| Summary: | With the aim of supporting the process of scheduling a hybrid cyclic timetable and adapting traffic needs, this paper is concerned with inserting additional train paths problem for tactical and short-term planning applications with multiple objectives. Focusing on an existing cyclic timetable on a high-speed passenger rail line, the problem is to minimize both the total adjustments for initial trains and the number of required train-sets. The timetable scheduling, train-set planning and rescheduling are three complex optimization problems respectively and usually solved in a sequential manner. In this paper, these phases are integrated in a mixed integer programming model, and the multi-objective adding train paths (ATP) model is proposed, which decides simultaneously initial trains' modifications, additional trains' schedules and train-set circulation. The tolerance of disruption for initial trains including allowed adjustment and periodic structure is taken into account in light of the practical concerns. The difficulty of this integrated problem is that train-sets circulation is usually determined after all of the train lines and timetable have been fixed. However, in the adding train paths problem, the additional trains do not exist in the initial timetable. In order to solve the problem in a reasonable time, a relaxation approach to the adding paths problem is presented. We start from fixed train-set route, and then apply flexible train-set route that provides possible alternative turning activities to decrease the number of required train-sets. A case study based on Shanghai-Hangzhou high-speed rail line in China illustrates the methodology and compares the performance of various settings of perturbation tolerance, time window and train-set applications.
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