Pareto Optimal Path Generation Algorithm in Stochastic Transportation Networks

Routing problems play a crucial part in urban transportation network operation and management. This study addresses the problem of finding a set of non-dominated shortest paths in stochastic transportation networks. Instead of the previous practice of assuming the travel time variability to be tracked by a known probability density function, it is extracted from the existing correlation between the traffic flow and the corresponding links’ time. The time horizon is divided into time intervals/slots in which the network is assumed to experience a static traffic equilibrium with different traffic conditions for each slot. Starting with Priori demand information, prior generated paths, and a chosen traffic assignment method, the proposed methodology conducts successive simulations to the network intervals. It manages to draw both links and paths probability distribution of their travel time considering the correlation among them. Then, multi-objective analysis is conducted on the generated paths to produce the Pareto-optimal set for each demand node pair in the network. Numerical studies are conducted to show the methodology efficiency and generality for any network. The expected travel time and the reliability could be drawn for each path in the network.