Mountain railway alignment optimization is known as a very complex engineering problem that should consider many factors, such as drastically undulating terrain, geological hazard impacts, and additional constraints. Moreover, many mountain railway projects are located in earthquake‐prone regions and hence are greatly threatened by seismic activity. Thus far, most alignment optimization studies aim at finding the least‐cost solutions within budget but slight attention has been paid to reducing the complex seismic risk through optimization. In this paper, the first known quantitative seismic risk assessment model for railway alignment optimization is presented, which combines probabilistic seismic fragility analysis and probabilistic seismic loss analysis. Three methods for fragility analysis of bridge, tunnel, and earthwork sections are designed and a specific event tree is developed for seismic loss analysis. Moreover, multiple preliminary constraints are specified for alignments traversing active faults. Afterwards, the seismic risk assessment model is combined with a least‐cost model to formulate a bi‐objective optimization model. To solve it, a particle swarm optimization algorithm is improved by blending the crowding distance computation (CDC) and, especially, a novel marginal benefit analysis (MBA) to search for pareto‐optimal solutions during optimization. A prescreening and repairing operator is also designed to handle the fault constraints. Finally, when applying the proposed procedure to a complex realistic railway case, the results show that the hybrid CDC+MBA bi‐objective solver can find better pareto‐optimal solutions than the generic CDC method. Besides, detailed data analysis shows that the present method can produce less expensive as well as safer solutions than the best alignment designed by experienced human engineers.

中文翻译：

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结合地震风险评估的双目标山区铁路路线优化

山区铁路路线优化是众所周知的一个非常复杂的工程问题，应考虑许多因素，例如急剧起伏的地形，地质灾害影响和其他限制。此外，许多山区铁路项目位于地震多发地区，因此受到地震活动的极大威胁。到目前为止，大多数对准优化研究的目的都是在预算范围内找到成本最低的解决方案，但是对通过优化降低复杂地震风险的关注却很少。本文提出了第一个已知的用于铁路路线优化的定量地震风险评估模型，该模型结合了概率地震易损性分析和概率地震损失分析。桥梁，隧道脆弱性分析的三种方法 设计了土方部分，并开发了用于地震损失分析的特定事件树。此外，为遍历活动故障的路线指定了多个初步约束。然后，将地震风险评估模型与最小成本模型相结合，以形成双目标优化模型。为了解决这个问题，通过混合拥挤距离计算（CDC）尤其是新颖的边际收益分析（MBA）在优化过程中寻找最优解决方案，改进了粒子群优化算法。还设计了预检和维修操作员来处理故障约束。最后，将建议的程序应用于复杂的现实铁路案例时，结果表明，与常规CDC方法相比，混合CDC + MBA双目标求解器可以找到更好的对等最优解。此外，详细的数据分析表明，与由经验丰富的人类工程师设计的最佳对齐方式相比，本方法可以产生更便宜，更安全的解决方案。