EAAI Journal 2026 Journal Article
Two-stage automated design of railway vertical alignments with topography-driven Fourier transform and constrained A-Star search
- Taoran Song
- Hao Pu
- Hong Zhang
- Paul Schonfeld
- Lihui Peng
Vertical alignment design is crucial for a railway project since it largely determines its construction investment, lifecycle costs, and various other impacts. However, among the theoretically-infinite numbers of possible alternatives, it is difficult to optimize a vertical alignment matching the drastically-undulating terrain line along the railway, while also considering large structure tradeoffs (such as bridges and tunnels) and various design constraints. To solve this problem, a two-stage method is proposed for automated vertical alignment optimization. In stage I, the railway terrain line is converted to a spatial wave and modelled through the spectral signature analysis of a topography-driven Fast Fourier Transform (FFT). Afterward, by identifying the key terrain characteristic locations based on the derived Fourier series function, feasible search regions for vertical alignment design are determined by processing specific design constraints. For stage II, an A-Star algorithm is customized for vertical alignment search. First, A-Star nodes are discretized within the above feasible search spaces. Then, a comprehensive constraint-handling operator is devised to guarantee a solution’s feasibility during optimization. Moreover, a deterministic simulation algorithm is integrated to create a weighted directed graph for A-Star path generation. Ultimately, the developed method is applied to a complex mountain railway alignment case. The algorithm performances of the two stages are both discussed in detail.