Bi-level optimization for customized bus routing serving passengers with multiple-trips based on state–space–time network

The emerging customized bus (CB) can serve personalized trip requests in a more flexible and convenient way, especially for passengers who have multiple-trip requests in a short time period. Considering the CB service for passengers with multiple trips (CSPMT), a loading-state-oriented state–space–time network-based bi-level programming model is proposed to optimize the routing of CBs, with the objectives of maximizing the operational profit and minimizing the travel cost, while considering the characteristics of multiple trips, time windows, capacity and mixed loads. Besides, a nested algorithm combining the genetic algorithm (GA) and the augmented Lagrangian relaxation-based dynamic programming algorithm is proposed. Then, the proposed model and algorithm are verified and analyzed through a Sioux Falls network and a Beijing sketch network. It can be found from the results that the method can optimize a CB routing plan for passengers with multiple-trip requests and for different network scales. The proposed bi-level model and corresponding algorithm can better adapt to passengers’ personalized trip requests, and promote a higher level of public transport service which will attract more residents from private cars to public transportation, ultimately reducing energy consumption and exhaust emissions, and promoting the sustainable development of modern metropolises.