Parallel Three-Dimensional Distance Transform for Railway Alignment Optimization Using OpenMP

Railway alignment optimization is a large-scale and time-consuming civil engineering problem. To solve it, a three-dimensional distance transform (3D-DT) algorithm, which is a variant of the three-dimensional Euclidean distance transform (3D-EDT), was previously designed. However, that algorithm is quite computationally intensive. In addition, the 3D-DT is inherently sequential, and it is thus challenging to parallelize. Thus, this study focuses on improving the sequential 3D-DT by transforming it into a parallel one. First, existing representative parallel EDT methods are reviewed and assessed. Then the railway alignment optimization model and the sequential 3D-DT are described. After that, critical execution properties of the 3D-DT that significantly influence its parallelization are explored in depth. Lastly, a novel so-called parallel linkage method is presented. This parallel implementation, which is developed using the OpenMP library, is highly effective and scalable by fully exploiting the parallelism of the algorithm. Using this parallel 3D-DT method, a large-scale, real-world railway case is tested and analyzed in detail. The outcomes verify that the proposed parallel method can accelerate the optimization process significantly without reducing the quality of computation results.