Balanced train timetabling on a single-line railway with optimized velocity

This paper aims to find an optimal balanced schedule with the least delay-ratio (i.e., the ratio of the total delay time and the total free-run time) by considering the impacts of the train velocity. A rigorous optimization model is proposed under the consideration of feasible speed constraint for finding the optimal velocity for each train on the railway line. To obtain an approximately optimal scheduling strategy, a combination of the improved TAS (ITAS) method and the genetic algorithm (GA), called GA-ITAS method, is in particular proposed to effectively solve the proposed model. The results of numerical experiments demonstrate the efficiency and effectiveness of the proposed approaches.