Integrated optimization of customized bus routes and timetables with consideration of holding control

Customized bus (CB) is an innovative urban transport system that plays a significant role in meeting personalized travel needs of passengers. This paper deals with the CB service design problem, which is the problem of driving a fleet of capacitated vehicles to pick up and deliver passengers, with consideration of holding control that keeps vehicles at stops for a period of time. A mixed-integer linear programming model is proposed to jointly optimize a set of vehicle routes and timetables with passenger assignment scheme. Through decomposing the model into a bilevel one, we combine genetic algorithm (GA) and large neighborhood search (LNS) with embedding branch-and-bound (BB) method, and develop a GA-LNS-BB hybrid algorithm. Furthermore, an order clustering based divide and conquer (OC-D&C) approach is provided for the ultra-large-scale problems, in which the order clustering problem is formulated as solving an integer linear programming. Finally, we conduct several numerical experiments on the Sioux Falls network and a real-world city-scale network to evaluate the performance of the proposed model and solution methods. The results indicate that: (1) holding control could enhance the flexibility of CB service, and significantly increase the CB carrier's profit; (2) the GA-LNS-BB hybrid algorithm and the OC-D&C approach could provide high-quality solutions in short time for large-scale/ultra-large-scale problems compared to other standard algorithms.