Joint Optimization of Multi-Cycle Timetable Considering Supply-to-Demand Relationship and Energy Consumption for Rail Express

Rail expresses play a vital role in intracity and intercity transportations. For accommodating multi-source passenger traffic with different travel demand, while optimizing the energy consumption, we propose a multi-cycle train timetable optimization model and a decomposition algorithm. A periodized spatial-temporal network that can support the integrated optimization of passenger service satisfaction and energy consumption considering multi-cycles is studied as the basis of the modeling. Based on this, an integrated optimization model taking the planning of the train spatial-temporal path, cycle length and active lines as variables is proposed. Then, for solving the issues caused by the complex relationships among the cycle length, line and train spatial-temporal path in large-scale cases, a hybrid heuristic Lagrangian decomposition method is investigated. Numerical experiments under different passenger flow demand scenarios are performed. The results show that the more fluctuating the passenger flow is, the more obvious the advantage of a multi-cycle timetable is. For the scenario with two passenger flow peaks, compared to a single-cycle timetable, the demand satisfaction ratio of the multi-cycle timetable is 4.44% higher and the train vacancy rate is 11.49% lower. A multi-cycle timetable also saves 3.24 h running time and 15,553.6 kwh energy consumption compared to a single-cycle timetable. Large-scale real cases show that this advantage still exists in practice.