Bi-objective optimization of last-train timetabling with multimodal coordination in urban transportation

When urban rail transit (URT) does not provide 24-hour services, passengers who travel at late night may not be able to reach their destinations with only URT trains. As a result, passengers have to find alternative transport means, or combine URT trains with other transport services to fulfill their journeys. This paper investigates the integrated optimization of last train timetabling and bridging service design with consideration of passenger path choices. Two bridging services are considered: taxis and buses. Based on pre-constructed path sets, a bi-objective mixed-integer nonlinear programming (MINLP) model is developed, aiming at minimizing total passenger travel time and total passenger travel cost. To reduce the model scale and improve solution efficiency, three path dominance principles are proposed to remove redundant passenger paths without loss of optimality. An adaptive iterative algorithm is designed to obtain the Pareto frontier curve. The proposed model and solution methods are demonstrated on the Chengdu URT network. Results indicate that passenger travel costs and travel times can be significantly reduced by the integrated optimization. It also provides passengers with a safer night travel environment due to the reduction in passenger travel times in taxis.