Owing to wide-ranging searches (there are various alignments between two points) as well as complex and nonlinear cost functions and a variety of geometric constraints, the problem of optimal railway alignment is classified as a complex problem. Thus, choosing an alignment between two points is usually done based on a limited number of alignments designed by experts. In recent years, the study of railway alignment optimization has shown the importance of optimization and the introduction of various algorithms and their usefulness in solving different problems. It is expected that applying meta-heuristic optimization algorithms such as methods based on swarm intelligence can lead to better alignments. In this study, we tried to modify models based on previous studies in order to design and develop a model based on a single framework to provide three-dimensional optimization of alignments applicable in the real world. To obtain this, the particle swarm algorithm is used and a geographic information system is incorporated as a means of search in three-dimensional space. In particular, the cost function used in previous studies considering the costs related to structures (bridges and tunnels) are improved regarding hydraulic structure alignments. Furthermore, the transition curve of horizontal alignment and slope restrictions of curves are considered in this project by using the penalty function in order to obtain the most practical results possible. Finally, this study examines three problems for which the results are acceptable in cases of railway alignment geometry and its application in the real world.

中文翻译：

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考虑桥梁成本，隧道成本和过渡曲线的铁路路线优化模型

由于搜索范围广泛（两点之间存在各种路线）以及复杂和非线性的成本函数以及各种几何约束，因此，最佳铁路路线问题被归类为复杂问题。因此，通常基于专家设计的有限数量的路线来选择两点之间的路线。近年来，对铁路路线优化的研究表明了优化的重要性以及各种算法的引入及其在解决不同问题中的实用性。预计应用基于启发式算法的元启发式优化算法可以带来更好的一致性。在这个研究中，我们试图根据以前的研究来修改模型，以便设计和开发基于单个框架的模型，以提供适用于现实世界中的路线的三维优化。为此，使用了粒子群算法，并结合了地理信息系统作为在三维空间中进行搜索的手段。特别是，先前研究中考虑与结构（桥梁和隧道）相关的成本的成本函数在水工结构对齐方面得到了改善。此外，在该项目中，通过使用惩罚函数考虑了水平对齐的过渡曲线和曲线的斜率限制，以便获得最实际的结果。最后，