Floyd-A ∗ Algorithm Solving the Least-Time Itinerary Planning Problem in Urban Scheduled Public Transport Network

We consider an ad hoc Floyd-A ∗ algorithm to determine the a priori least-time itinerary from an origin to a destination given an initial time in an urban scheduled public transport (USPT) network. The network is bimodal (i.e., USPT lines and walking) and time dependent. The modified USPT network model results in more reasonable itinerary results. An itinerary is connected through a sequence of time-label arcs. The proposed Floyd-A ∗ algorithm is composed of two procedures designated as Itinerary Finder and Cost Estimator. The A ∗ -based Itinerary Finder determines the time-dependent, least-time itinerary in real time, aided by the heuristic information precomputed by the Floyd-based Cost Estimator, where a strategy is formed to preestimate the time-dependent arc travel time as an associated static lower bound. The Floyd-A ∗ algorithm is proven to guarantee optimality in theory and, demonstrated through a real-world example in Shenyang City USPT network to be more efficient than previous procedures. The computational experiments also reveal the time-dependent nature of the least-time itinerary. In the premise that lines run punctually, “just boarding” and “just missing” cases are identified.