Optimizing customized bus services for multi-trip urban passengers: A bi-objective approach

Customized bus services typically focus on single-trip requests, which often struggle to accommodate the growing needs for varied multiple trips in urban daily travel. This paper addresses the customized bus routing problem for passengers with multiple trips. A bi-objective mathematical model is established for maximizing the operational profit and minimizing the travel costs by considering the characteristics of the multi-trip requests and time-dependent travel time. Besides, a novel profit objective function is proposed considering the service's completion status and the starting price. Since the proposed mixed integer linear programming model is an NP-hard problem, a non-dominated sorting genetic algorithm II-based method is proposed to handle different sizes of instances. Finally, the instances with multi-trip requests are carried out to test the accuracy of the model and the effectiveness of our method compared with Gurobi and the local search-based multi-objective algorithm approach.