Stochastic Risk Assessment with a Lagrangian Solution for the Optimal Cost Allocation in High-Speed Rail Networks

In large-scale high-speed rail networks (HSRNs), the occurrence of occasional malfunctions or accidents is unavoidable. The key issue considered in this study is the optimal allocation of the maintenance costs, based on the stochastic risk assessment for HSRNs. Inspired by the theoretical risk evaluation methods in the complex network, three major factors, including the local effects, global effects, and component self-effects are considered in the process of assessing the impact on the network components (nodes or lines). By introducing the component failure occurrence probability, which is considered to be an exponential function changing with the component maintenance costs, a feasible stochastic risk assessment model of the HSRNs together with the component impact assessment is proposed that can better unify the impact assessment of both the high-speed rail stations and railways. An optimal allocation algorithm based on a Lagrangian relaxation approach is designed. Correspondingly, the optimal cost allocation scheme can be determined using the algorithm to eliminate the various HSRN risks under the given costs. Furthermore, a real-world case study of the HSRNs in eastern China is illustrated. Compared with the genetic algorithm, the simulation shows that the approach can solve the optimal cost allocation problem to more effectively reduce the risks of large-scale HSRNs in practice.