Exact algorithms for multi-criteria multi-modal shortest path with transfer delaying and arriving time-window in urban transit network

This paper investigates the solution algorithms for the multi-criteria multi-modal shortest path problem (M-SPP), which belongs to the set of problems known as NP-hard, in urban transit network (UTN). The related M-SPP is one of the important and practical problems in several fields such as urban transportation system and freight transportation. The UTN is composed of multiple modes (e.g., automobile, bus, subway, light rail, pedestrian and so on). To get their destination, the passengers can alternate between different modes. As a special demand, the time-window is usually associated with the M-SPP. Because of the service time-limit of modes, the available modes at a stop are varied with the time. So the optimal M-SPP with arriving time-window cannot be simply obtained by finding the optimal M-SPP firstly and then reversely deducing the leaving time-window of the origin according to the arriving time-window of destination. In this paper, the M-SPP with arriving time-window is firstly proposed. To solve the multi-criteria M-SPPs (MM-SPP) with transfer delaying, an improved exact label correcting algorithm (LCA) is designed and, to solve the proposed MM-SPPs with both of transfer delaying and arriving time-window, an exact reverse LCA is designed. Finally, some computing examples are given to test the effectiveness of the designed algorithms.