Abstract This paper deals with a new mathematical model for designing railway bypasses. The model was developed with applications to urban areas in mind, and presents useful tools to avoid forbidden areas, buildings, and level crossings with secondary paths and other linear infrastructures. It takes into account technical constraints (minimum radii, minimum length of tangents and transition curves, maximum slopes, and also maximum azimuth changes), and ensure a suitable connection with the current layout, for both horizontal and vertical alignment. In addition, the model searches for the best bypass from an economical point of view, taking into account expropriation costs, cleaning and terrain preparation, earthwork (considering different type of materials), and railroad construction costs. This model is applied in a case study located at the Northwest of Spain, in a section of A Coruna-Lugo line, which is currently under consideration for its redesign. By using this model, a railway bypass without level crossings is obtained, avoiding the urban area of Parga and any buildings in the surrounding area, and which is optimal from an economical point of view.

中文翻译：

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优化城市铁路旁路。西班牙西北部拉科鲁尼亚-卢戈线的案例研究

摘要 本文讨论了一种用于设计铁路旁路的新数学模型。该模型的开发考虑到了城市地区的应用，并提供了有用的工具来避开禁区、建筑物和带有二级路径和其他线性基础设施的平交道口。它考虑了技术限制（最小半径、切线和过渡曲线的最小长度、最大斜率以及最大方位角变化），并确保与当前布局的适当连接，用于水平和垂直对齐。此外，该模型从经济的角度搜索最佳旁路，考虑征地成本、清洁和地形准备、土方工程（考虑不同类型的材料）和铁路建设成本。该模型应用于位于西班牙西北部拉科鲁尼亚-卢戈线的一段的案例研究，目前正在考虑对其进行重新设计。通过使用该模型，获得了一条没有平交道口的铁路旁路，避开了帕尔加市区和周边地区的任何建筑物，从经济的角度来看这是最佳的。