Bi-objective mountain railway alignment optimization incorporating seismic risk assessment

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.