An A* Label-setting Algorithm for Multimodal Resource Constrained Shortest Path Problem

Multimodal resource constrained shortest path problem consists of finding a least travel time path with multiple resources and mode chain constraints on a multimodal transportation network. Existing solution approaches based on Lagrangian relaxation technique cannot take into account the sequence constraint of used modes in a multimodal path. In this study, we propose a fast A*-based label setting algorithm to solve efficiently dynamic multimodal resource constrained shortest path problem. A multilevel graph is proposed for modeling multimodal network provided with time-dependent travel time functions and timetable information. The mode chain constraint of a multimodal path is efficiently examined in a labeled graph by applying non-deterministic finite automata method. A speed-up technique based on the A*-algorithm and Access-Node routing is proposed to effectively reduce search space in the resource constrained route searching process. The computational results show that the proposed algorithm can efficiently find constrained shortest path for realistic multimodal network.