Abstract
With the rapid development of high-speed railway (HSR) systems, the increasing demand for passenger traffic has put forward higher requirements for HSR train timetabling problems (HSRTTPs). This paper establishes two mathematical optimisation models with different optimisation objectives for an HSRTTP and solves these models through a column generation-based algorithm. However, the column generation-based algorithm has the disadvantage of a slow convergence rate, thus we put forward corresponding acceleration strategies for five stages of the algorithm: preprocessing, restricted master problem, pricing problem, branch-and-bound and postprocessing from a symmetry point between the computation efficiency and the accuracy. The effectiveness of the acceleration strategies was validated by a case study of the Beijing–Shanghai HSR. The results show that the proposed optimal acceleration strategies can increase the computation efficiency of the algorithm by 11.8× on average while ensuring the accuracy.
Highlights
In 2018, the total volume of passenger flow in China was 17.9 billion, which was 30% higher than that in 1998 according to the National Bureau of Statistics of China
Chen and Shen [20] proposed a column removal strategy, strong label cutting rule and shift pool acceleration strategy for the application of a column generation-based algorithm in crew problems, and this approach had a significant effect in controlling the scale of the restricted master problem (RMP), improving the solution speed of the pricing problem (PP) and reducing the time required for finding an integer solution
Using the integer solutions that are to RMP, the current upper bounditeration value asstrategy the newisinitial feasible solutions, the solutions that areissuperior to the current upper bound as the new initialimproves feasible solutions, the whole algorithm re-operated from the root node, and value this strategy the operation whole algorithm re-operated from the root node, and this strategy not computation, only improvesa the operation efficiency but alsoiseffectively controls size of the problem
Summary
In 2018, the total volume of passenger flow in China was 17.9 billion, which was 30% higher than that in 1998 according to the National Bureau of Statistics of China. Yue et al [9] established an optimisation model of train timetables based on a space-time network to simultaneously consider both passenger demands and train scheduling. The column generation algorithm is a common approach used for solving large-scale linear programming problems and has been successfully applied to the study of TTPs [9,17,18,19]. Chen and Shen [20] proposed a column removal strategy, strong label cutting rule and shift pool acceleration strategy for the application of a column generation-based algorithm in crew problems, and this approach had a significant effect in controlling the scale of the RMP, improving the solution speed of the PP and reducing the time required for finding an integer solution.
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