Pruning algorithm for the least expected travel time path on stochastic and time-dependent networks

This study addresses the problem of determining the path with the least expected travel time on stochastic and time-dependent networks. The Bellman’s optimality principle is not applicable to this problem —because of its non-linear objective function— making it difficult to solve. In this light, we propose a pruning-based algorithm that progressively determines subpaths from the source and eliminates those that are non-optimal. The algorithm uses a novel bi-level, bounds-based pruning criterion to determine whether subpath can belong to the optimal path. We show that the pruning criterion is valid and that the algorithm terminates with an exact solution. Computational experiments demonstrate that the algorithm can successfully solve the problem even on large real-world networks and that its practical computational complexity is polynomial. Finally, we show that the pruning algorithm outperforms the existing non-dominance based procedure by a factor proportional to the network size on medium-sized networks and more so on large-sized networks. This work has the potential to aid in a wider application of stochastic time-dependent networks for modeling and analysis.