passenger train scheduling on a single-track or partially double-track railway with stochastic information

This article investigates a scheduling problem for passenger trains on a single or partially double-track railway in which the total passengers’ trip time with a penalty function is minimized. Owing to the uncertainty of the real traffic system, the number of passengers boarding (leaving) the train at each station is treated as a random variable. Three kinds of criteria are introduced to compute the total passengers’ trip time, including the expected value criterion, the pessimistic value criterion and the optimistic value criterion. A 0-1 mixed integer programming model is constructed for the problem, and a branch-and-bound algorithm is also designed to solve the model, in which two strategies are introduced to resolve the conflicts on tracks. Finally, some numerical experiments are performed to show the performance of the model and the algorithm.

Rescheduling trains with scenario-based fuzzy recovery time representation on two-way double-track railways

Severe weather conditions and inherent uncertainties in various components of railway traffic systems can lead to equipment breakdown and reduced capacity on tracks and stations. This paper formulates a two-stage fuzzy optimization model to obtain a robust rescheduling plan under irregular traffic conditions, and a scenario-based representation is adapted to characterize fuzzy recovery time durations on a double-track railway line. The model aims to minimize the expected total delay time in the rescheduled train schedule with respect to the original timetable. Two decomposed sub-models are further developed corresponding to the trains in different directions, and then GAMS optimization software is used to obtain the robust rescheduling plan. The numerical experiments demonstrate the effectiveness of the proposed approaches.

Efficient Real-Time Train Operation Algorithms With Uncertain Passenger Demands

The majority of existing studies in subway train operations focus on timetable optimization and vehicle tracking methods, which may be infeasible with disturbances in actual operations. To deal with uncertain passenger demands and realize real-time train operations (RTOs) satisfying multiobjectives, including overspeed protection, punctuality, riding comfort, and energy consumption, this paper proposes two RTO algorithms via expert knowledge and an online learning approach. The first RTO algorithm is developed by a knowledge-based system to ensure the multiple objectives with a constant timetable. Then, by considering uncertain passenger demand at each station and random running time errors, we convert the train operation problem into a Markov decision process with nondeterministic state transition probabilities in which the aim is to minimize the reward for both the total time delay and energy consumption in a subway line. After designing policy, reward, and transition probability, we develop an integrated train operation (ITO) algorithm based on Q-learning to realize RTOs with online adjusting the timetable. Finally, we present some numerical examples to test the proposed algorithms with real detected data in the Yizhuang Line of Beijing Subway. The results indicate that, taking the multiple objectives into account, the RTO algorithm outperforms both manual driving and automatic train operations. In addition, the ITO algorithm is capable of dealing with uncertain disturbances, keeping the total time delay within 2 s and reducing the energy consumption.

A subjective capacity evaluation model for single-track railway system with δ-balanced traffic and λ-tolerance level

In this paper, we propose a method to measure the capacity of single-track railway corridors subject to a given degree of balance between the two directional traffic loads and a permitted overall delay level. We introduce the concepts of δ-balance degree and λ-tolerance level to reflect the subjective measures of the railway administrator for capacity evaluation. A train balance scheduling problem with initial departure time choice of trains is embedded into the measure of railway capacity. The combined scheduling and capacity evaluation method is formulated as a 0-1 mixed integer programming model, and solved using a simple dichotomization-based heuristic method. A highly efficient heuristic procedure based on the concept of compaction pattern is developed to solve the train balance scheduling problem, and the numerical results demonstrate that the method yields high-quality solutions close to the optimal ones using the CPLEX solver. The two-way traffic loading capacity of a single-track railway corridor is analyzed in detail under different tolerance levels and balance degrees. The transition regions of traffic loading capacity are identified, and provide a useful decision support tool for the railway administrators in dealing with train rescheduling requests under disturbance or disruption scenarios.