Hyperstar: A multi-path Astar algorithm for risk averse vehicle navigation

The Astar algorithm, which forms the backbone of vehicle navigation systems, is capable of producing only one path. Given uncertainty about link travel times, there is interest in algorithms that can deliver all the paths that may be optimal, termed collectively a hyperpath, to improve travel time reliability. The actual path taken within the hyperpath will typically be determined by on-trip events, like incidences of congestion leading to delay. In this paper, the Spiess and Florian algorithm for generating hyperpaths in transit networks is adapted to road networks by assuming that drivers follow a risk averse strategy whenever a choice of path arises. To improve the efficiency of the resulting algorithm for vehicle navigation applications, the Astar approach to link selection is incorporated, leading to the Hyperstar algorithm. Proof of the optimality of the algorithm is provided, followed by numerical examples.