Mountain railway alignment optimization integrating layouts of large-scale auxiliary construction projects

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.