This paper considers a high-speed rail corridor that requires high fidelity scheduling of train speed for a large number of trains with both tight power supply and temporal capacity constraints. This research aims to systematically integrate problems of macroscopic train timetabling and microscopic train trajectory calculations. We develop a unified modeling framework using three-dimensional space-time-speed grid networks to characterize both second-by-second train trajectory and segment-based timetables at different space and time resolutions. The discretized time lattices can approximately track the train position, speed, and acceleration solution through properly defined spacing and modeling time intervals. Within a Lagrangian relaxation-based solution framework, we propose a dynamic programming solution algorithm to find the speed/acceleration profile solutions with dualized train headway and power supply constraints. The proposed numerically tractable approach can better handle the non-linearity in solving the differential equations of motion, and systematically describe the complex connections between two problems that have been traditionally handled in a sequential way. We further use a real-world case study in the Beijing-Shanghai high-speed rail corridor to demonstrate the effectiveness and computational efficiency of our proposed methods and algorithms.
The train-set circulation plan problem (TCPP) belongs to the rolling stock scheduling (RSS) problem and is similar to the aircraft routing problem (ARP) in airline operations and the vehicle routing problem (VRP) in the logistics field. However, TCPP involves additional complexity due to the maintenance constraint of train-sets: train-sets must conduct maintenance tasks after running for a certain time and distance. The TCPP is nondeterministic polynomial hard (NP-hard). There is no available algorithm that can obtain the optimal global solution, and many factors such as the utilization mode and the maintenance mode impact the solution of the TCPP. This paper proposes a train-set circulation optimization model to minimize the total connection time and maintenance costs and describes the design of an efficient multiple-population genetic algorithm (MPGA) to solve this model. A realistic highspeed railway (HSR) case is selected to verify our model and algorithm, and, then, a comparison of different algorithms is carried out. Furthermore, a new maintenance mode is proposed, and related implementation requirements are discussed.
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