An Interactive Multi-Objective Optimization for Tactical Revision of Train Timetables: A Computationally-Tractable Method for Planners

Railway timetable planners often face the challenge of aligning ideal timetables with limited vehicles and fluctuating capacity needs during their tactical planning phases. To address this, we have developed a multi-objective timetable revision approach using mixed-integer linear programming (MILP) that optimizes trip cancellations and carriage type assignments. Unlike computationally intensive, fully integrated optimization methods that generate timetables from scratch, our method refines an existing draft timetable, offering a practical and efficient tool for planners. It utilizes a multi-product flow model to balance cost-service trade-offs while considering vehicle scheduling feasibility. Evaluation results from a case study on a commuter rail line in Japan demonstrate the method’s practicality. The revised timetable successfully reduced the number of trips by 5% and the total number of carriages by 4%, whereas satisfying user-defined goals for service quality, such as congestion rates. Interactive searches can be completed within 6 minutes, even when user-defined goals are changed. The optimization process is completed in a timeframe suitable for interactive planning, enabling planners to efficiently explore trade-offs. This approach offers a practical and computationally efficient solution for refining timetables under varying demand conditions, supporting the transition from draft planning to operational scheduling.