Restoration sequence optimization for vulnerable metro stations with limited budget: A case study of Beijing, China

Urban rail transit networks are essential components of urban transportation systems, but they are vulnerable to disruptions that can severely affect passenger mobility and network efficiency. Traditional methods for determining restoration sequences often rely on experiences or importance-based approaches, lacking precision in identifying critical vulnerable station combinations and struggling to find optimal restoration sequences under limited budgets. This paper introduces a three-level model framework aimed at addressing these issues. The middle and lower levels jointly identify the most vulnerable station combinations, while the upper level optimizes the restoration sequence by taking into account budget constraints and changes in resilience metric throughout the restoring period. The effectiveness of the proposed model was validated using four subway lines in Beijing, China. Results demonstrate that the model can effectively identify critical vulnerable station combinations. Additionally, the resilience-based restoration strategy effectively determines the optimal recovery plan for damaged stations under limited budgets, outperforming traditional restoration strategies based on complex networks and offering strong extensibility.