Resilience-based protection decision optimization for metro network under operational incidents

The protection decision optimization problem for metro networks was studied to alleviate the negative impacts triggered by operational incidents and improve the capability of metro networks to tackle these incidents. For the network resilience, the variation characteristics of the resilience curve and cumulative loss of the performance in the degradation and recovery of network performance were considered, and a two-layer optimization model for metro network protection decisions was constructed. The upper model was a stochastic integer programming model for identifying the optimal choice of the stations to be protected in the scenarios of uncertain operational incidents. The lower model was a user equilibrium assignment problem, and the variations in the queueing passenger flow and waiting time for recovery at the stations with limited capacity were prioritized to accurately estimate the delay time for passenger travel under operational incidents. The genetic algorithm and Frank-Wolfe algorithm were used to solve the upper and lower models, respectively. The metro network in the central area of Xi'an was taken as an example to verify and analyze the proposed models and algorithms. Analysis results show that the resilience-based protection decision is capable of reducing the loss of network performance by more than 50% by protecting 37.5% of the stations in the research region. It is superior to the vulnerability-based protection decision and the one without considering the substitution role of the bus network. Compared to the situation of the vulnerability-based one, the losses of network performance and passenger flow time reduce by 6.18% and 582 h, respectively, when half of the metro stations in the network are protected by the resilience-based protection decision. The protection priorities of more than two-thirds of stations in the metro network alter due to the substitution role of the bus network. For the same type of stations, their dependence on the substitution role of the bus network enhances with the increase in the passenger flow. The protection priority of a metro station is dependent mainly on the passing passenger flow and transportation capacity. A larger passenger flow is accompanied by a lower transportation capacity and higher protection priority of corresponding stations. The station type is also a factor determining the protection priority, especially for the stations with large passenger flows, and higher protection priorities are required for the non-transfer stations.