Railway alignment optimization is considered one of the most complicated and time‐consuming problems in railway planning and design. It requires searching among the infinite potential alternatives in huge three‐dimensional (3D) search spaces for a near‐optimal alignment, while considering complex constraints and a nonlinear objective function. In mountainous regions, the complex terrain and constructions require additional and more complex constraints than in topographically simpler regions. In this paper, the authors solve this problem with an algorithm based on a 3D distance transform (3D‐DT). Compared with previous two‐dimensional distance transform (2D‐DT) methods developed in this field, the feasible search spaces of 3D‐DT are greatly increased. Consequently, this new method can find more alternatives with higher qualities. In this approach, an erythrocyte‐shaped 3D neighboring mask is developed to narrow local search spaces and speed up the search process. Besides, a stepwise‐backstepping strategy is designed to dynamically determine feasible 3D search spaces and efficiently search the study area. During the 3D‐DT search process, multiple constraints, including geometric, construction, and location constraints, are effectively handled. After the 3D‐DT search, a genetic algorithm is employed to optimize the 3D‐DT paths into final alignments. Finally, this novel approach is applied to an actual case in a complex mountainous region. The comprehensive cost of the best solution generated by 3D‐DT is 16% below a manual solution produced by very experienced human designers. Furthermore, the total number of feasible alternatives found by 3D‐DT is 4.3 times greater than by 2D‐DT. The comprehensive cost of the best 3D‐DT solution is 10% below the best one generated by 2D‐DT.

Sustainable railway construction and operation are threatened by densely occurring geological hazards in complex mountainous regions. Thus, during the alignment optimization process, it is vital to reduce the harmful impacts of geological hazards to a railway. However, current alignment-related studies solely consider such threats in existing geological hazard regions and, outside these regions, slight attention has been devoted to the assessment of potential hazardous impacts along the alignment. To this end, this paper proposes a novel railway alignment optimization model considering both existing and potential geological hazards based on quantitative geological hazard evaluation criteria from a sustainable safety perspective. More specifically, a geohazard zone classification method, within which an energy–slope model is integrated, is first developed. Three geohazard regions, namely the geohazard outbreak region, buffer region and fuzzy region, can then be obtained. Afterward, a spatial geological hazard assessment model is constructed considering the geological danger of three kinds of geohazards (debris flows, landslides and rockfalls) and railway construction vulnerability. This model is incorporated into a previous cost–hazard bi-objective alignment optimization model. Finally, the effectiveness of the proposed model is verified by applying it to a real-life case of the Sichuan–Tibet railway. The results show that this method can effectively optimize mountain railway alignments by concurrently reducing geological hazards and costs, which is beneficial to railway safety and sustainable construction and operation.

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.

The problem of railway alignment optimization is studied, with particular attention given to computing lifecycle costs while considering train speed profile optimization and traffic demand. Recurring expenses, including energy, user, and maintenance costs, are considered in the lifecycle. A novel speed profile optimization method for the energy-efficient operation of trains is developed and incorporated in a simulation model, which considers regenerative braking energy. According to the train motion simulation results, the energy consumption and travel time per round trip are obtained, based on which the recurring costs are computed by taking traffic demand into account. The horizontal and vertical alignments are jointly optimized with the train speed profile based on the computed recurring and initial expenses, which include rolling stock, earthwork, bridge, tunnel, right-of-way, and length-dependent construction costs. A case study and sensitivity analyses are presented to discuss the impacts of traffic demand on the optimized railway alignment. The effectiveness of the speed profile optimization method is demonstrated by comparing its simulated results with those without speed control.

The design of railway alignment and station locations involves two intertwined problems, which makes it a complex and time-consuming task. Especially in mountainous regions, the large 3-dimensional (3D) search spaces, complex terrain conditions, coupling constraints and infinite numbers of potential alternatives of this problem pose many challenges. However, most current optimization methods emphasize either alignment optimization or station locations optimization independently. Only a few methods consider coordinated optimization of alignment and stations, but optimize them sequentially. This paper proposes a concurrent optimization method based on a 3-dimensional distance transform algorithm (3D-DT) to solve this problem. It includes the following components: (1) To optimize the location of stations within specified spacing intervals, a novel perceptual search strategy is proposed and incorporated into the basic 3D-DT optimization process. (2) A combined-alignment-station 3D search neighboring mask is developed and employed to search for both the alignment and stations. In order to implement the perceptual process, two additional kinds of 3D reverse perceptual neighboring masks are also developed and employed in the algorithm. (3) Multiple coupling constraints between alignment and stations are also formulated and addressed during the search process. In this study, the effectiveness of the method is verified through a real-world case study in a complex mountainous region. The optimization results show that the proposed method can find high-quality alternatives satisfying multiple coupling constraints.

Station elevations and vertical alignment between adjacent stations often influence each other. Therefore, they should be optimized concurrently. However, existing studies mainly focus on optimizing station elevations or links separately. In this paper, a concurrent optimization model of stations and links is developed, in which the vertical points of intersection in stations and links are design variables. The comprehensive cost including construction, energy consumption, and travelling time, is the optimized objective function. Particle swarm optimization (PSO) is a method for searching in continuous space and is widely used for alignment optimization. Considering the characteristics of concurrent optimization for stations and links, the PSO algorithm is improved by modifying the updating formulas for particles and designing two strategies for particle updating, namely “Stations before Links” and “Links before Stations” strategy. A dynamic adaptive feasible region is proposed to handle the complex constraints during optimization. This method is applied here to a real-world case. The applications demonstrate that this method can automatically generate vertical alignments which jointly optimize the locations of stations and links and satisfy all the complex constrains.