Optimizing Train Routing Problem in a Multistation High-Speed Railway Hub by a Lagrangian Relaxation Approach

As the intersection of multiple high-speed railway lines, the multi-station high-speed railway hub is the key to improve the transport efficiency of the high-speed railway network. This paper focuses on the optimization of the multi-station high-speed railway hub and models it as a train routing problem (TRP). Considering the capacity of railway infrastructures and the demand of passengers, a mixed integer linear programming model is proposed to minimize the total cost of train routes and passenger routes. The optimized train routes include the macroscopic routes between stations and the microscopic track allocation inside stations and Electric Multiple Units (EMUs) depots. A Lagrangian relaxation (LR) approach is developed to dualize the hard constraints and decompose the origin model into train and passenger subproblems, then a shortest path algorithm is designed to solve the subproblems independently. Numerical experiments based on an illustrative railway hub network and a real-world network are implemented to demonstrate the effectiveness of the model and algorithm. The solution results prove that the LR approach can obtain high-quality solutions within an acceptable computational time. Compared with the existing fixed scheme, the optimization scheme can reduce the total cost by 37.18% and utilize the railway lines and tracks more reasonably.