Abstract
To avoid conflicts among trains at stations and provide passengers with a periodic train timetable to improve service level, this paper mainly focuses on the problem of multi-periodic train timetabling and routing by optimizing the routes of trains at stations and their entering time and leaving time on each chosen arrival–departure track at each visited station. Based on the constructed directed graph, including unidirectional and bidirectional tracks at stations and in sections, a mixed integer linear programming model with the goal of minimizing the total travel time of trains is formulated. Then, a strategy is introduced to reduce the number of constraints for improving the solved efficiency of the model. Finally, the performance, stability and practicability of the proposed method, as well as the impact of some main factors on the model are analyzed by numerous instances on both a constructed railway network and Guang-Zhu inter-city railway; they are solved using the commercial solver WebSphere ILOG CPLEX (International Business Machines Corporation, New York, NY, USA). Experimental results show that integrating multi-periodic train timetabling and routing can be conducive to improving the quality of a train timetable. Hence, good economic and social benefits for high-speed rail can be achieved, thus, further contributing to the sustained development of both high-speed railway systems and society.
Highlights
High-speed railways that meet the requirements of the modern passenger market and sustainable development, compared with conventional railways, are a new type of green transportation due to their operating characteristics of high speed, high density, large capacity, low energy consumption and little pollution
Integrating multi-periodic train timetabling and routing at stations can realize the reasonable utilization of resources at stations and improve the quality of train timetables to achieve good social and economic benefits of high-speed rail, which will contribute to the sustained development of both high-speed railway systems and society
Contracting the range of running time of trains in sections and the dwelling time of trains at stations can strengthen the impact of simplified strategy to further improve the solve efficiency of model, while expanding their range will cut down its effect of simplified strategy, it still can reduce the number of constraints to shorten the computational time as the gaps in instances 1–8 are all more than 0
Summary
High-speed railways that meet the requirements of the modern passenger market and sustainable development, compared with conventional railways, are a new type of green transportation due to their operating characteristics of high speed, high density, large capacity, low energy consumption and little pollution. Our paper focuses on the multi-periodic train timetabling and routing simultaneously based on some predetermined trains of each period-type on a high-speed railway network including one-way and two-way tracks It aims to optimizing the routes of all trains at their visited stations and their entering and leaving time on visited sections and stations. (1) A mixed integer linear programming model is formulated for the simultaneous multi-periodic train timetabling and routing, and the commercial solver WebSphere ILOG CPLEX (International Business Machines Corporation, New York, NY, USA) is applied to solve it This model optimizes the entering time and leaving time of all trains and searches for their routes of arrival–departure tracks at their visited stations.
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