Structure Optimization of Mixed-Speed Train Traffic for Cyclic Timetable: Model and Algorithm Development

Trains can be optimally spread over the period of the cyclic timetable. By integrating sequencing issue with headway time together, this paper studies the structure optimization of mixed-speed train traffic for a cyclic timetable. Firstly, by taking it as a job-shop problem with sequence-dependent setup times on one machine, in the type of infinite capacity resource with headway (ICR + H), the problem is transformed to alternative graph (AG) and then recast to the mixed-speed train traffic planning (MSTTP) model. For the multiobjective in MSTTP, three indicators are optimized, i.e., heterogeneity, cycle time, and buffer time, which correspond to diversity of train service toward passenger, capacity consumption of rail network, and stability of train operation, respectively. Secondly, the random-key genetic algorithm (RKGA) is proposed to tackle the sequence and headway simultaneously. Finally, RKGA is coded with visual studio C# and the proposed method is validated with a case study. The rail system considered is a line section encompassing a territory of 180 km with 15 mixed-speed trains in each cycle of the timetable. Results indicate the comprehensively balanced train plan for all stakeholders from random variations of train sequence and headway time. Both the quantitative proportion of heterogeneity/homogeneity (e.g., 2.5) about the optimized distribution of the mixed train traffic and the link between train headway time and the sequence for each traffic scenario are found. All the findings can be used to arrange the mixed-speed train traffic more scientifically.