An Optimization Algorithm for Hyper-path Problem under Travel Time Uncertainty

We consider a hyper-path optimization problem under travel time uncertainty. In the multimodal networks, the waiting time to take transit should be considered in determining the optimal route to the destination. The hyper-path is a union of simple paths between the origin and destination, which enables the traveler to reduce the total travel time by taking more than one route into account. We extend the hyper-path problem to the case where the travel times are uncertain, so the reliability of the hyper-path should be addressed. We formulate the problem as a nonlinear integer programming problem and develop a heuristic algorithm based on the column generation method. The presented algorithm was verified on the real-life public transportation network with an extensive computational study. A proof-of-concept app for recommending public transportation routes utilizing the proposed algorithm was also developed.