Exact bidirectional algorithm for the least expected travel-time path problem on stochastic and time-dependent networks

The Least Expected Travel-time Path on Stochastic and Time-Dependent networks (LETP-STD) is the problem of finding, for a given departure time, the path between an origin and a destination that guarantees the minimum expected travel time. The difficulty in solving this problem arises from the nonlinear objective function and the fact that Bellman's principle of optimality does not hold. To tackle the LETP-STD, we propose an extension of the pulse algorithm, an exact method based on a recursive search that combines various pruning strategies to avoid complete exploration of the solution space. To accelerate our solution approach, we adapt several strategies that have proved their effectiveness in the deterministic context to the time-dependent stochastic domain, including a bidirectional adjustable search, an effective preprocessing method to remove nodes that are not part of the optimal solution, a lower bound on the objective function, and an upper-bound update procedure that joins the most promising paths. Finally, we derive the theoretical and empirical time complexity expressions of the algorithm. Experiments over a set of real-world transportation networks reveal that the algorithm compares favorably against the state-of-the-art methods.