Combined line planning and train timetabling for strongly heterogeneous railway lines with direct connections

•We develop a multi-frequency line planning optimization model.•We develop a multi-period timetabling optimization model.•Overtaking constraints are presented based on dwell time stretches.•An iterative framework finds high-quality multi-periodic timetables for heterogeneous rail lines.•A real-life case-study on a Chinese railway corridor demonstrates the method. Rail systems have been developing rapidly in recent years aiming at satisfying the growing passenger demand and shortening passenger travel time. The line planning problem (LPP) and train timetabling problem (TTP) are two key issues at the strategic level and tactical level, laying the foundation of a high-level service quality for railway operation. In this paper, a multi-frequency LPP (MF-LPP) model and a multi-period TTP (MP-TTP) model are introduced for direct connections, with consideration of both periodic and aperiodic nature to meet strongly heterogeneous train services and reduce the capacity loss of train operating companies. A combined LPP and TTP method is designed considering timetable robustness, timetable regularity, and passenger travel time. For a given line pool, a multi-objective mixed integer linear programming model for the MF-LPP is formulated to obtain a line plan with multiple line frequencies by minimizing travel time, empty-seat-hour and the number of lines. Using the acquired line plan from the previous step, a MP-TTP model is proposed to achieve the minimal travel time, the maximal timetable robustness and the minimal number of overtakings. The two models work iteratively with designed feedback constraints to find a better plan for the rail transport system. Numerical experiments are applied to verify the performance of the proposed model and solution approach.