Train Schedule Adjustment Using Flexible Train Composition Strategy under Bidirectional Metro Line Disruptions

This study addresses disruption recovery in metro systems employing flexible train composition and unpaired operation strategies, which often face compounded challenges like rolling stock imbalance and coupling failures during disruptions. We propose an integrated solution featuring: (1) a “flexible composition + short-turning” adjustment strategy, (2) a multi-objective MILP model simultaneously optimizing timetable adjustment, rolling stock circulation, and dynamic coupling plans, solved efficiently via a Lagrangian relaxation algorithm (LR), and (3) validation through Shanghai Metro’s morning peak case. The LR algorithm demonstrates superior computational efficiency (66% faster than Gurobi with below 3.5% optimality gap), enabling real-time decision-making. Compared to conventional methods, our approach reduces train cancellations by 49% in non-disrupted sections and decreases timetable deviations by 58%, while dynamic coupling optimization improves rolling stock utilization. The framework effectively resolves operational conflicts during disruptions while maintaining service quality in unpaired operation scenarios, providing both theoretical and practical advancements for metro emergency management.