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- Title
Optimization of High-speed Railway Train Timetabling Based on Lagrange Relaxation and Fuzzy Subgradient Optimization.
- Authors
Lihui An; Xuelei Meng; Ruhu Gao; Zheng Han; Yanxin Fu; Dongzhi Li; Ruidong Wang
- Abstract
To address the formidable challenge of optimizing and accurately solving the extensive scale of train timetables for high-speed railways, this study adopts a directed space-time network to depict the train timetable. By introducing incompatible arc sets, constraints such as minimum headway time and train overtaking are consolidated into mutually exclusive arc segment constraints, forming an integer programming model. The model is processed using the Lagrangian relaxation method, coupled with fuzzy theory, and an enhancement is made to the key iterative algorithm--the subgradient optimization algorithm--within the Lagrangian relaxation algorithm. The aim is to eliminate potential conflicts in the allocation of transportation resources among different train operation lines. The improved fuzzy subgradient optimization algorithm effectively leverages historical subgradient information and updates the subgradient reasonably. Finally, using the Beijing-Shanghai high-speed railway as a case study, experiments are conducted to optimize and compile the train timetables of 82 train lines in the segment. The computational performance of the standard subgradient algorithm and the fuzzy subgradient algorithm is compared. The results demonstrate that, while ensuring computational accuracy, the Lagrangian relaxation algorithm based on fuzzy subgradient optimization significantly enhances the quality of the optimal solution, reducing the dual gap value from 8.51% to 7.18%. This refined Lagrangian relaxation algorithm serves as an effective approach to obtain a higher-quality train timetable for high-speed railway trains.
- Subjects
SHANGHAI (China); BEIJING (China); RAILROAD trains; OPTIMIZATION algorithms; FUZZY algorithms; HIGH speed trains; INTEGER programming; RESOURCE allocation
- Publication
IAENG International Journal of Applied Mathematics, 2024, Vol 54, Issue 5, p877
- ISSN
1992-9978
- Publication type
Article