Concurrent Optimization of Subway Vertical Alignments and Station Elevations With Improved Particle Swarm Optimization Algorithm

Station elevations and vertical alignment between adjacent stations often influence each other. Therefore, they should be optimized concurrently. However, existing studies mainly focus on optimizing station elevations or links separately. In this paper, a concurrent optimization model of stations and links is developed, in which the vertical points of intersection in stations and links are design variables. The comprehensive cost including construction, energy consumption, and travelling time, is the optimized objective function. Particle swarm optimization (PSO) is a method for searching in continuous space and is widely used for alignment optimization. Considering the characteristics of concurrent optimization for stations and links, the PSO algorithm is improved by modifying the updating formulas for particles and designing two strategies for particle updating, namely "Stations before Links" and "Links before Stations" strategy. A dynamic adaptive feasible region is proposed to handle the complex constraints during optimization. This method is applied here to a real-world case. The applications demonstrate that this method can automatically generate vertical alignments which jointly optimize the locations of stations and links and satisfy all the complex constrains.