The design of grade-separated road and railway crossings can be complicated and time-consuming since the intersection point as well as the road and rail alignments should jointly optimize an objective such as minimum construction costs. Moreover, the design of grade-separated road and railway crossings should consider additional crossing constraints and possible revisions of the road alignments. However, research on alignment optimization with variable ends is scarce. In this article, a grade-separated road and railway crossing model is developed, the crossing point of which as well as both connection points with the road, are variable. Subsequently, by searching synchronously for the paths that connect different endpoints, a distance transform algorithm is applied. The effectiveness of the method is verified through a real-world case study. The results show that the proposed method can find various promising solutions that both satisfy multiple constraints and are considerable improvements on the designs produced by experienced human designers.

由于交叉路口以及道路和铁路路线应共同优化诸如最低建设成本之类的目标，因此，坡度分离的公路和铁路道口的设计可能既复杂又费时。此外，按等级划分的公路和铁路道口的设计应考虑额外的道口约束和可能的道路路线修改。但是，关于可变末端的比对优化的研究很少。在本文中，建立了一个坡度分离的公路和铁路交叉模型，该模型的交叉点以及与道路的两个连接点都是可变的。随后，通过同步搜索连接不同端点的路径，应用了距离变换算法。通过实际案例研究验证了该方法的有效性。