Mountain railway alignment design is an important but complex civil engineering problem. To overcome the drastically undulating terrain, long tunnels and high bridges are major structures used along a mountain railway, which poses great challenges for railway design and construction. Unfortunately, despite being studied for many years, the crucial construction factors of complex structures have received slight attention in alignment optimization. In this paper, for the first time, the layout of large-scale auxiliary construction projects (LACPs), including tunnel shafts and access roads, is incorporated into the alignment design process in order to consider construction practicability and economy. Primarily, an alignment–LACPs concurrent optimization model is built. After defining the comprehensive design variables, the alignment–LACPs total construction cost is formulated as the objective function. Besides, the separate constraints for designing the alignment and LACPs are considered. Also, a construction duration computation is proposed for constraining the alignment–LACPs integration. To solve the model, a four-step hybrid solution method is developed. Specifically, the alignment is first generated with a particle swarm optimization (PSO). Afterward, a new divide and conquer approach is devised to search for shaft alternatives along the alignment. Then, a customized Dijkstra algorithm is developed to search for complex access roads. Finally, a novel polynomial mechanism for time-varying acceleration coefficients (TVAC) is designed for PSO to evolve the alignment–LACPs solutions. The above model and methods have been applied to two complex actual mountain railway examples. Their effectiveness is demonstrated through detailed analysis of resulting railway solutions and control experiments with contemporary TVAC-based methods.

中文翻译：

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大型配套工程山区铁路线形优化整合布局

山区铁路线形设计是一个重要而复杂的土木工程问题。为克服起伏剧烈的地形，长隧道和高桥梁是山区铁路沿线的主要结构，这对铁路设计和施工提出了巨大挑战。不幸的是，尽管经过多年研究，复杂结构的关键构造因素在对齐优化中却很少受到关注。本文首次将包括隧道竖井和进场道路在内的大型辅助建设项目（LACP）的布置纳入线形设计过程，以考虑施工的实用性和经济性。首先，建立了一个alignment-LACPs并发优化模型。定义综合设计变量后，alignment-LACP 的总建设成本被制定为目标函数。此外，还考虑了设计对齐和 LACP 的单独约束。此外，还提出了一种施工持续时间计算来约束对齐-LACPs 集成。为了求解该模型，开发了一种四步混合求解方法。具体来说，首先使用粒子群优化 (PSO) 生成对齐。之后，设计了一种新的分而治之方法来搜索沿路线的竖井替代方案。然后，开发了一种定制的 Dijkstra 算法来搜索复杂的通路。最后，为 PSO 设计了一种新颖的时变加速度系数多项式机制 (TVAC)，以演化对齐-LACPs 解决方案。上述模型和方法已应用于两个复杂的实际山区铁路实例。通过详细分析由此产生的铁路解决方案和使用现代基于 TVAC 的方法进行控制实验，证明了它们的有效性。