An Improved Adaptive Large Neighborhood Search Algorithm for the Heterogeneous Customized Bus Service with Multiple Pickup and Delivery Candidate Locations

Abstract

In order to tackle the congestion and environmental issues, customized bus services are proposed and deployed in metropolitan areas. As emerging public transportation services, customized bus services bring passengers more convenience and accessibility. Besides, conventional customized bus services generally organize homogeneous fleet and single location selection to passengers. In this paper, to enhance the mobility and flexibility of customized buses and increase companies’ profit, we propose a new form of customized bus service with heterogeneous fleets and multiple candidate locations. First, a mixed-integer programming model (MIP) is developed to describe the customized bus problem. Compared with the conventional model, the proposed MIP is involved in the case of one passenger with multiple candidate pickup or delivery locations and can be solved by GUROBI on small scale, quickly and efficiently. Second, an improved adaptive large neighborhood search algorithm ( ${\text{ALNS}}_{ip}$ ) is utilized to address the large-scale problem more efficiently. Time slack calculation method is then designed to optimize vehicle timetables, which provides stable and excellent performance for searching feasible solutions. In addition, we propose two inserting operators to deal with the problem with multiple candidate locations and analyse its influence on the results. Finally, we test the performance of the proposed model and algorithm on the numerical experiments. And they are verified the effectiveness and implication in a small-scale case on a simplified Sioux waterfall network and a large-scale problem in Beijing, China. The result shows that ${\text{ALNS}}_{ip}$ outperforms other algorithms in searching for more satisfying solutions with higher efficiency. However, the GUROBI solver can obtain the solution to small-scale problems within a shorter time than ${\text{ALNS}}_{ip}$ . Furthermore, it can be suggested that the heterogeneous fleets service with multiple candidate locations is helpful to facilitate collaboration among vehicles and optimize pickup and delivery routes in consequence.